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Runoff concentration in steep channel networks Kellerhals, Rolf 1969-12-31

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RUNOFF CONCENTRATION I N STEEP CHANNEL NETWORKS by  Dipl.  Rolf Kellerhals I n g . , Swiss F e d e r a l I n s t i t u t e o f Technology, Z u r i c h ,  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in  the  Department of  Geography (Interdisciplinary  We a c c e p t t h i s  Program  thesis  i n  Hydrology)  as c o n f o r m i n g t o t h e  required standard  THE UNIVERSITY OF B R I T I S H COLUMBIA August,  1969  I960  In p r e s e n t i n g t h i s  thesis  an advanced degree at  in p a r t i a l  the U n i v e r s i t y  the L i b r a r y s h a l l make i t  f u l f i l m e n t of of B r i t i s h  freely available  for  the requirements  Columbia, I agree  for  that  r e f e r e n c e and Study.  I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of  this  thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  this  representatives. thesis  It  for f i n a n c i a l  is understood that copying or p u b l i c a t i o n gain s h a l l  written permission.  Department The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada  not be allowed without my  ii  ABSTRACT The  objective  of t h i s  runoff routing procedure, in  study i s the development o f a  a p p l i c a b l e t o steep channel  the tumbling flow regime,  i n t o more c o m p r e h e n s i v e runoff process. into existing, slide  suitable  mathematical  "Steep"  for incorporation  representations of  i s meant i n t h e s e n s e  the  that degradation  coarse deposits (e.g. P l e i s t o c e n e m a t e r i a l s ,  d e b r i s , s c r e e ) i s assumed t o be  process.  Similarity  c i r c u m s t a n c e s two such  and  networks  the major  channel-forming  c o n s i d e r a t i o n s show t h a t u n d e r  relatively  as c h a n n e l s l o p e and  easily  available  these  parameters,  drainage area, or channel slope  w i d t h a r e a d e q u a t e t o d e f i n e t h e g e o m e t r y and h y d r a u l i c formance o f the The  hydrologically  conditions.  i n t h e f i e l d by  a wide range The  aspects of channel  flow  d i s c h a r g e , w i t h the  d e f i n i n g the channel performance  T h i s f u n c t i o n , A = f ( Q ) , c a n be  under  obtained  observing the d i s p e r s i o n of s l u g - i n j e c t e d  fixed test  ments o f t h i s  significant  l e n g t h ( a r e a ) and  r e l a t i o n b e t w e e n t h e two  through  per-  channels.  are s t o r a g e per u n i t  steady  and  reaches  over a range  of discharges.  t y p e w e r e made on t h i r t e e n t e s t of channel s i z e  and  d a t a from a l l t e s t  tracers  Measure-  reaches, covering  slope.  reaches  c a n be  closely approxi-  PA m a t e d by  exponential relations  i n d i c a t e d by and b  A  the s i m i l a r i t y  of t h i s  parameters."  steady  The  o f the form  A = a ^ Q"'  c o n s i d e r a t i o n s , the constants  flow e q u a t i o n are p r e d i c t a b l e  details  .  of the s t a t i s t i c a l  As • a  A  from b a s i n  l i n k between v a r i o u s  iii  b a s i n parameters Day  (1969)  on  and  the  above, c o n s t a n t s  the basis, of the  s u p p l e m e n t e d by  steady  are. d i s c u s s e d i n  flow, d a t a of. t h i s  e x t e n s i v e . a d d i t i o n a l measurements.  R u n o f f c o n c e n t r a t i o n i s an u n s t e a d y can  o n l y be  system this below  created  f o r steep  reaches  These surge t e s t s as k i n e m a t i c added and very  low  surges  lake outlets observed indicate  and  with  a markedly  i f the  reaches  (positive  their  and  flow  whether  were l o c a t e d  with  negative)  propagation  accurate water  t h a t the  certain  through  level  the r e s u l t  were the  gauges.  channels  dispersive  higher-than-kinematic  stage, which i s probably  which  f o r minor d i s c h a r g e m o d i f i -  consistently  flow systems but  with  equation  a l l test  suitable  step-like  was  flow  flow process,  In order to i n v e s t i g a t e  channels,  outlets  Small, at the  a single  kinematic.  lakes with  cations.  test  defined with  is truly  holds  study  act  effects  wave c e l e r i t y  at  o f dynamic waves i n  pools. Due dispersion  t o the can  differential large  o n l y be  equation  the  in linearized  surge  tests.  s i o n s L,  i s the  with  field  the  a good e s t i m a t e  data  result  storage  of s u p e r - c r i t i c a l  of storage channel  elements  form f o r s t e p - l i k e  The only  occurrence  f o r a kinematic  number o f i d e n t i c a l  solved the  frequent  i n pools. with  The  storage  i s derived  f r e e parameter of the  w h i c h has  solution.  to  dimen-  Comparison  shows, t h a t mean w a t e r s u r f a c e w i d t h parameter..  in a  and  input corresponding  dispersion coefficient,  of t h i s  flow,  provides  iv  As  a computationally- simpler a l t e r n a t i v e ,  model w h i c h r e p l a c e s t h e kinematic obeying for  channels  the  on  the  channels  two  ents  surge  f r e e parameters  the b a s i s of the  f o r an  on t h e This  test  d a t a and  field  both  o p e r a t i o n a l channel  above s t e a d y  i s supported  towards  they  linearity,  the  except  outlets,  field  truly  both  considered.  of t h i s  solution  approximately  a p p e a r t o be  r u n o f f model.  Rules are  equal  suitable Being  f i t to compon-  based  mainly  methods a r e n o n - l i n e a r .  data, which  possibly  of  data.  flow equation, both  by  a sequence  equation,is also  B o t h r o u t i n g methods p r o v i d e the  by  deep p o o l s w i t h w e i r  same s t e a d y - f l o w  determining  developed  and  actual  a routing  at very  show no low  tendency  stage.  V  TABLE OF CONTENTS Page Abstract Table  i i  of Contents  List  of Tables  List  of Figures  List  of Photographs  v ix x x i i  Appendix, L i s t . ofeContents  xiii  Acknowledgements  xiv  1.  2.  Notation 1.1  Notation  1  1.2  Abbreviations  6 8  Introduction 2.1 2.2  P a s t and p r e s e n t problem Separation  approaches  of the r u n o f f process  into  land 11  phase  2.3  The o b j e c t i v e o f t h e s t u d y  2.4  Assumptions  Field  to the r u n o f f 8  p h a s e and c h a n n e l  3.  1  and A b b r e v i a t i o n s  regarding  readily  15 16  a v a i l a b l e data.  Methods  '  23  3.1  S e l e c t i o n of t e s t  3.2  S u r v e y measurements  29  3.3  T r a c e r methods  30  3.3.1 3.3.2  reaches  Objective P r i n c i p l e s o f d i s c h a r g e and v e l o c i t y measurements w i t h s l u g i n j e c t i o n methods  23  30  30  .vi  TABLE OF  CONTENTS  (cont'd.) Page  3.3.3  Vertical  and  lateral  requirements  dispersion 32  . .  3.3.4  Longitudinal  3.3.5  A g a m m a - d i s t r i b u t i o n model f o r t h e f i n a l d e c l i n e of C(t) E q u i p m e n t and p r o c e d u r e s f o r s l u g  3-3.6  d i s p e r s i o n models  33  . . .  37 43  i n j e c t i o n measurements 3.3.7 3.4  ^8  Tracer losses  ^9  Surge t e s t s 3.4.1  O b j e c t i v e vfc  3.4.2  Discharge modifications  50  3.4.3  Stage  51  3.4.4  Stilling  3.4.5  Stage-discharge r a t i n g  .  measuring well  equipment  49  54  response curves  . . . 56  4.  Field  59  Results  4.1  Survey  4.2  Velocity 4.2.1  59  results and  Conversion of f i e l d concentration  4.3 5.  Channel 5.1  60  d i s c h a r g e measurements  4.2.2  Numerical  4.2.3  Results  4.2.4  Accuracy  data to  time60  curves'  6l  integration  64 65  •  77  Surge t e s t s Geometry and  S t e a d y ;Flow E q u a t i o n s  Similitude considerations f o r steep, d e g r a d i n g . c h a n n e l networks . . .  . . . . .  85  85  vii  TABLE' O F .-CONTENTS  (cont'd.)  Page  5.2  5.3 5.4  5.1.1  Assumptions  85  5.1.2  Conditions f o r s i m i l a r i t y  88  Basic equations  f o r steady, uniform  5.2.1  Theoretical  5.2.2  Flow e q u a t i o n s  Determining equation The f r i c t i o n  flow  . .  91  considerations of the test  the parameters . . . concept  reaches  of the steady  .•  100  applied  to tumbling 103  5.4.1  Open c h a n n e l  5.4.2  Comparison w i t h  Unsteady Flow i n Steep 6.1  6.2  6.3  Kinematic  104  flow formulas  106  the data  109  Channels  waves and t h e s u r g e  test  Some f e a t u r e s o f k i n e m a t i c wayes  6.1.2  I n d i c a t i o n s from results waves w i t h  research  D i s p e r s i o n through  6.2.2  The d i f f e r e n t i a l e q u a t i o n s o f k i n e m a t i c waves w i t h s t o r a g e dispersion  6.2.4  Comparison w i t h  A practical flow 6.3.I  approach  . .  109  112  6.2.1  A solution  109  test  storage d i s p e r s i o n  6.2.3  .  results.  6.1.1  Kinematic  93  flow  flow  6.  91  . . .  dynamic e f f e c t s  for step-like field  114  116 . . .  118 124  data  to- u n s t e a d y ,  Unsteady flow through reservoir  input  .  114  tumbling .  127  a non-linear 128  viii  TABLE OF CONTENTS  ( c a n t ' d. ) Page  6.3.2 6.3.3  A r o u t i n g model b a s e d on a c a s c a d e o f p o o l s and c h a n n e l s Evaluation  of the f r e e  from f i e l d 7.  . .  129  parameters 131  data  142  Conclusion 7.1  The H y d r a u l i c s  7.2  Basin  7.3  Towards an o p e r a t i v e  I *  o f tumbling'.:flow  1  2  144  linearity c h a n n e l r u n o f f model  8. Bibliography • Photographs Appendix Computer p r o g r a m s w i t h o p e r a t i n g i n s t r u c t i o n s , p r i n t o u t , and p l o t s  . .  145 147 152 160  ix  LIST' OF TABLES  Page 1.  Comparison  2.  Test  3.  Additional  4.  Summary  5.  o f morphometry b a s e d - o n  t h r e e map  scales.  r e a c h e s -below, l a k e s test  reaches  of tracer  19 24  (Day, 1 9 6 9 )  26  measurements:  A.  B r o c k t o n Creek  66  B.  Placid  Creek  68  C.  Blaney Creek  70  D.  Phyllis  73  Summary  Creek  o f surge  tests:  A.  B r o c k t o n Creek  79  B.  Placid  80  C.  Blaney Creek  D.  Phyllis  Creek  81  .  82  Creek.  6.  R e g r e s s i o n parameters  o f steady flow  7.  R e g r e s s i o n parameters  of steady flow  95 (Day, 1 9 6 9 ) • •  96  X  L I S T OF' FIGURES Page1.  The  2.  Morphometry of t h r e e b a s i n s a t d i f f e r e n t scales  3.  ;  two'runoff  13  phas.es . map  18  Comparison between channel p r o f i l e s measured o f f maps and  surveyed  21  i n the f i e l d  4.  Channel p r o f i l e s  5.  L o n g i t u d i n a l d i s p e r s i o n of s l u g - i n j e c t e d  6.  The  28  s t o r a g e model a p p r o x i m a t i o n  to  tracer  . .  36  longitudinal 39  dispersion 7.  Graphical f i t t i n g  8.  Circuit  9.  Response of r e c o r d i n g c o n d u c t i v i t y b r i d g e  47  10.  Schematic  s e c t i o n o f m a n u a l gauge  52  11.  Schematic  view  of s t o r a g e model  42  diagram of r e c o r d i n g c o n d u c t i v i t y b r i d g e .  of stage  recorder i n s t a l l a t i o n  .  for 53  mountain.streams 12.  Gauge r e s p o n s e  13.  Two  14.  Definition  15.  Surge t e s t  16.  18.  Hydraulic Gauge 1 Hydraulic ' - Gauge Valuesi-Of  19.  Exponents of Equations  20.  Definition  21.  E f f e c t o f /& on t h e s o l u t i o n o f t h e k i n e m a t i c wave equation with storage d i s p e r s i o n  17.  45  55  curves curves  . . . .  57  sketch f o r numerical  integration  . . . .  62  of October 13,  on B l a n e y  typical  stage  - discharge rating  1968,  Creek  . .  m e a s u r e m e n t s on t h e r e a c h , B r o c k t o n - Gauge 2 m e a s u r e m e n t s on t h e r e a c h , B l a n e y Gauge 3 5 c f o r best f i t to-Equation 5.21 2  5.23  and  sketch for Equation  5.24  vs.  . . . .  6.8  78 98 99 105 107 117 123  xi  L I S T OF FIGURES  (Cont'd) Page  22a. C o m p a r i s o n b e t w e e n f i e l d o b s e r v a t i o n s a n d k i n e m a t i c waves w i t h s t o r a g e d i s p e r s i o n  ± 2  22b. C o m p a r i s o n b e t w e e n f i e l d o b s e r v a t i o n s a n d . k i n e m a t i c waves w i t h s t o r a g e d i s p e r s i o n 23.  5  126  D e f i n i t i o n s k e t c h f o r t h e c a s c a d e o f c h a n n e l s and reservoirs  130  24a. V a r i a b l e number o f r e s e r v o i r s  a t f = 0,1  133  24b. V a r i a b l e number o f r e s e r v o i r s  a t cf = 0.28  134  24c. V a r i a b l e number o f r e s e r v o i r s  a t C = 0.7  135  25.  The r o u t i n g p a r a m e t e r  o"  137  26a. Computed and o b s e r v e d s u r g e s , B r o c k t o n C r e e k 26b.  Computed a n d o b s e r v e d s u r g e s , B l a n e y C r e e k  26c. Computed and o b s e r v e d s u r g e s , P h y l l i s  Creek  . . . .  138 139 1^0  xii  L I S T OF PHOTOGRAPHS  Page 1. 2.  Reach B r 1 - 2 ,  Brockton Creek, along upstream P l a c i d Creek, along downstream.  looking 152  Reach P l 3 - 4 , l o o k i n g  T y p i c a l l o g jam i n f o r e g r o u n d  3.  Blaney  4.  B l a n e y C r e e k , a t B l Gauge 4 , l o o k i n g u p s t r e a m from b r i d g e P h y l l i s C r e e k , a t Ph Gauge 2 , l o o k i n g downstream.  5.  C r e e k , a t B l Gauge 3,  . . . .  Stage r e c o r d e r 6.  Phyllis  7.  Barnstead  8.  Volumetric  9.  Vats,  conductivity  pail,  downstream  4, looking  upstream  . . .  ware f o r s a l t  dilution  rod f o rsalt  tests  . . . .  155  tests  155  dilution  11.  Recording conductivity bridge, with e l e c t r o n i c i n t e r v a l timer C o n t r o l s t r u c t u r e at the o u t l e t o f Blaney Lake. Three f l a s h b o a r d s i n p l a c e Timber  f o r Rhodamine W T s l u g i n j e c t i o n t e s t s  crib  additions  . . .  156  156 157  dam a t o u t l e t o f M a r i o n L a k e , w i t h two i n place  f o r a down-surge  Pump a t P l a c i d Lake  15.  Inverted  16.  P l e x i g l a s s t u b e f o r . s t a g e r e a d i n g s on r i g h t , c o n s t a n t r a t e i n j e c t i o n a p p a r a t u s on l e f t R e c o r d e r i n s t a l l a t i o n w i t h i n v e r t e d syphon a t B l a n e y Gauge 5  syphon a t p o o l  157 158  14.  17.  154 154  Equipment  13.  153  bridge  and s t i r r i n g  153  154  10.  12.  . . .  at r i g h t  C r e e k , a t Ph Gauge  glass  looking  152  o u t l e t above B r o c k t o n Gauge 1  158  159 159  xiii  APPENDIX  COMPUTER PROGRAMS WITH OPERATING  INSTRUCTIONS  PRINTOUT, AND PLOTS  L I S T OP CONTENTS  NACL  Source l i s t i n g Sample p l o t o f r a t i n g Sample p r i n t o u t  DQV  Source Sample  TAILEX  Source l i s t i n g Sample p r i n t o u t Sample p l o t s w i t h o f A, B, and D  161 curve 168.  listing printout  170 example  f o r determination subroutines  for  176  QVEL  Source l i s t i n g , i n c l u d i n g numerical i n t e g r a t i o nT h r e e sample o u t p u t s ' -  PL0TGA  Source l i s t i n g ' Sample p l o t s , w i t h and w i t h o u t  L0GRE  Source l i s t i n g , i n c l u d i n g t h r e e s u b r o u t i n e s P r i n t o u t and p l o t s f o r a l l 13 t e s t r e a c h e s  1^9  PD  Source Sample  l i s t i n g , including printout  two s u b r o u t i n e s  249  SNLR  Source Sample  listing, including printout  one s u b r o u t i n e  253-  F -extension  l85\  xiv  ACKNOWLEDGEMENTS  The American 1966  original  Society  Waldo E.  support  of C i v i l  for this  Engineers  Smith F e l l o w s h i p  Research C o u n c i l  o f Canada and  support  In the  ships It  later  respectively.  permitted  cial  on  results study,  are the  valuable  The  National  Killam Foundation funds  the  and  gave  fellow-  acknowledged;  of the  study without  serious  the  work o f Mr.  Day,  p o s i t i v e conclusions Engineering,  finanwhose  of  this  U.B.C., made a  contribution. o f the  field  a n d , s i n c e much o f t h e  occasional  often field  Purssell,and  Department  M e l t o n and  work had  t o be For  fairly  writer's G.  m e n t a l Ph.D. conducting  R.  large  done on their  the  w r i t e r i s indebted  rainy  help  t o many g r a d u a t e  t o Mr.  students  laboratory two  successive  G a t e s and  committee research  work, d a t a  other  supported projects  M. of  o f G e o g r a p h y , U.B.C., a l s o t o h i s w i f e  d i d much o f t h e The  required  a s s i s t a n t s , whenever s u i t a b l e w e a t h e r  t o Mr.  Roy  data  l e s s than enjoyable.  occurred,  in  writer.  award o f  is gratefully  of C i v i l  conditions  who  the  supporting  Department  d a y s , i t was as  to the  the  help  e s s e n t i a l f o r the  Collection parties  This  By  through the  form of r e s e a r c h  completion  constraints.  study, came f r o m  Woo,  the  Heather,  handling,  supervisors,  K.  and  Drs.  M.  typing. A.  members o f the  interdepart-  the  their  on  study with  related topics.  departmental arrangements, which p r o v i d e d  a very  The  experience inter-  successful  academic  and  administrative  through  the e f f o r t s  Graduate  Studies.  Dr. the  thesis  o f Dr.  0 . Slaymaker manuscript.  and  framework, were made Ian McTaggart  Mr.  M.  Church  possible  Cowan, Dean o f  kindly  reviewed  1  NOTATION AND 'ABBREVIATIONS  1.1' Notation A  Cross A  o  Ap A  t  a  sectional  Initial Area  i n the f o l l o w i n g r e g r e s s i o n s :  A  log A = f(log  Q)  a  v  log v = f(log  Q)  a  T  log T = f(log  Q)  )  discharge.  hA/et.  a  a;  2 i n a c h a n n e l . Cm )  area,  at formative  Constant  B(  area of flow  log( A g ^ / ^ / B , . Riemann  ^ l / S / . S / B , .  Function  b  C o e f f i c i e n t i n t h e above r e g r e s s i o n s subscripts).  b  Without  C  Concentration  of t r a c e r  (g cc" ') .  Concentration  of t r a c e r  i n reservoir i .  Wave c e l e r i t y  (ms  C^ c c. l D  Mixing over c  DA  4  Constants,  X  D  s u b s c r i p t : Time c o n s t a n t ( s ) .  Bed m a t e r i a l s i z e  D  (same  (m).  coefficient, 2—1 x Cm s ) .  f o r one. d i m e n s i o n a l d i s p e r s i o n  F l o o d wave d i s p e r s i o n c o e f f i c i e n t 2 D r a i n a g e a r e a (km ) .  Cm  2 -1 s ) .  d  Depth, o f f l o w d  s  In  channel  Depth, measure,, d e f i n e d  (m)  as- A/W,  o  E  Exciting voltage  e  Base o f n a t u r a l l o g a r i t h m s ,  "s  .  of. c o n d u c t i v i t y - b r i d g e  F(.  )  Function  f(  )  Unspecified function.  f  ( )  (volts)  2'. 7 1 8 3 .  of A ( x , t ) .  Probability  density function.  X  Conductivity  (mhos).  Acceleration  o f g r a v i t y (ms  -2  J  (  W  5  'w "  'S  S  ?s  "  )  ts  P^^fv:  H  Stage r e a d i n g  (ft))',  h  E l e v a t i o n d i f f e r e n c e between, s t r e a m gauge s t i l l i n g w e l l ( f t ) ; .  I.(u)  Modified of o r d e r  B e s s e l F u n c t i o n of the f i r s t k i n d i and argument u. With J\(u)  being a Bessel Function I. (u) = J . (Y7! u). 1  Integer,  j  Integer. )  of the  first  kind  1  i  k(  and  Function  counter,  of  gCx,t).  L  Tracer  los-s- r a t e  1  Length, o f t e s t  1^,1 = 0,1,2  Second  M  Mass o f t r a c e r ( g ) .  order  (_% p e r  reach  min.).-  (m)  i n t e r p o l a t i o n polyriomlmals-.-  I n t e g e r , number o f r e s e r v o i r s o r elements.  storage  Manning's n. Polynominal  approximation  Abbreviation  o f C ( t ) , (g c c "'") 1/2 f o r (240c//3 wjp 2  3 -1 Discharge Initial  (m s  discharge.  Formative Qutflow  discharge.  from r e s e r v o i r i .  Measured  discharge.  Discharge Relative  from upstream discharge,  Adjustable Input  ).  Constant  Q/Q^,  resistance  impedance  reservoir. s u b s c r i p t s as f o r  (ohms).  of recorder.  resistance.  Volume o f r e s e r v o i r i . Argument o f f distribution.  - f u n c t i o n , parameter of f  -  Slope Friction Valley  slope  slope  Mean w a t e r t r a v e l  time  (min.)  Lag  t o t r a c e r peak.'(min. ) .  Lag  between  Reservoir Lag  pools.  filling  t o the f irs-t  time  (s) .  arrival  o f t r a c e r (min-.) .  Mean t r a c e r , t r a v e l , t i m e '(.min-.) . t  Time', c o o r d i n a t e t  Starting  t  (min. or s ) .  time.  End t i m e . e  u  B e s s e l f u n c t i o n argument.  V  Potential  v  Velocity v  m  Vp W  Mean  difference, (ms  - 1  voltage  (volt),  ).  velocity.  Velocity  at channel  forming;  discharge.  W i d t h (m). Wp  Channel width  between h i g h w a t e r marks.  W  Water s u r f a c e  width.  g  w  Exponent  i n exponential r e l a t i o n  A and Q, Q <=x A X^  Shape f a c t o r s .  x  Length coordinate x. 1  Y. i = l , 2 , 3 1  Length  along  coordinates  Exponent W  s  channel  of c r i t i c a l  Parameters of Storage f -distribution. Abbreviation  (m). sections.  M o d e l b a s e d on  f o r exponent  (w - l ) / w .  i n exponential r e l a t i o n  and Q, W  s  between  W  ex.  Q  z  between  RelativeQ/Q -1.  change i n d is. c h a r g e d u r i n g  a surge  D  A  r(  Non-dimensional )  dispersion  coefficient  Gamma F u n c t i o n . Abbreviations  f o r terms  i n c and A t . . i  A  Finite  step.  0  Slope  angle.  K  Parameter  X  Length  /f  of  -distribution.  o f a r e s e r v o i r (m).  Viscosity.  2 -1 V  Kinematic v i s c o s i t y  |  Dummy l e n g t h v a r i a b l e (m).  ir  3.1416.  p  Specific  mass  Specific  mass o f b e d m a t e r i a l .  p  s  (g  (m s  cc~^~)  ).  .  <5"  S p e c i f i c mass o f w a t e r . P r o p o r t i o n o f channel length reservoir.  f  Dummy t i m e v a r i a b l e  o c c u p i e d by  (min. o r s ) .  test  6 1.2  Abbreviations  Bl  Blaney  Creek..  Br  Brockton  C.I.  Constant i n j e c t i o n .  cc  Cubic c e n t i m e t e r ,  d  Derivative.  0  Partial  D  Total  DO  Down-surge, downstream o f  ft  Feet.  K  1 0 0 0 ohms.  km  Kilometer.  Lo  Longitude  Lat  Latitude  1  Liter  Creek. .  derivative.  derivative  log x  Natural  logarithm  log-j^x  L o g a r i t h m t o base  mm  Millimeter,  m  Meter,  min.  Minutes  NaCl  Sodium c h l o r i d e ,  NTS  National  Ph  Phyllis  Pl  Placid  RhWT  Rhodamine WT,. Du P o n t .  f o r a moving o b s e r v e r .  o f x. 10.  common  salt.  topographic s e r i e s . Creek..  Creek. f lucres-cent  dye m a n u f a c t u r e d  by  RSQ  R-square,.. the. f r a c t i o n o f t o t a l e x p l a i n e d by- a r e g r e s s i o n .  SQD  Sodium  s  Seconds.  UP  Up-surge,  X  Time-concentration  dichromate  sample, v a r i a n c e  N a O ^ C R • 2R^Q . 2  2  upstream of c u r v e measured  here.  8  2.  • INTRODUCTION  2.1.  P a s t and P r e s e n t Runoff  o r snowmelt  the b a s i n o u t l e t .  complex p r o b l e m  over  flows  of hydrology,  solution.  at certain  fortunate be  logical  a b a s i n t o stream  discharge  locations  and  a satisfactory, generally  Hydrologists are often i n t e r e s t e d along  a stream,  stream  f o r the d e s i r e d s i t e .  r e c o r d s have t o be u s e d  rainfall  which t r a n s -  w h i c h has r e c e i v e d c o n s i d e r a b l e  a c c i d e n t i f adequate  available  Problem  T h i s t r a n s f o r m a t i o n i s an i m p o r t a n t  a t t e n t i o n , but remains without accepted  t o the Runoff  c o n c e n t r a t i o n denotes the process  forms r a i n f a l l at  Approaches  but i t i s a  f l o w r e c o r d s happen t o  I n many  to estimate  o r snowmelt, w h i c h a r e t h e n  i n peak  cases,  meteoro-  peak r a t e s o f  transformed  to  stream-  flow . Two d i f f e r e n t runoff  t r a n s f o r m a t i o n a p p e a r t o be f e a s i b l e ,  possibility  of combinations  approach avoids by  approaches towards t h e p r e c i p i t a t i o n -  the d e t a i l e d  with  between t h e two.  The s i m u l a t i o n  physics of the runoff  s i m u l a t i n g i t , or c e r t a i n parts of i t , with  may be c l a s s i f i e d  into  models, or e l e c t r i c  analogues.  the p h y s i c a l  approach,  process  clearly  dealt  into  with  " b l a c k box" systems;.,  as i t i n v o l v e s d i v i d i n g  on a p h y s i c a l  basis.  process  systems  which  conceptual  The a l t e r n a t i v e  identifiable  t h e added  subprocesses,  may be  called  the r u n o f f which are  Amorocho and H a r t  (1964)  9  discuss  the v a r i o u s p o s s i b i l i t i e s The  popularity  of the  represent  systems i s q u i t e  almost  unlimited  systems  i s the prime  ( o r hope) t h a t  most b a s i n r e s p o n s e s  linear  detail.  " b l a c k box"  of which the U n i t Hydrograph of the widely h e l d b e l i e f  in  example, I s a linear  adequately.  advanced  and  approach,  systems  The  theory  i t lends i t s e l f  number o f m a t h e m a t i c a l  result 1  of  to  an  exercises.  2 Recently as e v i d e n c e strong  i s accumulating  non-linear effects  dangerous  (leading  There use  t h e number o f n o n - b e l i e v e r s has  t h a t most b a s i n s have  to render the  to underestimates  a r e , however, f u r t h e r  of "black box"systems.  take p l a c e over the  extremely  variable,  systems approach aspects  entirely,  linearities  o f peak  and  entire  at p r e s e n t ) .  to such may  better  o f a b a s i n may  approximation  flows). reasons  physical  A pure  f o r the  t o good r e s u l t s . a l s o be  be  description  " b l a c k box"  a process, ignoring  lead  sufficiently  b a s i n a r e a and may  rendering detailed  (at l e a s t  linear  growing  Some o f t h e r u n o f f c o n c e n t r a t i n g  processes  impractical  been  type  the  physical  The  non-  concentrated i n a  few  "'"To be l i n e a r , a s y s t e m has t o s a t i s f y t h e f o l l o w i n g conditions: A s s u m i n g f-j_ ( t ) . and f 2 ( t ) a r e t h e r e s p o n s e s t o i n p u t s . f 3 ( t ) and f i j ( t ) r e s p e c t i v e l y , t h e n ( f i + f 2 ) I s t h e r e s p o n s e due t o i n p u t ( T 3 + fi\). The. m a t h e m a t i c a l f o r m u l a t i o n o f l i n e a r systems l e a d s t o l i n e a r d i f f e r e n t i a l e q u a t i o n s .  2 Numerous p a p e r s i n t h e P r o c e e d i n g s o f t h e I n t e r n a t i o n a l H y d r o l o g y Symposium, h e l d a t F o r t C o l l i n s , S e p t . 6 - 8 , 1 9 6 7 and i n t h e P r o c e e d i n g s o f t h e Symposium on A n a l o g u e and D i g i t a l C o m p u t e r s , T u c s o n , 1 9 6 8 , c a n be c i t e d as e v i d e n c e o f t h i s trend.  10  processes,  so  that, e v e n l i n e a r  mations to  others.  Much o f t h e based  on  s u c h as  simple linear  'parallel, on  1967;  Diskin,  conceptual  work on  or n o n - l i n e a r  good  approxi-  simulation  total  runoff  process,  r e s e r v o i r s , i n s e r i e s or permeable  soil  in  l a y e r s , or  (Overton,  1967;  systems Sugawara,  problem  with  a l l simulation  of parameter  approaches  identification.  Most  even q u i t e p r i m i t i v e o n e s , have enough f r e e p a r a m e t e r s permit  close  data.  The  events  of d i f f e r e n t  requiring recently the  to a p a r t i c u l a r set  somewhat more s e v e r e magnitude  proposed  simulation  should  This  by  t o be  to  runoff  without  many o f really  r e l a t i o n s with  c o n d i t i o n i s not  the useful  identifiable  met  by  any  p h y s i c a l approach c o n s i s t s e s s e n t i a l l y  of  identify-  available simulation  The  processes  that  precipitation-runoff equations  same b a s i n  systems, but  systems,  rainfall-runoff  of r e p r e s e n t i n g  from the  have f i x e d  characteristics.  the  test  of  p a r a m e t e r a d j u s t m e n t s , i s a l s o met  presently  ing  fitting  parameters  basin  is  1967)-.  major d i f f i c u l t y  i n the  give  runoff  models o f t h e  one-dimensional dispersion-  The lies  most r e c e n t  systems of u n i f o r m  based  s y s t e m s may  governing  and  finally  the  f r e e parameters  model.  contribute  significantly  transformation, them, s e a r c h i n g  developing  field  and  to  formulating for practical  office  the  the  differential  solutions,  procedures which  from r e a d i l y a v a i l a b l e  data.  supply  11  Such a t r u l y  physical  p r o c e s s would a v o i d the unfortunately lack  that the  runoff  identification  problem, but  i t is  of the major p r o c e s s e s  o f most b a s i n s  the p r o c e s s e s processes  .of. t h e t o t a l  q u i t e i m p o s s i b l e a t p r e s e n t , not  of understanding  complexity  treatment  from  the  each o t h e r .  are both  the p h y s i c a l  and  separable  a p p r o a c h has  of such  processes  i n p r i s m a t i c channels, e v a p o r a t i o n from uniform  large,  are  fairly  superceded  l a k e s , and  important  by  so  avoiding  simulation. of f l o o d  waves  paved s u r f a c e s ,  infiltration  into  soils.  profitable  direction  i n the p h y s i c a l  f o r new field,  t o the w r i t e r t h a t the  r e s e a r c h on r u n o f f aiming  models.  The  t h e s i s was  research project  designed  S e p a r a t i o n of the Runoff  processes of  representative physical  w h i c h forms t h e b a s i s o f  i n accordance  most  at a gradual replacement  s i m u l a t i o n models w i t h more c l o s e l y  2.2  the  w e l l understood,  s u r f a c e r u n o f f from deep  to  of s e p a r a t i n g  the p r o p a g a t i o n  In c o n c l u s i o n i t appears  lies  difficulty  due  become p o s s i b l e and,  i d e n t i f i c a t i o n p r o b l e m , has  Examples  as  However, some  and  so much f o r  with  this  belief.  Process  into  L a n d Phase  this  and  C h a n n e l Phase Larson process fall  into  (1965) two  suggests  the  and  runoff  phases; a l a n d phase, which t r a n s f o r m s . r a i n -  o r snowmelt t o r u n o f f s u p p l y  inflow),  s e p a r a t i o n of the  a channel  (Larson's  term  for  channel  phase, t r a n s f o r m i n g r u n o f f supply  to  12  basin  outflow.  Figure  1 illustrates  phase i s s i m i l a r to the basins can  and  includes  take place  constant soil  total  a l l the  over the  over regions  runoff process  complex  The  from v e r y  area,  but  should  evapo-transpiration,  etc.).  out  c h a n n e l s y s t e m , w h i c h i n c l u d e s most b a s i n s  zone, t h e  process  In b a s i n s  I n open  representation  a p p r o a c h a p p e a r s t o be stances.  The  data  of the  best  parameters  rainfall-runoff  can  from  small  test  interest.  Parameter c o n s i s t e n c y  due  assumption  the  l a n d phase the  be' e v a l u a t e d  the  the  remain  losses  the  in  the  single  on  basins  simulation  present  i s not  an  circum-  the b a s i s (small i n  c h a n n e l phase i s n e g l i g i b l e ) i n the  that  and  channels".  s u i t e d under the  sense t h a t  to  n e g l i g i b l e water  c h a n n e l p h a s e i s d o m i n a t e d by  "wave p r o p a g a t i o n For  with  which  infiltration, .  interflow,  humid  small  s i m i l a r topography, v e g e t a t i o n  c h a r a c t e r i s t i c s (e.g.  of the  land  i n t e r a c t i n g processes  entire basin  of  this, d i v i s i o n .  of the  region  absolute  of  necessity  l a n d phase i s r e g i o n a l l y con-  stant . Under c o n d i t i o n s eable the  or t h o r o u g h l y  l a n d p h a s e may  wet  time  lag.  basins  e v e n be  Flow-Runoff Supply" gible  o f heavy r a i n f a l l  (Figure  The  effect  hydrograph i n the  vicinity  I n most c a s e s  has  the  one  volume o f r u n o f f  with  high  reducible 1)  with  of the of the  fairly  drainage  imperm-  density,  "Rainfall-Overland  small  losses  and  negli-  l a n d p h a s e on  the  outflow  p e a k may  t o assume t h a t and  to  on  contributes  the in a  t h e n be n e g l i g i b l e . l a n d phase  controls  non-negligible  13 I n put: i Precipitation)  >  Interception  Depression Storage Eva potransp.  J  • Overland Flow  A, •  Loss  Infiltration  T Deep  1  Percol.  Inter flow  Groundwater  The  Land  Phase  (excluding  snowmelt)  Input:  Runoff Supply  Summation  from  Translation  through  sub-areas • Evap. from lakes  Storage  in  The  THE  TWO  channels  channels and lakes and  Loss * Deep  Percol.  lakes  C h a n n e l  RUNOFF  Phase  PHASES Fig. I  manner t o t h e shape o f t h e h y d r o g r a p h . Larson's will  justify  assumptions  f o r the d i f f e r e n c e s  shape and t h a t  data.  He e n v i s a g e d  i f proven,  are that  the channel  i n that  r e p r e s e n t a b l e from this  certainly  between b a s i n s due t o s i z e  t h e dominant p r o c e s s  p r o p a g a t i o n ) may be f u l l y able  which,  t h e two-phase a p p r o a c h ,  phase a c c o u n t s and  basic  phase  readily  r o u g h l y as f o l l o w s :  (wave avail-  Maps  show t h e c h a n n e l n e t w o r k i n p l a n ; c h a n n e l d i m e n s i o n s and roughnes's photos.  c a n be o b t a i n e d i n t h e f i e l d Alternatively  mates o f c h a n n e l  maps c a n be u s e d  forming  o f knowledge on r e l a t i o n s charge  system give  t o make r o u g h  between s i z e ,  performance  permit  Once t h e d i m e n s i o n s  good r e p r e s e n t a t i o n s o f t h e c h a n n e l two p h a s e a p p r o a c h  at p r e s e n t .  cannot  one p a r t  speculation realized  be c o n s i d e r e d o p e r a t i v e  dlsproven  of the runoff process  clearly,  concepts  hinges  or  assuming  from  on t h e  I f this  c a n be  the realm of  L a r s o n does n o t seem t o have  as h i s c h a n n e l p h a s e  s u c h as u s i n g a s i n g l e  Manning's n f o r l a r g e  should  does r e p r e s e n t a s t e p f o r w a r d by  and s i m u l a t i o n .  this  routing  phase.  p h y s i c a l r e p r e s e n t a t i o n o f the channel phase.  removing  and d i s -  of the channel  The u s e f u l n e s s o f t h e c o n c e p t  done, t h e n t h e c o n c e p t  esti-  estimates of the  a r e e s t i m a t e d , s t a n d a r d methods o f f l o o d  The  scale a i r  d i s c h a r g e and t h e c o n s i d e r a b l e body  of s e l f - f o r m e d channels w i l l  necessary parameters.  o r on l a r g e  flow ranges  i s based  on l o n g  constant value of  i n many n a t u r a l  channels  f l o o d wave movements a t mean w a t e r v e l o c i t y , and  15  he  never I n v e s t i g a t e s the  parameters of h i s channel by 2.3  curve  fitting,  The  Objective  For priori  are r e l a t e d to the of This  particularly  routing.  Soil  cover  the  two  phase approach appears  s u i t a b l e i n mountainous areas.  i s o f t e n t h i n and  glaciers  and  ice-phase,  land phase.  The  i ) The l a w s and  channel  present  approach remains  and  term "tumbling 6 illustrate ii)  The  and  (i960)  flow" for this  tumbling  therefore in  r e p l a c e d by  an  valid. two-phase  channels  sub-critical  t o r a p i d changes i n c r o s s  Mohanty  steep,  l a c k o f i n f o r m a t i o n on t h e  a l t e r n a t i n g super-  (Peterson  flow  concept  are:  h y d r a u l i c performance of steep  d i s s i p a t i o n due  slopes,  system at d i s c r e t e  major o b s t a c l e s to a p p l y i n g the  i n mountainous areas  on  of  I n a f a s t - a c t i n g and  s u p p l y i n g water t o the the g e n e r a l  channel  l a n d p h a s e c a n be  The  network w i t h  type  lying  a  traceable  I f runoff o r i g i n a t e s mainly  s n o w f i e l d s , the  l o c a t i o n s , but  easily  channel  p a r a m e t e r s i n any  impermeable l a y e r s , r e s u l t i n g less important  as.obtained  values.  a r e a s , maps a l s o s u p p l y  o f t h e most i m p o r t a n t  the  Study  I n a d d i t i o n t o a p l a n of the  c o n t r i b u t i n g drainage  i z e d by  field  s y s t e m i s g e n e r a l l y w e l l d e v e l o p e d and  on maps.  one  phase r e p r e s e n t a t i o n ,  several reasons,  t o be  channel  c r u c i a l q u e s t i o n whether  flow.)  introduced  formative character-  f l o w and  s e c t i o n and  by  energy  slope,  the very d e s c r i p t i v e  f l o w regime.  Photographs 1  to  and  lack of a r e a l i s t i c  r o u t i n g m e t h o d , w h i c h does  16  not r e q u i r e v i r t u a l l y u n o b t a i n a b l e i n f o r m a t i o n on t h e c h a n n e l system. The p r e s e n t t h e s i s r e p r e s e n t s an attempt  t o s o l v e these  problems by i n v e s t i g a t i n g t h e p h y s i c a l laws g o v e r n i n g and unsteady f l o w i n steep channels  steady  and by t r y i n g t o s t a t e  them i n such a form t h a t a l l parameters can be o b t a i n e d from data r e a d i l y a v a i l a b l e even i n ungauged b a s i n s .  The d e t a i l s  of t h e l i n k between t h e f l o w parameters and map measures a r e d i s c u s s e d i n Day ( I 9 6 9 ) .  H i s l i n k s a r e s t a t i s t i c a l but based  on c o n s i d e r a t i o n s o f dynamic s i m i l a r i t y . The problems were approached e m p i r i c a l l y , s t a r t i n g w i t h f i e l d measurements and c o n c l u d i n g w i t h a n a l y s i s o f t h e d a t a , a sequence which has been m a i n t a i n e d i n t h i s w r i t e - u p . 2.4  Assumptions r e g a r d i n g R e a d i l y A v a i l a b l e Data The  d e s i g n o f t h i s p r o j e c t i s based on the assumption  t h a t ungauged b a s i n s have ( i ) map-., coverage,  ( i i ) high a l t i t u d e  a i r photo coverage and ( i i i ) d a t a on p r e c i p i t a t i o n and r u n o f f f o r a t l e a s t one l o c a t i o n i n t h e same c l i m a t i c r e g i o n . Some o f t h e channel phase models developed  subsequently  r e q u i r e a very rough e s t i m a t e o f mean annual peak f l o w , o r a h i g h f l o w o f some o t h e r f r e q u e n c y .  I t e m ( i i i ) , combined  w i t h map i n f o r m a t i o n , s h o u l d p e r m i t such an e s t i m a t e t o + 50%. Map coverage s u p p l i e s t h e f o l l o w i n g i n f o r m a t i o n : ( i ) a p l a n o f t h e channel network, ( i i ) c o n t r i b u t i n g d r a i n a g e areas a l l a l o n g each c h a n n e l , and ( i i i ) channel s l o p e s .  The  17 accuracy and  of t h i s  contour  I n f o r m a t i o n depends p r i m a r i l y  interval  o f t h e maps, b u t  as t h e p r o c e d u r e s  used  density  of ground  cover i n the  photos,  may  a l s o be  i n map  other f a c t o r s ,  making and case  Important  on t h e  the h e i g h t  scale such  and  o f maps made from a i r  (Morisawa,  1957;  Scheidegger,  1966) . The ft  standard Canadian  contour i n t e r v a l  val.  Only  and  but  scales  1:250,000 w i t h  a small f r a c t i o n  1:50,000 c o v e r a g e  map  this  are 500  1:50,000 w i t h f t contour  o f the Canadian  inter-  Cordillera  i n c l u d e s most d e v e l o p e d  50  has  areas  and  highway r o u t e s . To scales three  g a i n some i d e a  of the degree  of the b a s i n s used Blaney  Creek)  in this  and  (Blaney  be  Creek)  1:2400 w h i c h , reasonably first  mean s t r e a m  Creek,  lengths.  spot  checks,  appear  season. i n this  1 and  Phyllis f o r stream One  basin of  to give a  system,  includ-  w h i c h c o n t a i n some f l o w d u r i n g most  (The  S l e s s e and  analysis  is significantly results  map  C.,  a n a l y s e d on maps t o a s c a l e  Ashnola  because  S t a t e s , where t h e a c c u r a c y  The Table  on a few  o r d e r streams  included  coverage  (Furry  t r u e r e p r e s e n t a t i o n of the drainage  o f t h e wet  United  could also based  study  were a n a l y s e d m o r p h o m e t r i c a l l y  o r d e r s , number o f s t r e a m s  be  two  r e p r e s e n t d r a i n a g e n e t w o r k s i n s o u t h - c o a s t a l B.  Creek,  ing  to which these  they  and  b a s i n s c o u l d not  l i e partly  scale  of the  i n the map  different.)  of the morphometric  on F i g u r e 2. The  analysis  are  shown i n  c h a n n e l n e t w o r k measurements  are  18;  STREAM  MORPHOMETRY  OF  ORDER  THREE MAP  BASINS  SCALES  AT  DIFFERENT  TABLE I COMPARISON OF MORPHOMETRY BASED ON THREE MAP SCALES Map S c a l e and Type • 1:250,000 NTS 1:50,000 NTS 1:2400 UBC Research Forest, Topography and F o r e s t Cover.  Stream Order 1 2 3 1 2 3 4 1 2 . 3 4 5  P h y l l i s Creek F u r r y Creek No. o f Mean (km) No. o f Mean (km) Length Length Streams Streams 14 1. 62 1.35 3 1 3.25 3 1.75 1 6. 50 34 10 2 1  0.785 0.985 3.800  4.100  6 2 1  0.79 1.27 2.05  Blaney Creek Mean (km) No. o f Length Streams 2 3.75 1 2.00 12 3 1  0.63  86 21 42 1  0. 23 0.44 0.56 2.38 1.90  1.18 4.10  Notes: - F i g u r e 2 shows t h e same d a t a g r a p h i c a l l y . - The c h a n n e l network i s based on the b l u e l i n e s shown as the maps w i t h a d d i t i o n s based on t h e c o n t o u r p i c t u r e . - P l a c i d Creek i s p a r t o f t h e Blaney Creek b a s i n .  "  M  20  based  on t h e b l u e  extensions  based  lines  on t h e c o n t o u r  Lakes a r e r e p l a c e d is  basins,  logarithmic or  by s t r e a m  not a c h i e f agent  these  stream  segments.  i n developing  order  increasing basin  and some s e c o n d  relations  may be d i f f e r e n t  comparative  results  photos  order  study  should  of the t h i r d basins.  Particularly flow  directly  canyon.  This  to f i r s t  1 : 2 5 0 , 000  order.  data  s c a l e s by c o m p a r i n g  of 2 test }  part  channels.  reaches with  profiles  .  of the e s s e n t i a l data  and on b e d - r o c k  on b e d - r o c k , o f t e n w i t h o u t does a f f e c t  little  exposures. some  streams  as much as a m i n o r  the channel performance  and t h e p r e s e n c e  slope i s  the survey  b e c a u s e t h e C a n a d i a n maps p r o v i d e cover  These  obtained  order  a t t h e l o w e r end o f h a n g i n g v a l l e y s ,  Dense t r e e c o v e r  scales,  t o which channel  1:2400 and 1 : 1 2 . 0 0 0 .  on v e g e t a t i v e  basins.  I f possible, a  be made b e f o r e  the extent  profiles)  i n many  streams, while*the  i n other  are considered  ungauged b a s i n s  information  and s t r e a m number  t h e 1 : 5 0 , 0 0 0 maps m i s s most  from maps o f v a r i o u s  f r o m maps o f s c a l e s  for  geometry o f  logarithmic.  s e c o n d and p a r t  3 illustrates  (hand l e v e l  Air  water  and i n c r e a s i n g map  a l a r g e s c a l e map a r e e x t r a p o l a t e d Figure  running  the surface  size  2 i n d i c a t e s that  the f i r s t ,  obtainable  Since  as f o u n d by H o r t o n and o t h e r s  maps m i s s  similar  1957).  (Morisawa,  i t i s n o t s u r p r i s i n g t h a t F i g u r e . 2. does n o t show  length,  Figure  on  picture.  r e l a t i o n s become more c l o s e l y  first  some a d d i t i o n s • and  r e l a t i o n s between s t r e a m o r d e r  However, w i t h the  o f t h e maps w i t h  of logging  considerably.  slash result i n  1,000 I700i  2p00  Chainage  3Q00  (meters)  4.000  5000  6,000  •Placid Lake 500  1500 Gauge I \  Placid Creek  CD13001  400  Gauge 3 CO  £  CD  Blaney Lake  E  IIOO-  Blaney Creek  Gauge 4 o >  CD900 ®  Gauge I J  300  Gauge 3  UJ  c o  ;  Gauge 5 7001  I" = 200' map 200  Handlevel profile I" = 1000' map 500  3] (O OJ  J  5,000  10,000  Chainage  COMPARISON  BETWEEN  OFF MAPS  Gauge 4 15000  20,000  (feet)  CHANNEL  AND SURVEYED  PROFILES IN  THE  MEASURED FIELD  5  UJ  frequent  l o g jams, i n s m a l l s t r e a m s ,  performance. the it log  The p r e s e n t d a t a a r e n o t a d e q u a t e  conditions appears jams  B. C.  Channel  formation debris  that  cease  under  which  channel  to define  l o g jams become s i g n i f i c a n t , b u t  at a channel width t o be s i g n i f i c a n t , s l o p e has a l s o  of approx. at l e a s t  a pronounced  o f l o g jams, w i t h f l a t  choked.  again affecting  reaches  1 2m to 1 5m  i n south  coastal  influence  on t h e  being generally  more  3.  F I E L D METHODS  3.1  Selection The  o f T e s t Heaches  criteria  for selection  of test  r e a c h e s were as  follows: (i) range  The d a t a were t o c o v e r t h e l a r g e s t . p o s s i b l e  of size (ii)  ( w i d t h ) and s l o p e . To t e s t  lakes with outlets were  c o u v e r was a l s o Four  an i m p o r t a n t  easy  flow  modifications  slope.  c o v e r i n g a range  forest  on e a c h  stream,  (Photograph  f l o w , some w a t e r  p r o p e r on t h e u p s t r e a m some p a r a l l e l Placid  from  covering a f a i r l y of reaches.)  wide  reaches range  None o f t h e  The s m a l l e s t  stream  h a s no o f f i c i a l name and does n o t a p p e a r  Due t o i t s l o c a t i o n  mean a n n u a l  Van-  and 2 t o 5. t e s t  had p r e v i o u s d i s c h a r g e r e c o r d s .  debris  from  o f mean w i d t h  selected  (See T a b l e 2 f o r a l i s t  (Brockton Creek) map.  accessibility  consideration.  m t o 14.0 . m were f i n a l l y  4 streams  by  as p o s s i b l e ,  streams,  were e s t a b l i s h e d  any  f o r minor  upstream  S i n c e measurements were t o be made o v e r as l a r g e  a d i s c h a r g e range  in  suitable  flow behaviour,  required. (iii)  0.b9  the unsteady  test  at tree 1).  line  on  i t i s not a f f e c t e d  At flows I n the o r d e r o f t h e  spills  out o f the stream  r e a c h and f o l l o w s  channel  the stream i n  minor d e p r e s s i o n s . Creek  i n t h e UBC R e s e a r c h  an a r e a c o v e r e d by dense  second  Forest  growth f o r e s t  flows  through  approximately  TABLE I I TEST REACHES BELOW LAKES Location (mid-reach)  Creek  Reach (going downstream)  L e n g t h Drop S l o p e (m) (m) sin Q #3 xlO'  No.of Width Steps D in Survey (m) W  Coeff.of Variation for W D T  Drain- Estimated age Mean A n n u a l Area Peak (km ) 2  Brockton Creek M.t. Seymour Park, Elev. 4,000' Lo:122Q56' Lat:49°23' Placid Creek  Blaney Creek  part  119. 0 ,.8.„8  Br 2-3  80. 5 2 8 . 1  3  _1  74  36  0.89  ' .499  0.0655  0.20  349  27  0.99  . 611  0.0880  0.20  UBC R e s e a r c h P l Forest, Pl Elev. 1,400' Lo:122°34' Lat:49°l8.5' Pl  1-2  960  79. 7  83  64  2.75  .387  0.614  1.5  2-3  610  21.6  35.5  41  3.16  ,.373  1.17  2.5  3-4  1844  62.4  33.9  122  7.02  . 400  2.60  5.0  UBC R e s e a r c h B l Forest > Bl Elev.950' Lo:122034.5' Bl Lat:49°17  1-3  685  31.9  46.6  46  12.76  .435  7.43  12.0  3-5  335  17.5  39. o '  23  11.06  .414  7.70  12.0  5-4  930  85.3  94.7  62  12.92  .292  7.94  13.0  Ph 1-2  770  23.7  30.5  52  11.48  .314  8.69  15.0  Ph 2-3  716  34.9  48.7  48  12.57  .216  10.41  17.0  Ph 3-4  617  39.5  64  42  12.64  .190  10.99  17.0  Ph 4-6  305  30. 2  99  21  1 2 . 28  .226  11. 34  18.0  Ph Lo  140. 5 30.8  219  10  14.04  .167  11.81  19.0  T  Phyllis Creek  B r 1-2  (m s ~)  Nr.Britannia B e a c h , B.C. Elev.1,400' Lo:123°H' Lat:49°34'  i T h i s r e a c h has a sudden i s shown h e r e  s t e e p drop  x  In the l a s t  40 m.  The s l o p e o f t h e l o n g  flatter  IY)  25  20 y e a r s jams two  o l d and  (Photograph  is affected  2).  Placid  bulldozed f i r e Blaney  over by  Its. flow regime The  lowest  p o o l s , and  Creek flows  an  ago.  through  irregular.  a r e a t h a t was  I t s flow regime  150  l o g jams a t a p p r o x i m a t e l y  reach flows  slope i s  through  80 y e a r s  approximately  the  by. f r e q u e n t l o g  m intervals  burnt i s affected 3  (Photographs  and  4). The ago  but  cleared  valley  the  creek  itself  In  addition  f o r two,  (1969)  tested  he  wider  and  discharge  to these  tested  another  the reaches of steady  r e c o r d s and  i n slope. The  and  of s u f f i c i e n t Only  5 and 13  test  f o r steady 12  reaches  the  6).  the  reaches  test  are  t o have  flattest  top  reach  r e a c h e s , which were, unsteady  f o r steady  flow,  Day  conditions only.  c h o i c e was  much  i n g e n e r a l more s a t i s f a c t o r y  the t e s t  reaches  3 lists  reach  length varies ratios  the  12  vary  between 30 and  for  Some o f Day's s t r e a m s  Table  have r a t i o s  size  years  1  and  flow t e s t s .  length to width  20 t o 30  logged  d i d not r e q u i r e upstream l a k e s , the  the purpose  form  seems t o be  (Photographs  except  As  C r e e k was  o f most d e b r i s .  2 l o g jams  has  of P h y l l i s  are u s u a l l y  reaches  more  tested  from  80.5  from  10  by  have uniDay.  m to 1 8 4 4 . 0  and  349,  but  m most  80 .  The l o w e s t r e a c h , on P h y l l i s . C r e e k was. t e s t e d by Mr. T . D a y . F o r c o n v e n i e n c e , , the. r e s u l t s a r e p r e s e n t e d together with a l l other P h y l l i s reaches.  here,  TABLE I I I ADDITIONAL TEST REACHES ( f r o m Day,  Creek  Location  Reach  Length (m)  Drop (m)  Slope sinQ xl 3 0  Fury Creek  Near B r i t a n n i a Beach , B . C .  1969)  No. o f steps i n survey  Width D (m.) W  Coeff. of Variation for W D  Drainage Area  (km2)  16  20.2  .304  39.0  34.3  21  27.0  .222  105.1  23.5  43.3  18  22.8  • 239  110.  1402  47.0  33.5  47  19-5  .285  126.0  610  81.5  .407  21. 8  579  20.2  1125  45.9  229  29.5  584  20.0  541  129:-  Lo:123°12» Lat:49°35'  Sless e Creek  South of Upper C h l l l i w a c k , - B.C. Lo:121°38' Mid  Lat:49°01' Lo:121038' Lat: 4 9 0 1 '  4  o ,  Low  Lo:121°39' Lat:49°02'  J u n i p e r South of Keremeos Creek  B'. C .  4l  6.03  34.8  19  16.36  . 267  80. 8  40.8  36  14. 2  .302  95.8  134  Lo:120O02' Lat:49°06'  Ewart Creek  South of Keremeos ,• B.. C .  Upper  Lo:120O02' Lat:49°06' Lo:120°02' Lat.49°08'  Low  TABLE I I I ( c o n t ' d . ) Creek  Ashnola River  Location  Reach  South of Upper Keremeos, B.C. Lo:120°11* Lat:49°09 ' Lo: L  a  t  ? ' .49010-'  1 2 0  1 0  Lo:120oi0' Lat:49°10'  Mid L  o  w  Length (m)  Drop (m)  490  1003 747  5-09  2  2  Slope sin Q xl03  No. o f steps i n survey  Width W  Coeff.of Variation f o r W^  D  Drainage Area (km ) 2  10.4  17  21.1  .170  221.5  6.0  25.9  33  28.2  .218  408.5  6.0  35.1  25  2  2  -  l  .  2 2  5  409.5  ro  500  t—-Marion  28  Chainage (meters)  1000  1500  2000  Lake  in E c o  Elevation (meters)  1900  Gauge 2  1800  Gauge  3 \  cn O  600  Gauge 1  a •1700 > UJ  Gauge 4 X 5 0 0 1600  Phyllis  Creek , Handlevel  profile Gauge 6  1000  2000  3000  4000  5000  Chainage 0  Chainage (meters) 100  150  1  <  -1320  in  Gauge 1  ^^^^ Gauge Z  CO  E  V  c 3960 o o > 3940  UJ  -1310  c  O  \  \  V  > <> l  1300  ^  1290  3920 3900  8000  (feet)  f-Pool  Z 4000-1 0)  7000  (meters  4020  50  6000  1  Brockton  Creek  !  1  100  profile  200  300  400  Gauge 3-4H 2 8 0  5 010  600 —i  Chainage (feet)  CHANNEL PROFILES  Fia^4_  29  With reach  e x c e p t i o n o f t h e most u p s t r e a m  the p o s s i b l e  on B l a n e y C r e e k ,  none o f t h e t e s t  r e a c h e s have  flood  plains. 3.2  Survey  Measurements  While  the o b j e c t i v e  of  t h e c h a n n e l phase  it  was  and be  slope  i n the f i e l d ,  located  with f i e l d  chaining profile  possible,  and  and  riffle  sequence.  a i r photo  are the deepest  levelling test i t had  p a r a m e t e r s , w i d t h and  apparent  from  that  mark, was  surface.  reaches  could  t o compare  c o u l d be  The  Figures of t h i s  no  f t . steps.  o f t h e c h a n n e l where step s i z e  3 and  is  i s a redundant  point  check  4 show t h e  hydraulic method  When i t became  similitude in a  (Section hydrological  abandoned.  c h a n n e l w i d t h , f r o m h i g h - w a t e r mark t o measured a t each p r o f i l e  pool-  as a  satisfactory  parameter  i t were  suffic-  study.  designed.  o f dynamic  t o measure  not  map  b e e n p l a n n e d t o measure two  considerations  roughness  length  of the c h a r a c t e r i s t i c  errors.  data,  obtained simultaneously  parts  roughness, but  roughness  flow model, attempts The  also  A n e r o i d measurements were u s e d  o f t h e 13  measuring  the reaches  i n 50 f t . o r 1 0 0  hand-levelling  Originally  5.1)  and  definition  2.5).  (Section  t o e l i m i n a t e most  large  profiles  data  otherwise water  long  against  mainly because  s l o p e were u s u a l l y  points  iently  for  o f map  a d e q u a t e l y on maps, b u t  Length  The  on the b a s i s  c a l l s for  n e v e r t h e l e s s c o n s i d e r e d n e c e s s a r y t o measure  profiles  by  o f the t h e s i s  (50  high-water  f t o r 100 f t  30 intervals). is  fairly  As  well  indicated defined  by  h i g h - w a t e r mark f o l l o w s consists  of  an  c h a n n e l bed values  and  abrupt  by a  line  this  of  c o e f f i c i e n t s of  the  field  proved  t o be  3.3  Tracer  3.3.1  Obj e c t i v e The  establish  line  (exposed g r a v e l ) .  suitable  closely.  Tables  variation a survey  each r e a c h .  f o r t h i s type  relations  of  the  tracer  of  discharge.  possible  range  times t r a c e r  of  uniform  Most  towards  the which  survey.  methods were a l s o  stage-discharge  rating  Principles  curves  of D i s c h a r g e  Injection  and  covering  used  for  simple  to  define  mentioned  and  Velocity  ideally suited  which are  of  -of d i s c h a r g e Q and  tracer the  local  the  i n Section  3.4.5.  Measurements  o f mass M  tracer  f o r measuring  with  the  s i g n i f i c a n t i n runoff  namely d i s c h a r g e , mean v e l o c i t y , and a slug  and  Methods  T r a c e r methods a r e channel flow v a r i a b l e s  as  velocity,  to  flow  d i s c h a r g e measurements, w h i c h were needed  If  to  mean  measurements was  between d i s c h a r g e ,  the  Slug  3 show t h e  t a p e , but  The  generally  f l o o r o r meadow  for  of  3-3-2  It  2 and  channel a r e a under c o n d i t i o n s  At  width  Methods  main o b j e c t i v e  largest  channel  work a r a n g e f i n d e r became a v a i l a b l e ,  very  the  6,  o f permanent v e g e t a t i o n .  change f r o m f o r e s t  measurements were made w i t h end  1 to  Photographs  studies,  channel storage  (area).  is injected  a  concentration  C  into  (mass p e r  stream unit  31  volume) i s m e a s u r e d a t a l o c a t i o n to permit the assumption mixing  o f complete  3.3-2),  (see S e c t i o n  mass t a k e s t h e f o l l o w i n g  lateral  the p r i n c i p l e  form  f a r downstream  and v e r t i c a l  c-f c o n s e r v a t i o n o f  (Replogle e t a l . ,  1966)  t  j  M =  sufficiently  ... 3 . 1  Q C dt  t i n which  t  i s the a r r i v a l  s  time a t which  time  of the t r a c e r ,  a l l t h e t r a c e r has p a s s e d  Q i s steady d u r i n g the i n t e r v a l Q = M /  (  and t e  3  the sampling  i s the site.  If  - t , Equation 3.1 gives  t  ... 3 . 2  C.Vdt  t which  shows t h a t  of t r a c e r  into  concentration The point et  Q c a n be m e a s u r e d by i n j e c t i n g  a stream  of i n j e c t i o n  al.,  r  t  =  j t  and  this  the point  C t  s  dt /  j t  i s (Thackston  e C  3.3  dt  s  t o t h e mean t r a v e l  i f instantaneous v e r t i c a l  upstream-  c l o u d between t h e  location t  e  of i n j e c t i o n  being dispersed the t e s t  t i m e T^ o f a t r a c e r  i s only i d e n t i c a l  stream water,.T, at  t  the time-  location.  and t h e s a m p l i n g  1967) T  and o b s e r v i n g o r s a m p l i n g  c u r v e a t a downstream  mean t r a v e l  a known volume  time  of the  and l a t e r a l  mixing  c a n be assumed w i t h no t r a c e r o r i f the. t r a c e r  i s injected  r e a c h and T i s o b t a i n e d as t h e d i f f e r e n c e  above  between t h e  T^-  v a l u e s f o r the upstream  and downstream end p o i n t s  of the  reach. The  mean w a t e r v e l o c i t y a l o n g . t h e r e a c h o f l e n g t h  1 Is  v and  from  1 T  m  3.4  continuity,  the channel  area of the t e s t  reach  becomes Q v  A =  3-3.3  QT 1  m  3.5  V e r t i c a l and L a t e r a l D i s p e r s i o n The  straight, 1963;  mechanics  of v e r t i c a l  u n i f o r m open c h a n n e l s  Fischer,  1966).  Criteria  Requirements  and l a t e r a l i s well  dispersion i n  developed  f o r t h e time  (Diachishin,  or distance  which  2 assure  adequate  cation  to tumbling  such  as s a m p l i n g  the d i s p e r s i o n the  m i x i n g have b e e n d e v e l o p e d  lateral  flow i s not reasonable.  across the channel  requirements  t h e t e s t r e a c h e s were l o c a t e d  Empirical  methods,  and v i s u a l i n s p e c t i o n o f  o f dyes were t h e r e f o r e  mixing  but t h e i r a p p l i -  used  t o determine  were b e i n g met.  so t h a t  they  whether  I f possible,  started  at severe  channel d i s c o n t i n u i t i e s ( w a t e r f a l l s , c o n s t r i c t i o n s ) , which assure  f a s t mixing.  On some o f t h e s h o r t  n e c e s s a r y , however, t o i n j e c t  due 3.7  reaches  i t was  t h e t r a c e r above t h e r e a c h and  Complete d i s p e r s i o n , i s n o t p o s s i b l e i n f i n i t e t i m e to the continuous nature o f the process (see Equations and 3 . 1 3 ) - .  33  to  observe, two  t i m e - c o n c e n t r a t i o n curves  for. one  measurement  of v . m On  several occasions  measured t w i c e tracer  at the  at c l o s e l y starting  f u r t h e r upstream. between t h e s e 3.3.4  similar  f l o w s by  p o i n t of a reach  T h e r e a r e no  require  tracer  the  techniques  curves.  f o r the  (t) - curves  outlined  by  the  injecting  discrepancies  the  interval  I f the  - t  adequately  t  ignored.  However, i n t h e  ( t ) had  that f i e l d  the  observed for  o f d i s p e r s i o n can  of t h i s  o b s e r v a t i o n s had  s a r y , t h e r e f o r e ,to d e v e l o p  3.3),  course  d e c l i n e d to n e g l i g i b l e  extrapolation.  time-  curves.  I n t e g r a t i o n , the mechanics  frequently  observed  3-3.2  Longitudinal dispersion i s primarily'  shape o f t h e s e  cover  i n Section  over  numerical  study  to be  values  and  be  i t happened  terminated i t became  before neces-  a d i s p e r s i o n model w h i c h w o u l d  Particularly  i n the  equation  d e c l i n e of C at l a r g e values  permit  f o r T^_  (Equation  of t c a r r i e s  consider-  weight. The  are:  and  significant  e v a l u a t i o n of i n t e g r a l s  responsible  able  injecting  was  results.  concentration  C  of long reaches  L o n g i t u d i n a l D i s p e r s i o n Models The  C  the v e l o c i t y  t h r e e main p r o c e s s e s  longitudinal  stream  lines  i n pools  and  causing  longitudinal dispersion  t u r b u l e n c e , t u r b u l e n t mass exchange  of d i f f e r i n g  velocities,  dead  Molecular  :  zones.  and  storage  diffusion  of  i s only  between tracer important  34  at  extremely  small scales.  T a y l o r ( 1 9 5 4 ) showed t h a t t h e one-dimensional  diffusion  e q u a t i o n g i v e s a f a i r l y good r e p r e s e n t a t i o n o f l o n g i t u d i n a l d i s p e r s i o n i n uniform, turbulent pipe flow. extended t h e a n a l y s i s t o i n f i n i t e l y  Elder  (1959)  wide open channels and  F i s c h e r ( 1 9 6 6 ) , Church ( 1 9 6 7 ) , Thackston and K r e n k e l  (1967),  and many o t h e r s have examined i t s a p p l i c a b i l i t y t o n a t u r a l channels. The  one-dimensional  rr  +  T—  V  6t  ID  =  h  d i f f u s i o n equation i s  D x  J  i n which x i s the l o n g i t u d i n a l c o o r d i n a t e , and D persion coefficient. at  3-D  ...  ?r  ^ 2  X  i s the d i s -  F o r s l u g i n j e c t i o n o f a t r a c e r o f mass M  t = o, x = o, t h e s o l u t i o n takes t h e f o l l o w i n g form a f t e r  v e r t i c a l and l a t e r a l m i x i n g a r e almost complete M C  (  X  J  T  )  =  (x - v t )  AV2?D1  ex  p (  inrT—  ••• -  }  3  X  x  I t shows t h a t t h e t r a c e r i s d i s t r i b u t e d  2  normally  over x,  w i t h t h e c e n t r e moving downstream a t v e l o c i t y v and t h e m v a r i a n c e i n c r e a s i n g as 2D t . Most d i s p e r s i o n d a t a a r e based on o b s e r v a t i o n o f C a t c o n s t a n t x, x = 1 . d i t i o n s , Equation with f i e l d  data.  Under these  con-  3 . 7 i s skewed t o t h e r i g h t , which agrees  7  35  3-7  Substituting  . , T  1 v  =  that  initially  Y  -2..  m  v : m  term  on t h e r i g h t  Although  2D / v  2  f o r the fact  upstream-. 1/v  < <  through-  s t u d y , E q u a t i o n 3 - 8 i s f u r t h e r p r o o f o f t h e need f o r  this  fast  accounts  some t r a c e r may be d i s p e r s e d  (Thackston et a l . , 1 9 6 7 ) . out  3-3 g i v e s  ;.2D' +  i n which the second  into  initial  mixing.  Equation concentration  3 - 7 was f i t t e d  to several  curves, using the least  observed  squares  time-  fitting  method  o  proposed cal  by T h a c k s t o n  data i s g e n e r a l l y predicted  fusion in  final  equation  Hays  It  close  decline  declines,  natural  dead  F i g u r e 5 shows a  typi-  The agreement b e t w e e n E q u a t i o n 3 . 7 and t h e f i e l d  fit.  observed  et a l . ( 1 9 6 7 ) .  o v e r most o f t h e C ( t ) - - c u r v e s b u t t h e o f C i s always  indicating  than  the one-dimensional  ( 3 . 6 ) does n o t r e a l l y  represent  dif-  dispersion  channels. (1966)  developed  zone s t o r a g e e f f e c t s  appears  that  much f a s t e r  a new m o d e l , w h i c h  besides one-dimensional  t o r e p r e s e n t t h e slow  unfortunately,  includes  decline  i t i s rather d i f f i c u l t  Fourier  t r a n s f o r m a t i o n of the f i e l d  fitting  i n frequency  diffusion.  o f C very w e l l , but  to-handle, requiring  d a t a and s u b s e q u e n t  curve  space.  3 T h i s method i s b a s e d on t h e IBM S h a r e ramme N L I N 2 , d e s c r i b e d b y M a r q u a r d ( 1 9 6 4 ) .  library  a  prog-  36  60  Time  LONGITUDINAL  from  injection  (min)  DISPERSION  INJECTED  OF  SLUG &  TRACER Fig. 5  37 3-3-5  A Gamma-Distribution  Model f o r t h e F i n a l D e c l i n e o f C ( t )  Since the f i e l d  o f the present  data  main p a r t o f the. G ( t ) - c u r v e s a d e q u a t e l y , to  develop  only  a s i m p l e model f o r t h e f i n a l  tracer  storage  (I)  The s t r e a m  steady  i n pools.  A l l reservoir  with T , the f i l l i n g R  (iii) (Iv)  Mixing  on t h e  assumptions:  of"reservoirs  an a r b i t r a r y  i s instantaneous  (t = 0) =  o  into  The i n i t i a l  i n each  to T  with  time  constant.  reservoir.  i s initiated  the f i r s t  Q,  R  by i n j e c t i n g  reservoir  concentration i n R  o  (R ) at Q  i s therefore ... 3 - 9  T^Q  (v) The t r a v e l constant  being  The d i s p e r s i o n p r o c e s s  = 0 .  s C  be  decline, considering  volumes FL a r e e q u a l  time,  a quantity M of tracer t  was made  f l o w Q. (ii)  time  d e f i n e the  an a t t e m p t  I t i s based  a c t s as a c a s c a d e  study  time  between two r e s e r v o i r s i s  f o r a l l water o r t r a c e r p a r t i c l e s  and c a n t h e r e f o r e  ignored i n the f o l l o w i n g . These assumptions  lead  homogeneous d i f f e r e n t i a l The  t o a system o f l i n e a r , non-  equations  of f i r s t  order f o r C ^ ( t ) .  g e n e r a l form i s dC. —dt i  =  C. , T~ 1  1  C. _1 T  0x u ... ^ j1 -  T h r o u g h a r e f e r e n c e i n Water R e s o u r c e s R e s e a r c h , V o l . 5 , No. 4 , p . 9 2 7 , A u g u s t 1 9 6 9 , a p a p e r by M a c M u l l i n and Weber ( T r a n s . Am. I n s t . Chem. E n g r s . , V o l . 3 1 , p p . 4 0 9 - ^ 5 8 , 1 9 3 5 ) has r e c e n t l y come t o t h e w r i t e r ' s a t t e n t i o n . I t c o n t a i n s an i d e n t i c a l - d e r i v a t i o n , b a s e d on c o n s i d e r i n g t h e o u t f l o w f r o m a s e r i e s of well-mixed v e s s e l s .  38  The  s o l u t i o n s are T  Reservoir R  C  o  o  ( t ) = =—•^ T Q  e  R  t T  • Reservoir  R,  C-.  (t) = — ^ — t e T Q R  t • T Reservoir  R.  C.  1  The  (t) =  t  M  i!T  1  s u c c e s s i v e peaks o c c u r  e  1  3.11  ...  R  Q  1 + 1 R  a t t = i T _ and  t h e mean t r a c e r  R  travel  time i s T  3.11  Equation  f  ( i + 1)  =  fc  can  be  T . R  compared  x <*> = r f ? T  to the  *~  gamma  > o  r  x >  Equation  3.11  i n mind t h a t c a n be  ... 3.12  Kt  K> Keeping  distribution  f(r  + 1)  0 0  = r! for r = 1,2,3  •. .  r e w r i t t e n as t  Cj(t)Q M  _ ." T  c  n  r  w h i c h shows t h a t t h e distribution  with  Initially could  represent  explored  by  (Figure  6),.  i (i+l)  the the  T„  T  "  T  R  N  _  e  n  general  parameters  fitting In  i  question  solution  i s p r o p o r t i o n a l to a  (I + 1 ) ,  (1/T ), R  of whether t h i s  t o t a l time-concentration  and  comparing  It with  the  t.  storage curyes  i t to s e v e r a l sets of f i e l d diffusion  f-  model was  data; model one  may  39  30  Storage  model  (Least squares  fit to all points)  Test. Ph R 10, G2 - 3 X - 4 - 6  140 Time  THE  STORAGE  from  injection  MODEL  LONGITUDINAL  160  (min.)  APPROXIMATION  TO  DISPERSION Fig. 6  40  say  that: ( i ) B o t h models, can be. f i t t e d  the  observed  resent  the  t i m e - c o n c e n t r a t i o n d a t a , but  The  s t o r a g e model can  l a g between t r a c e r i n j e c t i o n location.  t h e whole r e a c h (iii)  The  stability.  In the  The  the r e s e r v o i r  ( i v ) The  of the  C  that with  at  time  the  tracer  of these  final  i n the  storage  covers  decrease  with  field  length  w h i c h does  the  s t o r a g e model  ( t ) , i f the  parallel  f i t over  the  Equation  3.11  the  final  Y (t) = Y  i n w h i c h t h e Y.  are  1  t ^  _Y. e  constants.  t J  tracer  decline.  is essentially  can main  splitting  phases; a d i s p e r s i o n  p h a s e , r e s p o n s i b l e f o r m o v i n g most o f t h e phase, which dominates  the  not  ( t ) - c u r v e s i s i g n o r e d , w h i c h amounts t o two  Q.  results.  deficiencies,  d e c l i n e of C  flow  P-distribution-is  of the  decrease,  model  length, neither  i n c r e a s i n g channel  should  t h e d i s p e r s i o n phase i n t o  C  rep-  finite  arrival  channel  time,  moment r a t i o  consistent with  In s p i t e  part  f o r the  first  to  of t .  d i f f u s i o n model t h e  filling  skewness o f C ( t ) = c u r v e s  the  the  increase with  third  , indicating  represent  and  number o f r e s e r v o i r s  does T ,  a p p e a r t o be  account  fail  d i f f u s i o n model g i v e s b e t t e r p a r a m e t e r  necessarily  2/ V~r"  both  immediately.  does not R  e q u a l l y w e l l to  slow d e c l i n e of C at l a r g e v a l u e s  (ii)  sampling  almost  o f the  form  and  a  storage  41  Taking  logarithms  log  C  1 Q  on b o t h  = log  1 Q  w h i c h shows t h a t  (3-11) can  data  (log^C  i n the  values fall are  of  on  form •  Equation  a straight  attributable  values, Figure  the 7-  3.11  r  achieved  by  exponential equal  t o an  resulting  3  plotting  few  the  as  ( t ) , for selected data  exceptions,  shown by  the  the  the  curve  points  which low  C  examples  of  computer-made p l o t s a r e  shown i n  the  "TAILEX". ( t ) a p p e a r s t o be  r ^ 3•  similar  A good f i t was  ( i = 1 ) , but  Figure  complete  r = 1  7A  d e c l i n e of C  set of C  almost  Figure  Figure  i s plotted i n C - t coordinates. shown i n t h e  which  -distribution On  a  (negative  ( t ) and  (t)—data.  to  generally  shows a s e t o f d a t a  g r a p h i c a l f i t t i n g of a P  incomplete  field  two  r = 2  computer-made p l o t s a r e ine  Y t  d e c l i n e ) c o u l d have b e e n s e l e c t e d w i t h  almost  illustrates  t e s t e d by  t -  d i f f i c u l t i e s of determining  1<  justification.  covers  sion  setting  1 Q  i s a good f i t i f t h e  f i n a l d e c l i n e of C  - d i s t r i b u t i o n with  log  2  With very  Appendix under S u b r o u t i n e The  be  f i e l d data p l o t Some s i m i l a r  + Y  1  gives  - Y ^ o g ^ Q t ) vs.  line.  to the  Y  sides  5  7B extenthe  Similar  Appendix under  Subrout-  "PL0TGA". The  step  above s t o r a g e  t o w a r d s an  model r e p r e s e n t s  understanding  only  of l o n g i t u d i n a l  a small  first  dispersion in  4 in  the  The p a r a m e t e r s Y,, Appendix.  Y , ?  and  Y_ a p p e a r as ->  A,  B,  and  C  42  \0]  Fig. 7A  Test  covering  C(t) decline almost  completely  5^  Rg. 7B  Incomplete test with r~ extension Test BR R2, GIUP-|~2X  GRAPHICAL FITTING OF STORAGE MODEL Fig.7  43  tumbling, flow, c h a n n e l s . measured plete  In the  course  investigation,  of the  The  large  numher o f C . ( t ) - c u r v e s  o f t h i s .study- s h o u l d p e r m i t  c o n c e n t r a t i n g on  s t o r a g e model, but  t h i s - i s not  a more com-  the p r e d i c t i v e p a r t of the  qualities  present  obj e c t i v e . 3.3.6  Equipment  and  All  (t) curves  sured with (i) electrical (ii) detection  on t h e  the C either  Procedure  one  included i n this  of the  the r e l a t i v e  salt  d e t e c t i o n o f a Na t h e dye  following dilution  of a fluorescent  experience  gained  (Church  and  s t u d y were mea-  method, b a s e d  on  Cl-solution;  tracer  description  Measurements  methods:  d i l u t i o n method, b a s e d  A detailed  I n press. •  f o r Slug I n j e c t i o n  on f l u o r o m e t r i c  (Rhodamine  WT).  o f b o t h methods, b a s e d  i n the  course  Kellerhals,  of t h i s  1969).  Only  partly  study, i s a brief  summary  • 5  will  be  given The  1954;  here.  relative  0strem, 1964)  tration  of s a l t  and  salt  d i l u t i o n method  uses  the  linear  conductivity.  ( A a s t a d and  relation  between  A known volume  Sognen, concen-  (generally  5  I n i t i a l l y a few d i s c h a r g e s were m e a s u r e d by i n j e c t i n g t h e t r a c e r (Sodium D i c h r o m a t e o r Rhodamine WT) at. a c o n s t a n t r a t e and t h e n d e t e r m i n i n g t h e d i l u t i o n r a t i o between i n j e c t e d s o l u t i o n and s t r e a m w a t e r . This "constant rate i n f e c t i o n method" i s d e s c r i b e d i n C h u r c h and K e l l e r h a l s .(1969,) . The equipment i s , shown on Photograph. 1 6 . The method, was- n o t s u i t a b l e f o r t h i s study, b e c a u s e i t c a n n o t g i v e v e l o c i t y and o f f e r s no a d v a n t a g e s o v e r s l u g i n j e c t i o n methods f o r s i m p l e d i s c h a r g e measurements.  44  10  100.  to  not  be  liters)  of a s a l t  known, i s s l u g - i n j e c t e d i n t o t h e  of the  salt  wave i s o b s e r v e d  ductivity  m e t e r and  solution  is retained  concentration advantages discharge  i n the  sisting  f o r the  i s the  of NaCl per  with  flasks,  The  7,  8,  dye  Accurately  C at  Not recording the  tedium  low  flows. no  s  and  field  9 show t h e  The  main  computing  laboratory  work.  equipment,  conditions  Photograph  discussed  main  as  A  con-  by  10  conductivity bridge  severe  10  taking  (Rhodamine  i n t o the -  20  small  analysis  (Photograph  conductivity-time  t o be  stream water on  a  equipment.  & K e l l e r h a l s (1969)  appears  suitable  rainstorms.  tracer  directly  d e s c r i p t i o n of t h i s  s i m i l a r instrument  watch.  is particularly  during  shows the  volumetric  items.  liquid  pipet  stop  location for later  i n Church  of measuring  and  method u s e d h e r e  downstream  A brief  of  measured, p i p e t s , 2  t o be  (t)-curve i s defined the  conductivity-  dilution.  field  initial  gauges, p a i l s , a p p r o x i m a t e l y  i n j e c t e d from the  fluorometer.  as  bulky  m e a s u r e d amounts o f t h e  WT-dye) a r e  samples  of  con-  -1  dilution  under d i f f i c u l t  the  avoidance  needle  of a  need  passage  a portable  possibilities  c o n d u c t i v i t y meter, e l e c t r o d e ,  Photographs  and  m  the  the  sample o f t h e  successive  relatively  3 kg  and  A small  construction  method a r e  2 vats  of  electrode.  field  s t r e a m and  downs-tream w i t h  r a t i n g c u r v e by  of the  disadvantage  1  s o l u t i o n , whose c o n c e n t r a t i o n  11)  built  curves  bridge  at  may  available  is to  the avoid  extremely be  in  order  commercially.  45  -Interval timer  6 V Power pack  6 V. D.C.  •I'h-T  'IH  Inverter  6 V. Batteries  -115 V A C  Recorder (O.V-I.V) Galvo 100 K.  £-V  II5V,  Variable transformer  Isolation or stepdown transformers 40V  CIRCUIT DIAGRAM OF RECORDING CONDUCTIVITY BRIDGE Fig.8  46  The  principle  potential V with of  high  the  o f an A C - b r i d g e  input  bridge The  of o p e r a t i o n on  impedance, R  i s shown on  ER .  (RG  Q  Figure  i n which E i s the zero  and  40  take  any  value  between t h e  voltage  and  careful  selection  injected,  and  of  and  0.9  volts.  The  85  conserve  continuous  the  voltage  operated  and  adjustable  i s c a u s e d by  be  built^  3  K,  R  the  the  loss  i n the  an  of the  electronic  runs  o f f an  E  i n d e p e n d e n t power  5.11  K and  The  difference  but  neglected  v o l t a g e , amount adjustments,  during  interval and  can  Computed  r a n g e between  voltage  1 4  inverter.  background  linear  exciting  operation,  9.  of e x c i t i n g  initial  at  probe.  significant  i n s e r t e d between t h e b r i d g e  recorder  i s fixed  c  '  between  r e s i s t a n c e which  a r e p l o t t e d on F i g u r e  can  of  8.  c o n d u c t i v i t y m e a s u r e d by  bridge  To  diagram  v o l t a g e , which i s a d j u s t a b l e  between 0 K and  two  With  0.2  circuit  Q  R Is the  measured'responses  t o be  The  recorder  - .1) . .  exciting  volts,  G i s the  salt  K.  Rustrak  (RG+1) ( R + 2 R ) + 2 R  =  C  threshold  10Q  off-balance  response V i s  V  and  a 0 - 1 volt =  n  is. to r e c o r d the  of the  responses  long  timer  i t s power  periods was  supply.  source.  The d e s i g n of. t h e t i m e r was d e v e l o p e d r e c e n t l y by S. O u t c a l t o f t h e Dept.. o f G e o g r a p h y , UBC, and W. Schmitt, Dept. of C i v i l E n g i n e e r i n g , UBC.  47  Recorded  RESPONSE  potential  OF RECORDING  (Volts)  CONDUCTIVITY  BRIDGE  Fig. 9  48  3.3-7  ' Tracer  Losses  The t r a c e r methods f o r d i s c h a r g e measurements conservation that  tracer  result  o f t r a c e r mass.  Prom E q u a t i o n  discharge,while  seepage o f water out o f the c h a n n e l time,  3.3  Equation  tracer  results  loss  the C ( t ) - c u r v e .  To p e r m i t  however, i s i n d e p e n d e n t  3  correction  l o n g mean r e s i d e n c e t i m e s 3.3,  f o r T^ a c c o r d i n g t o E q u a t i o n with  a separate Almost  amount  minute  loss  discharge  for losses, were o n l y  interpreted  d i s c h a r g e b e i n g measured  test  results  The l o s s  from  show a  certain  position.  tests,  a short reach, both  one  over  ending  Assuming t h a t the measured  and t h e t r u e d i s c h a r g e Q a r e r e l a t e d 100  dis-  r a t e L, i n p e r c e n t p e r  two s i m u l t a n e o u s  and t h e o t h e r o v e r  leads to  most  the s h o r t e s t p e r m i s s i b l e reach.  of the t r a c e r .  t h e same s a m p l i n g  T  of the  t h e shape o f  due t o a b s o r p t i o n o r c h e m i c a l  c a n be e s t i m a t e d  a long reach at  over  a l l Rhodamine WT  of t r a c e r  integration  test  due t o  i n underestimates.  t r a c e r mass as l o n g as t h e l o s s e s do n o t a f f e c t  tests with  one c a n s e e  l o s s e s due t o a b s o r p t i o n . o r c h e m i c a l r e a c t i o n s  i n overestimated  The t r a v e l  3.2  assume  as " . . . .  3-15  t  " 100(1— L =  Q /Q] ) S  L  ...  3.16  m " ^ ° m t , l 'Q t,s :  1  i n w h i c h t h e s u b s c r i p t s 1 and s r e f e r short  reach r e s p e c t i v e l y ,  and Q and  t o t h e l o n g and t h e a r e computed  according  49  3.2  to Equations  3.3  and  order  of 0 . 1  to 0 . 3  found  f o r the observed  on Rhodamine WT 3.15,  salt  tests  result  conductivity  d a t a , but  of the  salt  t r u e i n very extended  Surge T e s t s  3.4.1  Ob,]* e c t i v e If  a channel  the d i s c h a r g e Q resulting  from  and  changes i n t h e  The  conductivity  wave c a n  t h e n one  adequate reach, steps.  tend  i s probably  o n l y be  end, may  changes  since  they  can be  storm  converted  to  remains of which  is linear,  of reproducing  of a t e s t  h o l d s over the  t h e method  reach, i n Q (t)  complete  should also  hydrographs  decompos.ed i n t o  T h i s g e n e r a l statement  channel response  observed  i n c r e a s e s or decreases  i f this  assume t h a t  t o r o u t e complex  a  tests.  step-like and  to  background  conductivity  r o u t i n g method i s c a p a b l e  small,  based  i n the  definitely  cause  ( t ) a t t h e downstream end  the upstream  o f Q,  appears  o r changes i n a p r e d i c t a b l e manner, n e i t h e r  3.4  at  of a s a l t  c o u l d be  tests.  loss  times  The  c o n c e n t r a t i o n i f the background  constant was  stream.  reason  according to Equation  double  long t r a v e l  losses  No  i n the  Most d i s c h a r g e s  of t r a c e r  discharges.  of t r a c e r  d u r i n g the passage  i n L.  were c o r r e c t e d  evidence  in unreliable  combination  variation  e s t i m a t e d from  consistent  dilution  L i s commonly  p e r c e n t per minute.  with L-values No  respectively.  through  range  be  the  channel  a sequence o f s m a l l  i s absolutely  correct  i f the  but. f o r a l l p r a c t i c a l p u r p o s e s i t  50  will  a l s o h o l d as  enough t o l e a d The impose  l o n g a a t h e n o n - l i n e a r i t i e s , a r e not  t o severe, d i ' s - c o n t i n u i t i e s  main o b j e c t i v e  small,steplike  u p s t r e a m end  of t e s t  of these p o s i t i v e c o v e r as  large  A few  3.4.2  on  surges.  the e f f e c t  the  The  o f d i s c h a r g e as  four lake outlets  Discharge  flashboards  Phyllis  was  c o u l d be  the o u t l e t  the  propagation  t e s t s were  of the r e l a t i v e large A  s m a l l and  at  to  possible.  Q's  of A Q  size  at constant  different by  Q.  Photograph  13  no  control  14).  The  i t was from  adding  control  The  steady  outlet  the p o o l i n f l o w .  The  rocks  s i p h o n was  with  built.  swamp i n t o  mi.nutes  v  Lake  Surges  reaches dissurge  at the p o o l  then used  two  the  steady  initial  at  the  of P l a c i d  c o u l d be  to maintain  f l o w f o r 5 t o 15  o r remov-  over  p o o l above t h e B r o c k t o n  o r r e m o v i n g a few  Lake.  shows t h e dam,  structure  difficult  study.  of Blaney adding  each  o l d t i m b e r - c r i b dam  L a k e gave e x c e l l e n t  A gravity-operated inverted more o r l e s s  1 2 ) . " An  at  of t h i s  by  by pumping w a t e r a c r o s s t h e  small that  produced  streams outlet  additions i n place.  (Photograph  charges  at the  (Photograph  so marshy t h a t  so  built  Creek r e a c h e s .  were p r o d u c e d  on t h e t e s t  i n c r e a s e d or decreased  of Marion  flashboard-like  was  to observe  methods f o r m o d i f y i n g Q were u s e d  A s m a l l dam  creek  t e s t s was. t h e r e f o r e t o  Discharge M o d i f i c a t i o n s  of the  was  and  negative  imposing  Different  ing  reaches  a range  were a l s o r u n by  surge  bores.  d i s c h a r g e m o d i f i c a t i o n s , A Q,  and  tests  of. t h e  s u c f i as  strong  was  outlet.  to' m a i n t a i n  (Photograph  15).  51  3.4.3  ' 'Stage M e a s u r i n g Discharge  Equipment  c h a n g e s a t t h e end p o i n t s  were m o n i t o r e d b y o b s e r v i n g establishing discharge. it  stage  discharge  rating  E v e n on t h e s t e e p e s t  curves  f o r conversion to  and most t u r b u l e n t stable pools,  f l u c t u a t i o n s and a i r e n t r a i n m e n t  reaches  either  (Photograph 1 8 ) .  o r between l a r g e b o u l d e r s  level  on F i g u r e  made d i r e c t  10 and P h o t o g r a p h s  on b e d -  The t u r b u l e n t level  measurements i m p o s s i b l e , b u t t h e p l e x i g l a s s s t i l l i n g illustrated  reaches  o r r e c o r d i n g stage, changes and  was g e n e r a l l y p o s s i b l e t o f i n d  rock  o f the. t e s t  16 and 18  wells  permitted  7  the  reading  factory in  o f water  levels  t o + 0.001 f t .  r e s o l u t i o n , s i n c e most  the order To  surge t e s t s  This  caused  gave level  satischanges  o f 0.02 t o 0 . 0 5 f t .  g a i n some i n f o r m a t i o n  the  test  reaches,  automatic  all  b u t one o f t h e t e s t  A-35  recorders, with  (9-6  in/24 hours),  about  stage  creeks.  the f a s t e s t  the discharge  range o f  r e c o r d e r s were i n s t a l l e d The i n s t r u m e n t s  were  available clock  gearing  and a 12:10 l e v e l  scale.  These  on  Stevens  large  s c a l e s made i t p o s s i b l e t o r e l y  on t h e r e c o r d e r s  f o r the surge  tests,  assistant.  careful  cedures  thereby  one f i e l d  With  pro-  t h e t i m e s c a l e c o u l d be i n t e r p r e t e d to' + 1/2 m i n . The  due  saving  recorder  i n s t a l l a t i o n s were somewhat,  t o the i n v e r t e d siphon  connecting  the stream  unconventional, t o the s t i l l i n g  ' A l l s t a g e measurements a r e i n f e e t and decimals t h e r e o f due to a l a c k o f r e a d i l y a v a i l a b l e m e t r i c e q u i p m e n t .  52  Tube cover Plexiglass tube, 2"O.D., 1/8" wall  Strip of rod cloth glued to plexiglass tube  "/^-Pocket mirror in position j/ for water level reading  Wooden post  1/4 Hose connector Nail tied into nearby BM  SCHEMATIC (from  SECTION  OF MANUAL  GAUGE  Church and Kellerhals, 1969)  Fig. 10  Airbleed plug,(rubber stopperi-  Glass or plastic container 1/2 to 2 gal.  Possible locations for taps (not essential) Automatic stage recorder  Recorder stand and stilling well (plywood)  -n  u5  oo  •%%S£HEMAft IC VIEW .,0F; STAGE "RECORJDER" INSTALL ATlbN '-FOR*-MOUNTAIN STREAMS" (from Church and Kellerhals^ 1969)  54  F i g u r e 11  well. method.  and P h o t o g r a p h s  The. e x p e r i e n c e  m e a s u r i n g equipment  gained  i n Church & K e l l e r h a l s  3.4.4  Stilling The  quency  essential as  t h a t t h e gauge  fluctuations  between p l e x i g l a s s cause  level  of the stream  f o r accurate  level  t o how much i t a f f e c t s  negligible. ing  cannot  and t h e i n e r t i a  The w e l l r e s p o n s e  but the q u e s t i o n  test  the  arises  data.  the flow  i n the connecting  o f the f l o w i n g water i s  I s t h e n g o v e r n e d by t h e f o l l o w -  equation: ... 3 . 1 7  which h i s the e l e v a t i o n  d i f f e r e n c e between the stream  s t i l l i n g w e l l and b i s a t i m e ' c o n s t a n t .  level the  fre-  T h i s damping i s  dh h = - b || in  wells or  follow high  level).  the surge  tube  c o n s i d e r a b l e damping  readings  Under n o r m a l c i r c u m s t a n c e s g hoses i s l a m i n a r  stage  Response  hose c o n n e c t i o n s  the sense  w.ith a l l t h e above  (1969).  r e c o r d e r w e l l s and t h e s t r e a m s (in  and 18 I l l u s t r a t e t h e  (.tubes and r e c o r d e r s ) i s d i s c u s s e d a t  length  Well  17  i s constant  solution  and t h e w e l l l e v e l  is  and  I f the stream  i s o f f by h  a t time  t ,  ^o~^  h = h e Q  .  ... 3 - 1 8  A s s u m i n g a s t e a d y r i s e o f 0.02 f t / m i n . i n t h e w e l l , w h i c h i s a p p r o x i m a t e l y t h e maximum o b s e r v e d d u r i n g s u r g e t e s t s , g i v e s R e y n o l d s Numbers o f 24. for. t h e c o n n e c t i n g hose o f p l e x i g l a s s t u b e s and 500 f o r r e c o r d e r w e l l c o n n e c t i o n s .  CD CB  31 ro  . "*:.v,:... • • •  GAUGE^:^RE^feo>JSE 'CURVES ^  '  ;  r  A  :  .  '  56  which i n d i c a t e s that a straight tions pipe  line  should  be  friction  Figure  12  h^  since Equation  there  are  of p l o t t i n g i t takes  the  on  ). v s . (h/h,) should,  expected  t o an  b  (t - t  (-b)  semi-log  paper.  3.17  c e r t a i n other  shows some t y p i c a l  time,At,  arbitrary  of  of slope  and  Instead the  a plot  a response stilling  arbitrary  h^  and  Some  only,  losses  gauge r e s p o n s e  give devia-  considers present.  curves.  curve,  one  can  measure  w e l l t o drop  from  compute b  follows:  as  an  logth*/h )  =  3 , 1 9  2  All  gauge and  manner and, rected the  where n e c e s s a r y ,  for lag according  gauges needed  3.4.5  recorder  the  the  the  of the  gauges were l o c a t e d a t p o o l s  lack  test  reaches  d e s t r u c t i v e f o r c e of the  flood  c o n d i t i o n s was  unstable.  About  were  one  cor-  third  of  Curves  severe  t o be  3-17.  records  this  lag corrections.  time when most o f t h e  were i n s t a l l e d ,  were t e s t e d i n  surge t e s t  to Equation  Stage-Discharge Rating At  setups  not  properly  of s t a b l e p o o l s ;  only  streams  appreciated.  that proved  In h i n d s i g h t , i t appears  of t h i s  that  study  under Many  subsequently there  a lack of experience  was  no  in locating  Q them.  As  the  gauges  could  not  be  moved w i t h o u t  altering  the  9 P o o l s f o r m e d by l a r g e , p r e f e r a b l y a n g u l a r r o c k s , a r r a n g e d i n s u c h a way t h a t t h e y do n o t e a s i l y c a t c h d r i f t wood, a r e b e s t . L o c a t i o n s below w e l l e s t a b l i s h e d l o g jams a r e e x c e l l e n t , as the jams t e n d t o c a t c h most d e b r i s and c o a r s e bed l o a d .  57  TWO  TYPICAL RATING  STAGE - DISCHARGE CURVES  58  test had  reach  l e n g t h , some p a r t s o f t h e s t a g e - d i s c h a r g e  t o be r e - d e f l n e d two o r t h r e e t i m e s ,  of the surge  d a t a from  were i n s t a l l e d Figure pool  of Blaney  stage  to discharge.  a t t h e most s t a b l e 13  shows two r a t i n g  Gauge 5 ( P h o t o g r a p h  more t r o u b l e s o m e  Blaney  Gauge  to permit  1.  gauging  curves  conversion  The s t a g e  recorders  sites.  c u r v e s , one f o r t h e s t a b l e 18)  and t h e o t h e r f o r t h e  59  4.  F I E L D RESULTS  4 .1  Survey  Results 2 and  Tables results width  which  3 and  consist  measurements  Figures  of the  (Section 3-2)'  The  a s e t o f programs  2 and  summaries  undoubtedly since  width  field  o f 10%  The  by  t o 15%  The  to. compensate could, s t i l l  and  d a t a were  pro-  (1969).  Day  Tables  There i s  i n the width  often, particularly  defined.  survey  on  the  l a r g e number  for this,  but  o c c u r between  data,  of  dis-  different  parties. most t e s t  between a c t u a l  that  rather i l l  measurements t e n d s  On  the  developed  the  reaches  width  a considerable operator effect  streams,  crepancies  test  o f the program o u t p u t .  t h e h i g h w a t e r mark was  bushier  4 summarize  of p r o f i l e s  cessed with 3 are  3 and  case the  o f the  few  very  there  significant  length i n plan steep  l e n g t h i s the  accuracy  i s no  of the  (map  l e n g t h ) , but  reaches  i t i s worth  actual  l e n g t h on t h e  c h a i n i n g and  difference In  noting slope.  hand-levelling is  at + 3 percent.  estimated  Slope Q i s the  l e n g t h and  surveyed  relative  reaches  i s d e f i n e d as  slope  The  drop  d i v i d e d by  length,  s i n Q, i f  the b e s t  available  angle..  drainage  areas  were measured on  maps and  refer  to the middle  Brockton  C r e e k b a s i n .does not  p o i n t of a t e s t a p p e a r on  any  reach. map,  as  The the  60  1:50,000, poor.  coverage, of. t h i s  The  drainage  a r e a happens, t o be  area  exceptionally  was. t h e r e f o r e m e a s u r e d  off air  photos. 4.2  Velocity  4.2.1  Conversion of F i e l d The  test  field  consist (i) (ii) (iii)  ponding  Discharge  Measurements  Data  to Time-Concentration  data r e s u l t i n g  of . the  location  and  time  volume o f b r i n e sampling  readings  dilution  injected,  location,  list  of times  c u r v e , c o v e r i n g range  rating  salt  injection,  (iv)  ( i t consists  and  corres-  of observed  of d i l u t i o n  rates  and  concorres-  conductivity readings),  Church  earlier  and  used,  in  the  Kellerhals  as t h e  stream  (1969).  on t h i s  correction  and  in rating  f o r c o n v e r t i n g the  developed  curve.  procedure  tank. time-  The  tank  background  i s i n error.  for this  readings A Fortran it  time-concentration data  operating instructions  and  in  s h o u l d not  conversion.'  program i s l i s t e d  detail  proposed  ( 0 s t r e m , 1964)  for different  t h e t i m e - c o n d u c t i v i t y and the r a t i n g  The  method  i n the r a t i n g  IVG p r o g r a m "NACL" was  together with  and  data to time-concentration i s described i n  publications  be  i n stream  computational procedure  conductivity  plots  of  readings,  The  prints  a relative  Curves  following:  (v) w a t e r t e m p e r a t u r e  in  from  conductivity  ductivity ponding  and  i n the  and  Appendix,  sample, o u t p u t .  61  The  f i e l d data r e s u l t i n g  (i)  location  (ii) (iii) 10  t o 30  of  dye,  sampling  list  location,  a rating  samples  are subsequently  on  of sampling  The  c e s s i n g by  necessary  laboratory  computations  an i n p u t p r o g r a m  listed  i n the  Numerical The  "DQV"  procedures  3.2,  time  "QVEL"  (see A p p e n d i x ) .  were done m a n u a l l y ,  Simpson's  f o r d i s c h a r g e Q,  a r e e v a l u a t e d by  rule  The  formulas  do not  numerical  and  rule  points.  on  analogous  but  cards f o r proto  "NACL",which  The  integral  over  then w i t h a second  but  procedure appear  capable  and  C ( t ) and  for tracer  o r d e r method  of h a n d l i n g unevenly  readily  the  on t h e b a s i s  i s discussed b r i e f l y t o be  3.3,  a F o r t r a n IV.G s u b r o u t i n e  moment o f C ( t ) a r e computed t w i c e , f i r s t  to  in. g r e a t  Appendix.  travel  trapezoidal  tracer.  Integration  Equations T,  Tluorometer,  of the  t h e f i n a l t i m e - c o n c e n t r a t i o n d a t a were p u t  4.2.2  times,and  a n a l y s e d on a  standard d i l u t i o n s  (1968) d e s c r i b e s t h e  also  are:  reading i s converted to c o n c e n t r a t i o n with  curve based  detail.  is  test  injection,  volume o f i n j e c t e d  the instrument  Wilson  time  a Rhodamine WT  samples.  The and  and  from  first of  the  similar  spaced  below, because  available  i n texts  the  on  analysis.  The C o u n c i l was  " T u r n e r M o d e l 110".fluorometer. o f t h e B.C. used here.  Research  62  Assume t h a t  C ( t ) is. defined  as shown on F i g u r e  The  2  14.  0 FIGURE 14.  a t t =. t , t ^ , and t  2  "I  DEFINITION SKETCH FOR NUMERICAL  INTEGRATION  f u n c t i o n C ( t ) c a n be a p p r o x i m a t e d by a s e c o n d  order  p o l y n o m i a l P ( t ) o f the form  P  (t) =  t h e 1^  i n which t^jtpand  t  2  (Herrio,  t  1  (t) + c  q  1963), - tt  1  = C  C(t)dt t„ o  J  1  i  1  1  order  (t) + c  2  i  polynomials  2  (t)  i n terms o f  e.g.  - t t •+-- t 2  <v- V  The i n t e g r a l t„ P(t)dt  Q  ( t ) are 'second  y t )  J  C  ( t  o  -  1  t . 2  V  c a n be e s t i m a t e d as t„ q  (t.).dt + C  1  /  1  (-t.).dt + C /  l (t)dt 2  Without t t  t The  l o s s o f g e n e r a l i t y , one. can = 0  o  = At  x  =  2  x  At  2  i n t e g r a l s over 1 ( t ) are At f  A  t  A t  -  At  1  i-)  2  A t  =  t  A t  2 ?  < - ^ ^  2 ( )dt  then:  !  2  J v*'*  0  substitute  0 2  6(A t  2 x  -A t  x  A.t ) 2  A t, 1  (t)dt =  ?  -r-' A\t 2  which  reduces An  t  = -A t  (  1  t o Simpson's R u l e  A t  1  At  3  i  0  i  3  2  At. 1 )  At  if.At-, = 1  a p p r o x i m a t i o n to the f i r s t  At  2  moment w i t h r e s p e c t  = o is At  A t  2  Jp(t)'tdt  = c  =  (  A t  2  fi (t)tdt+c  Q  o  <Ti r2 r  Ji (t)tdt+c  1  +  +  ) 3  - T --  r2  A t  2 r  A t  +  3  i  ]  rri  At  3  - f -  (  +  r i  A  t  2  Ji (t)tdt  2  1  At +  A t  2  2  A  v V A  3  i - ^  to  64  in  which C. r  &1  r  _  -  2  9_  At-jAt  At^  2  1  -At-^At^ C  ^3  2  =  At -At At  3  2  In those  1  2  c a s e s where t h e  concentration decline  been d e f i n e d a d e q u a t e l y  i n the  field,  (see A p p e n d i x ) i s f i r s t  called  from  (log  CY.'  l o g t) vs.  2  f-distribution  e x t e n s i o n , as  shown on F i g u r e 7 . read  (t) to permit  o f f the  The  "TAILEX" p l o t  and  o f t h e CXt.)-. .datac.che.Gk. I f t h e ;  called, over  i t will  can be  plotted  programs  "DQV"  Appendix, 4.2.3  punched  onto  the  and are  control  card  s u b r o u t i n e "QVEL" i s t h e n to extend  the  integral  time.  the C ( t ) - c u r v e s , w i t h by  of a  of the e x t r a p o l a t i o n  the / ~ " - d i s t r i b u t i o n  C(t) to i n f i n i t e Finally,  calling  o r "NACL".  together with  or without r - e x t e n s i o n ,  s u b r o u t i n e "PL0TGA" "PL0TGA"  i s also  from  listed  operating instructions  and  the i n p u t In  the  sample  plots  Results The  which  use  fitting  It plots  discussed i n Section 3.3-5  parameters  not  a s u b r o u t i n e "TAILEX"  "NACL" o r DQV".  the  has  146  tracer  slug  injections,  t i m e - c o n c e n t r a t i o n c u r v e s were d e t e r m i n e d .  words, a p p r o x i m a t e l y contain  of 111  data consist  one  two  thirds  downstream sample  of. t h e  o n l y ; the  slug  In  injection  other t h i r d  for other  tests  consists  65  mainly  o f r u n s "with two  samples.  sampling  there  a r e e i g h t d i s c h a r g e measurements w i t h  none o v e r  approximately  summarized  of the  7000 t i m e  appear j u s t i f i e d . form.  arranged  complete  and  Tables  4A  t o 4D  T h e r e i s one  in historical  t h e A p p e n d i x , as p r i n t o u t The  reference number.  from  table  4 refers  the d i s c h a r g e  at the  sequence.  refers  The  to the  sampling  to t e s t  in  with  the  test  exception of  the  same d a t a a p p e a r a g a i n i n  test  are  tracer  For  i t i s best slightly  data  and  (see S e c t i o n  reach.  and  p o i n t , whereas  reaches,  d i d not  identification  o f t h e p r o g r a m "L0GRE "  discharges  of  the  cross  t o use  the  test  different therefore gives  the  "L0GRE"  discharge  i s the  outflow.  Accuracy The  relative  appears  tests  on  stream runs)  rate  consist  stream,  With the  e s t i m a t e d mean between i n f l o w and  data  per  4 to the Appendix  Table  because Table  4.2.4  the constant  data, which  a r r a n g e m e n t t h e r e i s by  Note t h a t t h e  printout  over  addition,  show t h e r e s u l t s  d i s c h a r g e measurements, t h e  5.2.2).  In  concentration values  code i s e x p l a i n e d i n a f o o t n o t e . simple  four.  extend  method.  Presentation  runs  and  t h r e e runs  three  injection  locations  Only  the  (after and  similar  t o be  accuracy,  satisfactory.  same day  As  give s i m i l a r  correction  tests  or i n t e r n a l  made a t d i f f e r e n t  can be  flows  for tracer  consistency of  loss  times  f l o w s , show a c o n s i s t e n t t i m e  seen  from  Table  at a l l s t a t i o n s i n long but  with  the 4,  of a  dye-dilution apparently  distribution  of  the  TABLE IVA SUMMARY OF TRACER Test Identification  Date  r  Aug.15,67 Aug. 1 5 , 6 . 7 Aug.15,67 Aug.15,67 Aug.17,67  BrRl,2UP-2X-3 BrRl,2UP-2-3X BrR2,lUP-IX-2 BrR2,lUP-l-2X B r R 3 , 2UP-2X BrR4,lUP-lX-2-3 BrR4,1UP-1-2X-3 B r R 4 ,1UP-1-2-3X BrR5,2UP-2X B r R 6 ,1UP-1X B r R 7 ,1UP-IX BrR8,2-2DOX BrR9,lUP-lD0X  No. o f T " • P o i n t s .J\  1  Aug.17,67 Aug.17,67 Aug.17,67 Aug.17,67 Aug.17,67 Sept.15,67 Sept.15,67 Sept.24,67  MEASUREMENTS: Peak (min)  Mean Lag (mm)  BROCKTON CREEK Discharge / 3 -l\ m  forf  a  2. 61 0 .00564 3 7 . 6,'- 0 . 0 0 7 7 0 2. 28 ' "0 . 0 0 8 5 6 0 .0100 3 2 . 4\ 0 .00336  17 28 16 16  0.4 14. 0 0. 5 17. 5  1. 5 33- 0 1. 5 27. 0  19 18 13  1. 0 25. 0 52. 0  2. 2 '39. 5 74. 0  3 . 43 47. 9 82. 1  0 0 0 0  15 15 13 32  1. 0 4. 2 1. 0 4. 0  2. 2 9. 0 5. 0 19. 0  2. 99 14. 50 8. 71 39. 9  0 .00706 0,00067 0 .000703 0 .000154  . 00504 .00617 .00738 . 0108  extension + .' +  Method RhWT RhWT RhWT RhWT RhWT r 0. T j-.  +  RhWT RhWT RhWT RhWT P T 0 .I .  RhWT RhWT RhWT RhWT  1 The t e s t i d e n t i f i c a t i o n code i s as f o l l o w s : t h e f i r s t two l e t t e r s i d e n t i f y t h e s t r e a m ( B r = B r o c k t o n , P l = P l a c i d , B l = B l a n e y , P h = P h y l l i s ) , t h e n comes t h e t e s t r u n number ( R 1 , R 2 , . . . i n a more o r l e s s h i s t o r i c a l s e q u e n c e , n e x t i s t h e l o c a t i o n (gauge number) o f i n j e c t i o n s ; (UP o r DO meaning s h o r t l y u p s t r e a m o f ... o r s h o r t l y downstream from . . . ) , f i n a l l y t h e sample l o c a t i o n s (gauge n u m b e r s ) , w i t h an X i n d i c a t i n g t h e p a r t i c u l a r time c o n c e n t r a t i o n c u r v e one i s d e a l i n g w i t h . E x a m p l e s : P h R 5 , 2 U P - 2 X i s a s i m p l e d i s c h a r g e d e t e r m i n a t i o n a t Gauge #2 on P h y l l i s C r e e k , w i t h i n j e c t i o n s h o r t l y above Gauge #2 and s a m p l i n g a t t h e gauge. B 1 R 1 0 1-3-5X w o u l d i n d i c a t e t h a t t h e t e s t r u n #10 on B l a n e y Creek c o v e r s two reaches ' 1 - 3 , and 3 - 5 ' ) . 2 C . I . means  "constant  rate injection  test."  TABLE I V A  (Cont'd.)  SUMMARY OF TRACER MEASUREMENTS: Test Identification!  Date  No. o f "T" "'• Points', . ^ ^ 3  y  T n l n  BROCKTON CREEK  Peak Mean Discharge + Lag Lag (m s ) ^ (min) (min) extension :  3  - 1  f  o  r  Method'  BrR10,l-2X  Aug.18,68  18  70.  117,  160.  0 .00124  +  RhWT  BrRll,2-3X.  Aug.18,6 8  16  53.  97.  120 .  0 .00126  +  RhWT  BrR12,lUP.-IDOX  Aug.18,68  9  BrR13,2UP-2Dp"X  Aug.18,68  BrRl4,1-IDOX BrR15,2U,P-2X  ,  2. 5  0 .00122  RhWT  9  0 .00114  RhWT  Aug.26,68  9  0 .00453  RhWT  Aug.26,68  9.  0 .00555  RhWT RhWT  5. 7  8 . 50  BrRl6,l-2X  Sept.14,68  13  4. 9  8. 1  9 . 08  0 .0648  BrR17 , 2 - 3 X  Sept.14,68  12  3. 0  7. 2  8 . 50  0 .0556  BrRl8,l-2X-3  Sept.14,68  19.  7. 2  11. 6  12. 6  0 .0550 9  RhWT RhWT  BrRl8,l-2-3X  Sept.14,68  13  14. 5  20. 0  BrR19 l-2X  Sept.14,68  10  2. 5  5. 0  5 . 40  0 .175  RhWT  BrR20,2-3X  Sept.22,68  13.  2. 2  4. 7  5. 39  0 .0889  RhWT  BrR21,l-2X  Sept.22,68  11  4. 2  7. 3  8 . 33  0 . 102  BrR22,2-3X  Sept.22,68  12  1. 8  4. 0  4. 53  0 .109  BrR23,l-2X  Sept.22,68  11  3. 2  5. 5  6. 97  0 . 152  3  21. 2  + +  +  RhWT  RhWT RhWT  +  RhWT  0 —3  s  TABLE IVB SUMMARY OF TRACER MEASUREMENTS: Test Identification P1R1,2UP-2X  Date  No. o f Points  . June 3 , 6 8  18  PLACID CREEK  T Peak Mean Discharge + (min) Lag Lag , 3 -1\ for/ ' < (min) (min) extension  m ;  s  -  1. 8--  3. 5  4. 57  0. 0 6 8 7  P1R2,1-2X  June  3,68  14  P1R4,3UP-3X  June  9,68  17  P1R5 2-3X  June  9,68  17  P1R6,4-4DOX  June  9,68  46  4. 5  9. 3  14. 8  0. 0 4 0 8  P1R7,2UP-2X  June  9,68  16  5. 8  11. 0  13. 8  0. 0 1 1 7  P1R9,2UP-2X  June  18,68  18  1. 9  4. 8  P1R10,2-3X  June : 2 Y y 6 8  17  62. 0  94.  P1R11,3-3DOX  June  27,68  18  11. 0  20 .  P1R11,3-3DO-4X  June  27,68  6  211.  261.  P1R12,4UP-4X  June -27/68  27  119.  170.  206.  0. 185  P1R13,1-2X  June  28,68  17  165.  208.  281.  0. 045  PlRl4,2UP-2X  June  28,67  18  24. 0  28. 3  29. 7  PlRl6,4-4DOZ  Aug. 2 0 , 6 8  40  8. 8  11. 6  2  P1R17,3-4X  Aug. 2 0 - 1 , 6 8  3  Below c o n f l u e n c e  122. 3. 2 160.  674.  164. 6. 4 236.  210. 7- 8 351.  8 . 29 121.  RhWT  0. 064  +  RhWT  0. 0 1 8 3  +  .RhWT  0. 018  +  RhWT NaCl  +  0. 0 0 3 5 8 0. 085  26. 9  RhWT RhWT  +  0. 144^  RhWT RhWT  9  100. 0 1200.  Method  RhWT RhWT +  RhWT  0. 0 4 1 8  RhWT  0. 035  NaCl  0. 020  NaCl  o f Gauge 3 .  OA 00  TABLE IVB  (Cont'd.)  SUMMARY OP TRACER MEASUREMENTS: Test Identification  Date  No. o f Points  T.T Peak (min) L a g (min)  Mean Lag (min)  Discharge , 3 -1\  11. 5  12. 5  0. 0824  RhWT  71.  83. 3  0. 157  NaCl  s  8.  PLACID CREEK + forf extensions 1  Method  P1R17A,2UP-2X  Aug.28,68  9  PlRl8,2-3X-4  Aug.28,68  60  48.  PlRl8,2-3-4X  Aug.28,68  68  236.  294.  339.  0. 245  +  •NaCl  P1R19,3-4X  Aug.28,68  36  162.  199.  239.  0 .2 6 8  +  NaCl  P1R20,4-4D0  Aug.28,68  13  P1R21,3-4X  Aug.30,68  39  P1R22,4UP-D0X  Sept.21,68  12  8. 5  P1R23,2UP-2X  Sept.21,68  12  4. 0  PlR24,2-3X-4  Oct.12,68  73  PlR24,2-3-4X  Oct.12,68  52  205.  274.  P1R25 1-2X  Oct.12,68  92  115.  159.  P1R26,2UP-2X  Oct.12,68  12  4. 2  7. 3  P1R27,2-3X-4  Oct.22,68  80  36. 1  54. 8  PlR27,2-3-4X  Oct.22,68  38  157.  224.  271.  0. 5 6 0  +  NaCl  P1R28,1-2X  Oct.22,68  75  94.  130.  144.  0. 122  +  NaCl  P1R28A,2UP-2X  Oct.22,68  11  3. 2  5. 7  7 . 02  0. 122  RhWT  P1R29,4UP-4DOX  Oct.22,68  12  3. 0  6. 0  7 . 45  0. 474  RhWT  3  1. 15 302.  47. 5  3. 8 386. 14. 5 8. 0 74.  4. 82 482.  0 .249  NaCl  0 .097  RhWT  19. 2  0. 122  9. 4  0. 0 3 6 3  +  RhWT RhWT  0. 142  +  NaCl  346.  0. 3 6 8  +  NaCl  181.  0. 0 8 2 2  +  NaCl  92. 1  8 . 68 62. 1  0. 0 8 2 2  RhWT  0. 212  NaCl  TABLE IVC SUMMARY OP TRACER MEASUREMENTS: Test Identification  Date  No. o f ~Jis-' P o i n t s (min)  Peak Lag (min)  Mean  BLANEY  Discharge  (mV ) 1  &  (min)  CREEK + for r extension  Method  B 1 R 1 , 1 - 2 X  Mayl5,67  0  .190  SoD •CI.  B1R1,1-3X  May 1 5 , 6 7  0  . 260  SoD C.I..  B 1 R 2 , 1 - 2 X  May  0  .159  SoD .C.I.  B1R3,4UP-4DOX  May 1 9 , 6 7  0  . 123  SoD ,.C_,I.  B1R4,4UP-4DOX  May 1 9 , 6 7  0  .168  SoD C.I.  B 1 R 5 , 1 - 2 X  June 9 , 6 7  0 .064  BIR6,4UP-4DOX  June 9 , 6 7  10  B 1 R 7 , 1 - 2 X  June 9 , 6 7  11  B1R7A,5UP-5X  Sept.30,67  18  2.  B1R8,3-5X  Oct.6,67  14  8. 5  BIR9 ,4UP-4DO:X  Nov.19,67  B1R10,3-5X-4  Nov.19,67  22  12.  B1R10,3-5-4X  Nov. 1 9 , 6 . 7  14  BlRll,l-3X-5  Nov.19,67  BlRll,l-3-5X  Nov.19,67  18,67 .  9  4. 17.  0.  2  9.  0  10.  5  27.  0  36.  8  9  5. 5 16. 1.  2  82  5  0  .054  0  .060  +  RhWT  2  0  .0317  21.  2  0  .873  19  0  .595  RhWT RhWT  2.  26. 3  0  .538  58.  77. 5  89. 4  0  .588  15  30.  44. 5  54. 7  11  51.  67. 5  77.  20.  RhWT  12.  5  0  RhWT •C.I.  2  RhWT +  RhWT  +  RhWT  0 .517  +  RhWT  0 .5 2 0  +  RhWT  TABLE IVC  (Cont'd.)  SUMMARY OF TRACER MEASUREMENTS: BLANEY Test Identification  Date  No. o f Points  :T: : Peak (min) L a g (min) j  s  CREEK  Mean Discharge Lag , 3 -1\ (min)  + for F extension  Method  BlR12,l-3X-5-4  Dec.26,67  15  17.  23. 5  27. 5  1. 76  +  RhWT  BlR12,l-3-5X-4  Dec.26,67  19  28.  37. 5  43- 2  1. 86  +  RhWT  BlR12,l-3-5-4X  Dec.26,67  53.  67. 7  74. 0  2. 06  +  RhWT  B1R13,3-5X-4  Jan.20,68  9 18  3. 3  5. 6  7. 1  +  RhWT  BlR13,3-5-4X  Jan.20,68  12  14. 5  19. 5  21. 6  B1R14,3-5X  Jan.20,68  14  3. 2 • 5. 5.  BlR15,l-3X-5  Jan.20,68  13  7. 5  BlR15,l-3-5X  Jan.20,68  18  11. 5  BlRl6,l-3X-5  Feb.3,68  16  BlRl6,l-3-5X  Feb.3,68  B1R17,1-3X  6  10.  4  12. 0  RhWT  6. 24 11. 7  RhWT RhWT  12. 1 0  11.  8  18. 6  11.  8  19. 5  16. 5 26. 4  23  31. 5  40. 2  Feb.3,68  39  18.  25. 5  47. 8 29. 6  B1R18,3-5X  M a r c h 5,68  25  6. 2  B1R19,l-3X-5-4  March 5,68  16  15. 0  BlR19,l-3-5X-4  March 5,6 8  16  BlR19,l-3-5-4x  M a r c h 5,68  B1R20,3-5X  3  10.  30. 2  +  RhWT  1. 64 1.  66  RhWT  +  RhWT NaCl  1. 64  22. 4  0.  862  RhWT  22. 5  25. 4  1.  95  RhWT  26. 0  33. 7  38. 0  2. 0 0  RhWT  13  50. 0  61. 5  68. 3  2. 33  +  RhWT  March 20,68  62  10..  0  18. 2  24. 8  5. 34  +  NaCl  B1R21,5-4X  M a r c h 31,68  77  38. 5  51. 4  56. 6  0.  804  B1R22,3-5X  May  17  20. 0  36. 0  45. 5  0.  162  25,68  NaCl +  RhWT  TABLE IVC ( C o n t ' d . ) SUMMARY OP TRACER MEASUREMENTS: BLANEY CREEK Test Identification  Date  No. o f Points  .'i'- l Peak (min) L a g (min) s  Mean Lag (min)  Discharge , 3 -1\  + for/ extension  3. 70  0. 131  RhWT  7  Method  B1R22A,4UP-4DOX May  27,68  18  1.2  2. 0  B1R23,5-4X  May  27,68  '.. 9  98CV0  137. 0  165.  0. 130  RhWT  B1R24,1-3X  May  27,68  7  71.0  101. 0  123.  0. 120  RhWT  B1R25,3-5X  June 3,68  18  9.5  16. 6  20. 8  0. 682  RhWT  B1R26,3-5X  June 6,68  17  16. 0  26. 0  34. 2  0. 262  RhWT  B1R27,4-4D©X  June 6,68  18  0. 264  RhWT  B1R28,5-4X  June 6,68  67  56. 0  81. 0  93. 9  0. 280  NaCl  BlR29,3-5X-4  June 13, 68  45  21. 2  38. 5  50. 5  0 .140  NaCl  B1R29,3-5-4X  June 13,68  84 115.  202. 1  0. 140  NaCl  B1R30,4UP-4X  June 13,68  18  4.5  9. 6  0. 139  RhWT  B1R31,1-3X  June 13,68  18  57-0  90. 0  117. 0  B1R32,3-5X  June 18,68  56  27.5  53.  0  71. 4  0 .0903  B1R33,3-5X  June 18,68  18  29.0  54. 5  71. 4  0. 083  +  RhWT  B1R34,3-5X  Sept.21,68  12  8.9  15. 0  19. 5  0 .748  +  RhWT  B1R35,1-3X  Oct.1,68  69  40. 5  61. 0  71. 2  0 .285  B1R36 1-3X  Oct.12,68  16  24. 0  34. 0  40. 4  0. 741  BlR37,3-5X-4 •  Oct.13,68  31  7.5  12. 7  15. 5  1. 3 5  BlR37,3-5-4x  Oct.13,68  41  36. 0  45. 4  51. 4  1. 30  3  172.  11. 41  0. 146  +  RhWT NaCl  NaCl +  RhWT NaCl  +  NaCl  TABLE IVD SUMMARY OF TRACER MEASUREMENTS: Test Identification  Date  No. o f Points  3^ (mm)  Peak Lagi . \ (mm)  Mean Lag i • \ (mm)  PHYLLIS CREEK Discharge + , 3„-l\ forP (m s ; ) . . .> extension  Method  PhRl,1-1D0X  June 22,67  PhR3,2-3X-4  July  21,67  22  25. 0  38. 0  •43. 5  0. 7 4 8  +  SoDi C T RhWT  PhR3,2-3-4X  July  21,67  30  56.  75.  83. 1  0. 817  +  RhWT  PhR4,l-2X  July  27,67  18  38. 5  56.  69. 92  0. 369  +  RhWT  PhR5,3-4X-6  July  28,67  14  32. 0  45.  52. 9  0. 339  +  RhWT  PhR5,3-4-6x  July  28,67  21  52. 0  73.  82. 3  0. 385  +  RhWT  PhR6,2-3X-4  July  28,67  18  37. 5  57.  64.  4  0. 352  +  RhWT  PhR6,2-3-4x  July  28,67  12  77. 0  104.  118. 1  0. 338  +  RhWT  PhR7,1-2X  July  29,67  15  43. 5  61. 0  76. 0  0. 312  +  RhWT  PhR8,4-6X  July  29,67  17  15. 0  26.  31. 5  0. 366  +  RhWT  PhR9,4UP-4DOX  Aug.  8,67  PhRlO,2-3X-4-6  Aug. 8,67  PhR10,2-3-4X-6  1. 980  0. 232  RhWT P  L .  T ±.  19  43. 0  70.  87. 6  0. 228  +  RhWT  Aug. 8,67  14  96. 0  134.  152. 3  0. 239  +  RhWT  PhR10,2-3-4-6x  Aug. 8,67  12  169.  187.  0. 240  +  RhWT  PhRll,l-2X-3  May  17,68  17  21. 25  28. 5  36. 2  1. 47  +  RhWT  PhRll,l-2-3X  May  17,68  11  40. 0  58. 0  64.  2  1. 59  +  RhWT  PhR12,4-6X  May  19,68  14  5. 1  8. 4  PhR13,3-4x  May  19,68  16  11. 5  16. 8  127.  9. 54 18. 8  2. 37  RhWT  2. 49  RhWT  TABLE IVD  (Cont'd.)  SUMMARY OP TRACER MEASUREMENTS: PHYLLIS CREEK Test Identification  Date  No. o f Points  rip, ,.  -s(min)  Peak Lag (min)  Mean Lag (min)  Dis.charg je  15.  21.  23.4  2.55  +  RhWT  16. 5  22. 5  27.8  2 . 40  +  RhWT  Jl  (m s 3  - 1  )  + for r extension  Method  PhRl4,2-3X  May  19,68  12  PhR15,1-2X  May  19,68  16  PhRl6,l-2X  May  17,68  37  19.  28. 5  36.7  1 . 40  NaCl  PhR17,2-3X  May  19,68  32  14. 25  21. 2 . 24.2  2 . 42  NaCl  PhRl8,4-6X  May  24,68  13  8.00  12.8  14.4  1.10  RhWT  PhR19,3-4X  May  24,68  15  26.5  29.9  1.07  RhWT  PhR20,2UP-2X-3  May  30,68  16  0.945  RhWT  PhR20,2UP-2-3X  May  30,68  16  25.  38.5  49.8  0.985  PhR21,l-2X  May  30,68  18  24.  33.  39.8  1.05  RhWT  PhR22,l-2X  May  30,68  70  22.5  33.  38.8  1 . 02  NaCl  PhR23,2-3X  June  1,68  13  17.  24.  26.8  1.88  RhWT  PhR24,2-3X  June  22,68'  15  23.5  35.5  42.1  0.955  +  RhWT  PhR25,l-2X  June  22,68  17  23.  35.4  46.4  0 . 826  +  RhWT  PhR26  July  3,68  18  20. 0  31. 2  35.5  1.19  +  RhWT  PhR27,3-4X-6  July  3,68  35  17.  24.5  28.5  1 , 26  PhR27,3-4-6X  July  3,68  66  26.  38.5  44.8  1.25  PhR28,3-4X-6  Sept .17,68  28  10. 3  14.5  17.33  3.10  PhR28,3-4-6X  Sept .17,68  64  15. 0  21.8  24.9  3.10  ,2-3X  1  19. 2.6  5.0  6.31  +  RhWT  NaCl ^NaCl +  NaCl NaCl  -<1 4="  TABLE IVD  (Cont'd.)  SUMMARY OF TRACER MEASUREMENTS: PHYLLIS CREEK Test Identification  Date  No. o f Points  T£. • (min) 8.5?  PhR29,3-4X-6  Oct.17,68  31  PhR29,3-4-6x  Oct.17,68  31  PhR30,1-2X-3  Oct.17,68  PhR30,1-2-3X  Oct.17,68  r  Peak Lag (min)  Mean Lag (min)  D i s charge  (mV ) 1  + for r extension  Method  13.5  15.4  3.69  14.5  20.4  23.2  3.72  35  14.5  20.  25.1  3.48  NaCl  36  27.  37.2  44.5  3.61  NaCl  NaCl +  NaCl  —3 ui  76  tracer.  The r e l a t i v e  salt  d i l u t i o n method a l s o  agrees  t h e dye d i l u t i o n method on t h e few. o c c a s i o n s when  with  simultaneous  R 1 2 ; Ph R21-Ph R 2 2 ; B l R l 6 -  t e s t s were run,. (Ph R l l - P h  B l R 1 7 ; B l R 3 2 - B l R33)• Absolute ticularly  i s gauged by t h e Water S u r v e y  t h e Water S u r v e y  mean t r a c e r  methods c a n n o t The  or  Is  travel  -  1  times  o f o v e r one h o u r ,  indicated  tracer  -  1  Creeks  c o n c e i v a b l y observe low f l o w s .  lowest v e l o c i t y , The  of less  Run 9,  varies  from stream t o  travel  times  on a l l f o u r ,  so t h a t one  of several  on B r o c k t o n C r e e k  days  gives the  3 - 5 mmsT . 1  i s reasonably well  o f the four streams, Blaney  a stream  ,  than 1 f t throughout;  go d r y r e g u l a r l y  tracer  h i g h flow range  15 on. B l a n e y  1  adjustment  The low f l o w s a r e r e a s o n a b l y w e l l d e f i n e d  at extremely  -  .  b u t B r o c k t o n and P l a c i d  at  a discharge of  The c u r r e n t m e t e r measurement was  s e c t i o n with depth  75 I s  loss  Coverage o f the d i s c h a r g e range  two  the t r a c e r  , t h e dye d i l u t i o n method, Run 3 3 , gave 9 6 . 8 I s  made a t a p o o r  could  5 of Blaney  o f Canada m e a s u r e d d i s c h a r g e a t Gauge 1 .  83 I s ^ w i t h t h e c u s t o m a r y  stream.  During  be e x p e c t e d t o g i v e v e r y r e l i a b l e d i s c h a r g e s .  (L = 0 . 2 % p e r m i n u t e ) .  it  o f Canada.  d i l u t i o n method, Run 3 2 , i n d i c a t e d  salt  90.3  none o f t h e f o u r  B l R 3 2 and B l R 3 3 o v e r t h e r e a c h 3 -  the t e s t s  With  to estimate, par-  w i t h r e g a r d t o d i s c h a r g e , because  testestreams  Creek,  accuracy i s m o r e . d i f f i c u l t  Creek  and B r o c k t o n .  coincide with the largest  guage i n t h e n e i g h b o u r i n g v a l l e y ,  defined  on o n l y  Runs 1 3 , observed  l4,and  flow  f o r which t h e r e  77  are  3 years of records.  this  flow.  pletely  The  S e v e r a l m a j o r l o g jams were moved a t  control  submerged.  structure 19  Run  (Photograph  on B r o c k t o n C r e e k  t h e r u n o f f ' peak d u r i n g a v e r y s e v e r e r a i n and  Placid  extends  to approximately  occurred 4.3  Creeks,- t h e d i s c h a r g e r a n g e  d u r i n g the l a s t  Surge The  water  15  because  result  not  example.  consists  The  t v s . Q.  linear  have  This  showing  stream.  and  defined stage as  does,  t h e gauge r a t i n g  i n the s m a l l d i s c h a r g e range  t vs. H however,  curves encoun-  one  surge  test.  o f 22  surge  t e s t s were made; 7 on P h y l l i s  and B r o c k t o n C r e e k s , a n d  to e i t h e r  of a graph  the data are p l o t t e d  c o n c l u s i o n s , because  d u r i n g any  lack  of f i e l d  the tube  gauges.  complete  range  Lake was  submerged and  (Photograph  tests  curves are w e l l  3 on P l a c i d .  o r 2 gauges a r e m i s s i n g i n a p p r o x i m a t e l y  due  Phyllis  of the t r a c e r  h i g h accuracy of time  For convenience  the  A total  1  test  t h a n t h e more s i g n i f i c a n t  6 on B l a n e y  On  at  3 years.  of the i n h e r e n t l y  are p r a c t i c a l l y tered  observed  storm.  f o r a l l t h e gauges on one  is.a typical  affect  com-  20% o f t h e h i g h e s t f l o w s t h a t  of a surge  v s . time  measurements. rather  was  was  Tests  levels  Figure  12)  Only  The  control  inoperative  50% o f t h e  or d i f f i c u l t i e s  the B r o c k t o n Creek  of flows.  12).  assistants  Data  tests  structure  cover on  Creek,  from tests, with the  Blaney  d u r i n g the h i g h e s t flows :  Gauge I  Gauge 3 15.26  Gauge 4 4.80  1400  SURGE  TEST  OF  OCTOBER 13,1968  ON BLANEY  CREEK Fig. 15  TABLE VA SUMMARY OP SURGE TESTS, BROCKTON CREEK Date  E l e m e n t Used to Determine Lag  Q at  1)  G. 1  (mV  1  AQi  2  )  Start sharp start  o f UP ' peak o f DS  .0094 . 0107 .0101  -'+.0013  Start Start  of of  UP DS  . 0027 . 0040  +.0015 -.0006  Start Start  of of  UP DS  . 00675 . 0070  Start  of  UP  Aug. 2 6 , 6 8  Start Start  of of  Sept . 1 4 , 6 8  Start Start  Sept . 2 2 , 6 8  Start Start  Aug. 15,67  Aug. 1 7 , 6 7  3  )  t L )  -.0015  Lag 1-2 (min  Q at  6.25 5.50 5.00  .010 .011 . 011  AQ  G. 2  2  Lag 2-3  Q at (m s 3  (m s 3  _ 1  ) .0010 — .0012  AQ  G.3 _ 1  3  )  6. 5. 5.  .0084 .0086 . 0091  + . 0002  8. 5 9. 0  .0036 .0042  - + .0008  - .0012  11. 0 13.0  .0035 .0045  + .0011  +.00055 -.00145  7.8 8.2  .0066 .0070  + .00045  . 0068  -+.0008  8.2  .0072  + . 00095  7..0 . : < . 0 0 6 2  UP DS  .0043  -.0012  11.5 1.0  .0057 .0068  - .0011  - .0013  5. 8 7. 2  .0056  + . 00105 — .00085  of of  UP DS  . 047 . 052  +.0050 -.0130  4.2 4.5  .038 .045  + .0055  3. 2 3. 0  .041 .044  • +. 0 0 2 5  of of  UP DS  .082 .086  + .009  3.0 3.0  .084 .088  •4- .008  3. 0 2. 8  .081 .085  1) Q i s t h e f l o w i m m e d i a t e l y p r i o r t o t h e t e s t . 2) A Q i s t h e change i n f l o w as o b s e r v e d a t a p a r t i c u l a r 3) UP = U p - s u r g e ; DS = Down-surge.  - .0008  - .0006  - .0011  — .014  gauge.  - .014  + .00075  - .0080 . 0040  - .0045  TABLE VB SUMMARY OF SURGE TESTS, PLACID CREEK Date  June 2 8 , 1968  Aug.28, 1968  Aug.30, 1968  Element Used t o Determine Lag S t a r t of UP • UP MidS t a r t of DS DS MidS t a r t of UP-. MidUP S t a r t of DS MidDS  Lag  Q  (min)  (mV )  1-2  at G. 2  AQ  2  Lag 2-3  (min)  1  Q  A Q  at  3  G.3  (mV ) 1  92. 110.  . 042  +. 0.0 4  56. 56.  .065  + .004  113. 96.  .044  -.004  56. 49.  .067  -.004  .082  + .005  .086  -.006  40. 43.  .156  -.010  . 042  + .007  51. 57.  .058  + .004  .048  -.007  49. 56.  .061  -.008  69.5 77.5  S t a r t of UP-. 89. UP , 1 0 4 . MidS t a r t of DS 89. DS 106. Mid-  at  Lag  Q  (min)  (mV )  3-4  142. 142.  A Q  4  G.4  1  .109  -.006  co o  TABLE VC SUMMARY OF SURGE TESTS, BLANEY CREEK ,  n u  a  z  E l e m e n t Used t o Determine  e  L  a  ^  Q at G.l  A Q-, 1  (mV ) 1  Lag 1-3 (  m  l  n  Q at G.3 )  AQ.-,  Lag Q a t 3-5 G.5 (min)  (mV ) 1  ( m  AQ,-  Lag 5-4  3 -l (min) s  )  Q at G.4  A Qu  ^  l  -  .  3-4 May 19, 1967  Mid Start  UP-; •' o f UP '  Mid Start  DS o f DS .  a  1 1 8 + . 052 042  162  45. 37-5  .119  47. 38.  .158  + —  .047 1 6 . 5 15.  66.5  .038 1 7 . 12.  70. 52. 5-4 72. 72.  r—  UP-"  —.  040  066  + .  019  555  + .  015  —.  130  t1  +  .019 2 3 . 21.  .055  5 0 5 + . 0 20  31.5 24.5  .495  +  .020  9.  .435  + .  020 19. 21.  2. 100 — . 140  13.5 9.5  2 .180  — . 140  7. 8.  2.120  —.  120  160  13. 10 .  2 .180  +  .120  6. 5.  2.080  + .  120  1. 370 — , 180  18.5 13;  1 .090  —  .140  7. 8.  1.180  —.  130 21. 5 1. 170 20.  UP- ' 1-.240 + . 200 o f UP . M i d UP., ( is m a l l ) 1. 240 + . 020 S t a r t o f UP "  18.5 12.  .970  +  .180  7. 7.  1,050  +.  180 2 1 . 22.  1. 0 5 0  + .  170  19.5 16.  • 990  +  .030  9. 5 1.120 8.  + .  020 14.5 1. 0 6 0 18,  + .  030  —.  020 15. 1. 090 15.5  —.  030  + .  2'10  o f UP  Nov.19, 1967  Mid Start  UP o f Up  March 1968  Mid Start  DS o f DS  Mid Start  o f UP-  063 #  UP,' ' 2. 100  Mid Start  of  DS DS  + .  Mid Start Nov.30, 1968  016  165  .061  Mid Start  Oct.13, 1968  045  59. 49.  June 9, 1967  5,  018  123  62.  Mid D S ( s m a l l ) S t a r t o f DS  1. 260 — . 030  M i d UP ( l a r g e ) 1. 240 + . 210 S t a r t " o f UP ' -• 1  19.5 17.  1 .020  040  9. 5 1.140 7.  19 13...5  .980  240  8. 5 1.120 9-  210 16 .16  1 . 060  TABLE VD SUMMARY OF SURGE TESTS, PHYLLIS CREEK  Date  July 1967  28,  E l e m e n t Used Lag 1-2 to Determine (min) Lag Mid Start  of  Mid May 19, 1968  June 1, 1968  June 22, 1968  S e p t •17, 1968  Q at G.2  A Q  Lag 2-3  2  1  36. 29-  .338  DS  32.5  . 345  AQ  3  ( > (mV )  OmV )  UP-:' UP.  Q at G.3  1,1111  .+ .00  8  Oil  Start  of  DS  24. .  Mid Start  DS DS  16. 9.5  2. 340  —.  of  Mid Start  UP DS  17. 11.  2. 300  + . 050  Mid Start  DS DS  17. 11.  2.550  Mid Start  UP UP .  1-6. 5 12.  2.530  Mid Start  DS DS  25. 17.  .815  Mid Start  UP' UP  25. 17.  Mid Start  DS DS  16. 7.  Mid Start  UP UP  17. 10.  1  25. 22 .  .342  22.8  .350  Lag 3-4 (min)  A Q  Q at G.4  (.mV) 1  + .010 18.2 20 .  .340  - . 010 19.  .352  24.  a 4  Lag 4-6 (min)  + . 013  14.  Q at G.6  A  Q  6  mV ) 1  .370  + . 010  .377  + . 017  12. •  014 12.  22.  11. 2.380  - . 040  + .040 10.  2. 430  + . 060  -.070  8. 8.  2.570  - . 050  4. 5.  2.550  050  10.5>2. 500 9.  + .20  6. 25?  2. 540  + . 17  5. 6.  2.520  + . 150  - . 095  17.  -.090  14.  .345  - , 090  8. 7.5  . 880'  — . 105  .720  + . 10  16. 13.  14. 14.  .755  095  8. 6.5  • 775  + . 105  2.750  - . 33  11.5 2.770 13.5  + . 25  10. 2.450 + .27 10. 5  11. 2.450 11.5  -.040  10. 10 .  2.'440  + . 070  9. 11.  2.500  + . 20  040  14.  9.5 8. 8.  ..790  12. .700  + .10 -.27  00  TABLE VD  (Cont'd.)  SUMMARY OF SURGE TESTS, PHYLLIS CREEK Date  Nov.18, 1968  E l e m e n t Used Lag A Q at 1-2 to Determine G^ (min) Lag Mid Start Mid Start  Nov.29, 1968  DS DS UP . .. UP'  Mid Start  DS DS  M i d UP-.(small) S t a r t UP- ' (small) Mid Start M i d UP--. (large) S t a r t UP' (large)  DS DS  AQ ! d  Lag Q at 2-3 G.3 (min)(m3 -l)  3  s  1.8. 5 11.5  2 . 740  —.  18. 11.5  2 . 450  + . 16  19. 11.5  2 . 770  -.  21.  2 . 450  + . 030  32  35.5 25.5 8. 9.  3.200  1 1 . 5 2 . 820  2 . 480  20.  2 . 310  _  17  9.  12. 10. 5  ^  Lag Q at 4-6 G. 6 ( m i n ) ( m3 s - 1 )  2/-890  -.240  2.580  + .170  AQg  -.35  4 . 200  -.30  + .035  6.5  3 . 900  + .030  3 . 900  -.20  3 . 700  +.30  6. 2.850  -.13  10.  31  AQ,.  3-6 9.5 6.  14.  18. 5 10.512.5  Lag Q at G.4 3-4 (min) (m3s-l-0 2-4 36.5 25.5  26  17.  13.5  AQ  9.5 10.  2.720  + .28  5. 7.  or  LO  84  The  test  i n w h i c h the on  results  13).  observed  The  tube  data  shown i n T a b l e  as  particularly be  read  at  of  5 t o 10  of  10%  ing  i f they  are  second  minutes,  this  t o 20%.  The  The 5  3  surge  because  S  than  as  gauge  station  low  the to  to  accuracy, could  l a g s i n the  only order  immediate u n c e r t a i n t y  on t h e m i d - p o i n t s the  the m i d - p o i n t s  l e v e l - t i m e curve.  3.4.5  t h e gauges With  i n t r o d u c e s an  more r e l i a b l e  to discharges,  from  l a g s from  intervals.  l a g s based  p o i n t s because  constant  have r e l a t i v e l y  short  30 t o 60  substantially  the  stream.  (Section  to 5 D  consistent, insofar  change i n d i s c h a r g e r e m a i n s  station-  starting  curves  a p p e a r t o be  a test  i n T a b l e s . 5A  have b e e n c o n v e r t e d  rating  gauge a l o n g  are  summarized  gauge r e a d i n g s  the b a s i s o f the  Figure  are  o f the  l a g s based  on  were d e r i v e d by  surges the smooth-  85  5.  CHANNEL GEOMETRY AND  5.1  Similitude Considerations  STEADY FLOW EQUATIONS  f o r Steep,  Degrading  C h a n n e l Networks The as  c o n d i t i o n s under which r e a d i l y  defined  2.5,  i n Section  may  be  c h a n n e l network h y d r a u l i c s w i l l 5.1.1  be  available  adequate  information,  f o r e v a l u a t i o n of  discussed  here.  Assumptions Dynamic s i m i l i t u d e between r e l a t e d p h y s i c a l s y s t e m s  only  the  be  examined on  affecting possible  the  the  system.  basis  of a complete  Similarity  i f the major p r o c e s s e s  (Barr,  1968).  cesses  which  Obviously could  the  o f the  problem  forces  between c h a n n e l networks i s  of formation  are  similar  t h e r e a r e a l a r g e number o f  conceivably  mountainous b a s i n s ;  list  can  affect lies  the  pro-  c h a n n e l network  in identifying  the  of  dominant  ones . The towards  the  system t h a t able  formative present can  be  information.  indicating portion  that  of the  assumptions  are  the  processes  assumed h e r e may  problem i n the defined  sense t h a t  adequately  However, t h e  field  listed  i n and  and  they  with  the  data  supply  system i s reasonable  variation  be  and  biased describe  readily  avail-  evidence  explains  a major  between c h a n n e l n e t w o r k s .  discussed  below:;.  a  The  86  '(i) The d r a i n a g e tudinal The  s l o p e s j S y , a r e remnants  streams  form t h e i r  debris.-, w h i c h the  n e t w o r k o c c u p i e s , v a l l e y s whose  contains  channels  by d e g r a d i n g  sufficient  a channel  coarse  slope , S , s i g n i f i c a n t l y  I n o t h e r w o r d s , S i s imposed size  of the m a t e r i a l l i n i n g  of the channel-forming This  into  glacial  m a t e r i a l to prevent  that  a regime  tion,  until  respect  with  on t h e c h a n n e l the channel  slope.  i s one o f t h e r e s u l t s  o f t h e common r e g i m e - t y p e  to slope  and b e d m a t e r i a l , w h i c h  adjust  i t i s adequate  to handle  Most r i v e r s  The m a i n s u p p o r t  the upstream supply  fall  Figures  f o r the present  2 and 3 ) ,  role i n  l o a d , and v a l l e y  assumption  (ii)  The c o a r s e  lack of flood  plains,  is  adequate  the degraded  channels  f l o w s , which a r e t h e r e f o r e  f o r t h e channel, f o r m . to represent  these  close  o f the bed m a t e r i a l .  material lining  o n l y be moved a t extreme responsible  and s i z e  lies i n  o f t h e test- s t r e a m s  a b s e n c e o f b r a i d i n g o r m e a n d e r i n g , and t h e a p p a r e n t c o r r e l a t i o n between s l o p e  of  b e t w e e n t h e two e x t r e m e s  sediment  c o n s i s t e n t downstream s t e e p e n i n g valleys,  states  i t s s l o p e by e r o s i o n o r d e p o s i -  adjustment between water,  (hanging  S^.  network, but the  m e a n d e r i n g and b r a i d i n g p l a y i n g an i m p o r t a n t  reaching  from  opposite  canal w i l l  w a t e r and s e d i m e n t .  different  enough t o  process.  i s the very  assumption with  the  of the P l e i s t o c e n e p e r i o d .  s t r e a m f r o m r e a c h i n g b e d - r o c k o r from d e g r a d i n g  achieve  longi-  A single formative  solely  discharge high  value  flows.  can  87 This  assumption  ( 1 9 5 8 ) , who frequency  test  hydraulic  Day  reaches  bed m a t e r i a l channel. slides, with  study.  The  transport  a r e low  and  rockfalls,  i s well  s u p p o r t e d by  by  Stewart  g r a v e l and  lower  and  flood  assumption.  I t i s only  finer  than  the performance  to the  of the  field  channel and  the of the  through i n balance  channel.  o b s e r v a t i o n , but  conditions, (1967).  t h e n be  of h i g h e r v e l o c i t y  s u c h as t h e A sufficient  i n motion  to lower  thereby s t a r t i n g  - more bank and  bed  this  i t may event amount the  a chain  erosion  -  resistance.  o r bank e r o s i o n  mainly  performance  e t c . , i s low  significantly,  None o f t h e r e a c h e s bed  affect  LaMarche  sand may  channel r e s i s t a n c e reaction  channel  of material  bank e r o s i o n ,  down u n d e r extreme  of f i n e  not  capacity  f o r the  criteria.  rates  do  correlations  and  t o f l o w s i n t h e o r d e r o f t h e mean a n n u a l p e a k ,  assumption  described  Miller  as w i d t h , d e p t h  t h e o r y on  of coarse m a t e r i a l  the t r a n s p o r t i n g  break  The  the s i m i l i t u d e  Supply  Up  such  does n o t depend on t h i s  in stating (iii)  parameters  (1969) presents similar  of t h i s  developed here used  t h e work o f  f o u n d h i g h c o r r e l a t i o n between d i s c h a r g e s o f a g i v e n  and  velocity.  i s s u p p o r t e d by  except  showed much e v i d e n c e o f i n a few  isolated  active  locations,  a s s o c i a t e d w i t h damaged v e g e t a t i o n c o v e r o f t h e  banks due  to recent  ( i v ) The same f l o w r e g i m e ,  stream  logging.  channel forming process i s r e p e a t a b l e . I f the Q(t), i s diverted  down i d e n t i c a l  valleys,  88  containing  debris, o f i d e n t i c a l  of the r e s u l t i n g channels w i l l  gradation,, a l s o be  assumption i s w e l l  supported  situations,  where an i d e n t i c a l  supply  that  produces  The a p p l i c a t i o n o f t h i s  channel parameters  the  imposed  or independent  out  r e q u i r i n g a knowledge or roughness.  Conditions  gravity on  eliminates  a short,  c a n be d e r i v e d  from  the p o s s i b i l i t y  withs u c h as  of a large  process.  (Barr,  g acting  1967; B a r r  on t h e w a t e r  the v a l l e y slope,  t h e submerged g r a i n s  v i s c o s i t y , V.  s t r a i g h t channel reach,  forces,  1968):gravity  a c t i n g along  resultant  show  o f any d e p e n d e n t p a r a m e t e r s ,  This  the f o l l o w i n g  Herbertson,  5-3 w i l l  for Similarity  Considering identify  to the  e f f e c t s s u c h as Q ( t ) and S,  random e f f e c t i n t h e c h a n n e l f o r m i n g 5.1.2  identical  concept  s i t u a t i o n i s s p e c u l a t i v e , but Section  the s i g n i f i c a n t  width  i n regime-type  o f w a t e r and s e d i m e n t t o  a s t r a i g h t c h a n n e l segment e v e n t u a l l y  present  properties  identical.  This  channel dimensions.  t h e mean  ( ( p  -  s  i s imposed  m e a s u r e s ar'e W^,  p  w  ) / y  s  )  and (waves);  g'S; ; g r a v i t y g = g ,^  from upstream.  the water surface  g  one c a n  acting  and  Some o f t h e width a t flow  H e r b e r t s o n and B a r r l i k e , t o c o n s i d e r 4 g r a v i t a t i o n a l f o r c e s g, gS, as above and g as. t h e net. g r a v i t a t i o n a l f o r c e on t h e submerged g r a i n s as: i t a f f e c t s , t h e s u r r o u n d i n g g r a i n s , and g = ( ( p - $> )/rj> ) g as t h e n e t g r a v i t a t i o n a l f o r c e on t h e submerged g r a i n s as i t a f f e c t s t h e d i s p l a c e d , w a t e r . Since g c a n be computed f r o m g and g , i t need n o t be s p e c i f i e d . s  w  w  s  w  w  s  89  Q^;  A /W , a d e p t h D  charge  Q J . the. v e l o c i t y , v ^ ,  and  D  material in  measure based  D  lining  the  channel.  on  the. f l o w  D,. t h e  size  These, terms  d i m e n s i o n a l l y homogeneous f u n c t i o n a l  dimensions  of  i  f  <  p a r a m e t e r of. t h e  can be  forms  2/3  Q S  e.g.  2/3 0  1/3  .1/5  natively.  terms b e t w e e n v e r t i c a l 5.1  Note t h a t E q u a t i o n  of r a t i o s  dimensions  1  containing  n + 1  of a c t i v e  and  t are  bars  has  f o r c e s and  reduced  to 1  D  Of  only  the  experimental  set-up  the  g/g any It  s  , )? , and one  also  shows t h a t i n t h e p r e s e n t  resultant  can  be  reducing  groupings  the  posfor  a t hand;  (»g)  g are  form  f o l l o w i n g i s most s u i t a b l e  5/3 5-2  The  A functional  numerous n o n - d i m e n s i o n a l 5.1,  i t con-  actions.  form w i t h o u t  D  Equation  alter-  5 terms as  boundary  1/3 f (  used  d i m e n s i o n a l l y homogeneous v a r i a b l e s  with Equation  4  can be  only.  t o a n-term n o n - d i m e n s i o n a l  generality.  the  .5.1  D  i n which the  sible  . .  s  &  V  reduced  using  D  D  'D  sists  arranged  length  2/5 4  a r e a at. d i s -  1/3 vD  as W  Q  shows t h a t c o m p l e t e k i n e m a t i c  or v^  5.2  =  situation,  constant,, c o r r e l a t i o n s  measure s u c h  )  where  b e t w e e n Q , S , and D  s h o u l d be  similarity  complete  i s only  90  possible ing  i f the resultant  measures and \) v a r y w i t h  to the f o l l o w i n g p r o p o r t i o n a l i t i e s  accord-  ( B a r r and H e r b e r t s o n ,  1968),  A  4  D  v  «x  D  %  '  +  r-  2  -  5  3  2  S S i n c e i? I s n o t v a r i a b l e Q, t h e f i e l d ities,  In the f i e l d  and S i s i n d e p e n d e n t  of  d a t a do n o t have t o match t h e above p r o p o r t i o n a l -  but i t i s reasonable  t o expect  fairly  close corres-  pondence. Equation siderations o , V, p ,  2 c a n a l s o be d e r i v e d f r o m  (Yalim, 1966) . g, S, Q ,  s  D  There are 7 v a r i a b l e s dimensional for  form  a description The  ficant  system  processes.  affects  The  m e a s u r e , say D.  c o n t a i n i n g 3 dimensions  i n 4 terms,  such  as E q u a t i o n  so t h a t a n o n 5 - 2 i s adequate  o f the problem. d e s c r i b e d by E q u a t i o n In the f i e l d  formation of frequent  transport  con-  The b a s i c v a r i a b l e s a r e  and one r e s u l t a n t  the s m a l l e r streams  alluvial  dimensional  5.2 n e g l e c t s many  area of t h i s  study  signi-  vegetation  ( W < 15 m) c o n s i d e r a b l y t h r o u g h t h e D  l o g jams.  and may be a g g r a d i n g r a t e as a. v a r i a b l e ) ;  Some m i n o r r e a c h e s  (which others  t r a n s p o r t r a t e s and s e d i m e n t  a p p e a r t o be  would i n t r o d u c e the are- o c c a s i o n a l l y  supply  cn bed rock.  r a t e s a r e unknown.  91  5.2  ' Basic' E q u a t i o n s  5.2.1 T h e o r e t i c a l The  Uniform  Flow  Considerations  uniform  s u r f a c e width,W  T o r Steady,  f l o w parameters,'  , and f l o w  mean v e l o c i t y ,  v ,  area,A, o f a g i v e n s t r a i g h t  open  s channel  segment  (i)  are f u l l y  the Equation  d e f i n e d by t h r e e  equations:  o f C o n t i n u i t y w h i c h may be w r i t t e n  as ... 5.4  Q = v A (=• v'rW. d#) m • m sr * A  where d» = A/W (ii)  s  , and  a geometrical equation  linking  A and W  (e.g. s  W  g  <x VA" i n t h e c a s e (iii)  a flow  of a triangular  equation  linking  t h e p a r a m e t e r s v , A, W , and d f m s' * 5  independent will  5  of Equation  5.4.  depend on t h e b o u n d a r y  channel  w  relations  Q and one o r s e v e r a l o f i n a form  The c o n s t a n t s  which i s l i n e a r l y of this  and c r o s s s e c t i o n a l  of n a t u r a l "tumbling  between W  flow"  and A a r e v i r t u a l l y s  The  }  equation  shape o f t h e  segment. In the case  is  c h a n n e l ) and  channels, the  unobtainable  but t h i s  J  n o t a s e r i o u s drawback as l o n g as t h e a i m i s h y d r o l o g i c a l . main p a r a m e t e r s  channel  are then  storage per unit  r e l a t i o n becomes The relevant  flow  o n l y mean v e l o c i t y , v  l e n g t h , A, so t h a t t h e W  g  m ?  and vs. A  redundant. equation  possibilities  c a n t a k e many f o r m s .  are l i s t e d  Some o f t h e more  below, a l l assuming  broad  92  rectangular w i d t h W,  and  3  For rough  channels  flow governed  = depth  by  = hydraulic  friction  w i t h roughness  r a d i u s ) of  over a  hydraulically  r a t i o s between 7 and  130  1958) Q <x A  and  x  depth.^d.  boundary  (Ackers,  (d  5/3  (Manning's  r a t i o s between 1 . 5  f o r roughness  Equation)  and  11  7/4 Q cx A For  (Lacey's  Equation)  h o r i z o n t a l j f r i c t i o n l e s s c h a n n e l segments :  a step-like  drop  a t t h e downstream end,  Q -  A  controlled  an a p p r o x i m a t e  by  flow  equation i s  If  the c o n t r o l  3 / 2  is a triangular  w e i r w i t h apex on t h e  channel  floor Q <~ and  i n the case  A  of a p a r a b o l i c  Q If  the channel  5 / 2  A  weir  7 / 2  segment  i s o b s t r u c t e d ' b y a dam  with  outflow  below t h e w a t e r s u r f a c e Q Note t h a t Q °< A can a l s o  be  A since 1 / 2  w  stated  A = Q/v  , a r e l a t i o n of the m'  form . . . 5 . 5  ' as w  Q -x-v/-  1  ...  5.6  93  o r as  w-1  w  1  -  Q <* i n which W  s  T  5.7  #  refers to unit  i s usually  The  T  length.  In-natural  channels  r e l a t e d t o Q by an E q u a t i o n o f t h e f o r m W  observed exponents  z cover a range  o< Q , z  s  from 0 . 0 5 t o 0 . 5  1958), b u t t h e most common v a l u e s f a l l b e t w e e n 0 . 1 5  (Miller, to 0 . 2 5 .  e f f e c t i s i n c l u d e d , Q <x A  I f this  w  becomes  w Q « A  ... 5 . 8  z w + 1  C o n s i d e r i n g t u m b l i n g f l o w as a r a n d o m l y o f s h o r t c h a n n e l segments governed t h e ones l i s t e d times through  arranged  sequence  by f l o w e q u a t i o n s s i m i l a r t o  a b o v e , and' c o n s i d e r i n g  further that the t r a v e l  c h a n n e l segments i n s e r i e s  a r e a d d i t i v e , one c a n  e x p r e s s t h e r e l a t i o n between Q and T f o r l o n g  reaches  ( I > > W ) as  s Q  =  n  lim - ~  I,.-  n G [£ _A 0 i= i L  Y  T  ... 5 - 9  i ]  *+-  Wj_-1  The  c o n s t a n t s c. a n d t h e e x p o n e n t s 1  v a r i a b l e s w i t h unknown d i s t r i b u t i o n s . n o t be s o l v e d t o p r e d i c t 5.2.2  1  w. l  E q u a t i o n 5.9  ) a r e random can t h e r e f o r e  t h e form o f t h e Q = f ( T ) r e l a t i o n .  Flow E q u a t i o n s o f t h e Test With  y.(=  Reaches  t h e form o f t h e t u m b l i n g f l o w e q u a t i o n n o t b e i n g  p r e d i c t a b l e , a number o f p o s s i b i l i t i e s  w e r e t r i e d by p l o t t i n g  94  various  t r a n s f o r m a t i o n s , o f .the' Q - A d a t a  against  each o t h e r .  Pure, e x p o n e n t i a l s b  A = a  of s e v e r a l  of the  reaches  form  A  Q  A  5-10  ...  or =  ( — A  )  . . .5.10a  a  give  consistently  can be area and  slightly  at  improved  by  b a s e d on  test  linear  i n a few  cases  the f i t  a s s u m i n g a s m a l l remnant  Table  6 lists  the  reaches  of t h i s  study.  discharge.  f o r a l l 13  b^  are  zero  good f i t s , a l t h o u g h  flow  coefficients  r e g r e s s i o n s of l o g ^ A  on  The  a  A  coefficients  log-^Q of  the  form  l°g RSQ by  A  i s percentage  = log of the  1 0  degrees  of freedom.  listed  fitting  f o r the  1.  Q - v , m  Q = Av ,and m  data,  any  and  The  log  A  Figures  Q  of the standard  with  16  ... logarithms  high  collected 17  5.11  explained  e r r o r of estimate  fairly  and  number  by  Day  is  of  (1969)  show d a t a p o i n t s  and  reaches.  Q - T regressions.  of the  1 Q  program"L0GRE"was u s e d  since these  one  +j b  reaches  f o r 2 sample  A F o r t r a n IVG Q - A,  A  A d d i t i o n a l data  on T a b l e  lines  a  variance  the r e g r e s s i o n e q u a t i o n .  only meaningful  are  1 0  t o compute  Since v  = 1/T  the and  f a c t s were u s e d t o o b t a i n t h e r e g r e s s i o n  r e g r e s s i o n s i s adequate, t o e s t a b l i s h a l l  95  TABLE VI REGRESSION PARAMETERS OF STEADY FLOW  Degrees of Freedom  Reach Brockton Brockton  1-2 2-3  :  a  8  "'5  A  8104 • 7183  "h b  A  C o r r e l a - Approx. S t . E r r o r o f tlon . E s t i m a t e {%) Coefficient  .3376 . 2830.  0.98 0.99  12.5 4.0  Placid Placid Placid  1-2 2-3 3--4  <2 ••3 ::'4  1. 879 1. 930 3 . 943  .3403 .3065 .4656  0.96 0.95 0.99  3-2 6.2 5-3  Blaney Blaney Blaney  1-3 3-5 5-4  -.6  3 . 375 3 . 460 3 . 110  . 4784 .5339 .4389  0.99 0.99 0.98  7.8 9-0 8.9  262 202 021 199 207  • 5413 .4577 .4787 .4023 .3557  0.98 0.99 0.99 0.97 0.99  9.0 3-6 3.9 7-8 7.0  Phyllis Phyllis Phyllis Phyllis Phyllis  1-2 2-3 3-4 4-6 Lower  • 16 7 J .9 .7 "6  2  3. 3. 3. 3. 3.  96  TABLE V I I REGRESSION PARAMETERS  OP STEADY FLOW  ( f r o m Day, 1 9 6 9 )  Reach  Degrees o f :  Freedom  Furry  5  a  Gorrelation Coefficient  13 A  5.788  .5009  .95  Slesse  U  3  2.922  .5993  .99  S l e s se  M  4  4.179  .5213  .97  Slesse  L  4  2.926  .5765  3  3-377  .4075  .99  .4184  .99 .97  Juniper  1.0  Ewart  U  3  4.091  Ewart  L  4  3.253  .  .4365  Ashnola  U  3  3. 092  "  .5806  1.0  Ashnola .• M  3  4.638  .4647  1.0  L  3  •3.967  .4208  1.0  Ashnola  97  three  and  any  coefficients putational  significant from t h e i r  theoretical  errors.  With  ' T = a Q  '  T  d e v i a t i o n of the  regression  r e l a t i o n s i n d i c a t e s com-  ...  5.12  and b v = m  one  aQ  ...  v  v  obtains b v a  = - b„ T  v  b v  ...  T  = 1 - b. A _1 a A  "L0GRE"also computes two  sets  of Q - T  (T s  t i m e o f t r a c e r ) and  Q - Tp  using  one  a l l data,  has  and  5.14A  ...  ~&0~a~  av  dye  5.13  (Tp  using  been i n j e c t e d at  the  =  ...  5.14C  ...  5.14D  arrival  s  = peak t i m e ) r e g r e s s i o n s , only  5.14B  those t e s t s f o r which  upstream end-point  of the  one the  test  reach. The results and  above r e g r e s s i o n s  c o n s t i t u t e one  of the  main  of the  field  work, t h e r e f o r e  a l l the"L0GRE"printouts  p l o t s with  lists  of the  included  Inspection dix) there  of. t h e  shows t h a t , o v e r t h e a p p e a r t o be  no  data  plots  are  (Figures  1 6 and  range of d i s c h a r g e s  significant  i n the  deviations  Appendix.  1 7 , and covered  from  Appenhere,  Equation  98 1  1  1  r—  1  1  1  1—  :  1  1  1 1  —  y /*•  y  y  • • y •  .1 _ 1  ff>  fo  1  1.  '  e  ©  •s / -  .Ol  /  >  1 .1  /  J> y 4-  r\\  CM  E c 0 0) 0.001  < I  I  .0001  I  1 I  I  I  .001  0  •  mean  •  •  .01  .01  Discharge + mean  •  •  I  velocity  t  in m s-l 3  V  m  cross - sectional area , A  surge celerity observations, c  HYDRAULIC  MEASUREMENTS  BROCKTON  ON THE  GAUGE I - GAUGE  REACH  2 Fig.16  0.1  1.0 Discharge  in m  10.0 3  s-  1  4  mean velocity , V  ©  mean  cross - sectional area , A  •  surge  celerity  HYDRAULIC  m  observations  MEASUREMENTS  BLANEY  GAUGE  for mid - surge , c  ON THE  3 - GAUGE  REACH  5 Fig. 17  100  5.10. has  In particular,  the Q -  plots  of Blaney  Creek,which  t h e b e s t c o v e r a g e o f t h e d i s c h a r g e r a n g e , show no  towards  l i n e a r b a s i n response  f l o w s as o b s e r v e d by P i l g r i m absence o f f l o o d p l a i n s  (v  tendency  '.independent o f Q) a t h i g h  (1966).  With the almost  along the t e s t reaches  this  total i s not  surprising. 5.3  Determining the Parameters The b a s i c  of the Steady Flow E q u a t i o n  f l o w e q u a t i o n ( 5 . 1 0 ) c a n be r e - w r i t t e n i n  v a r i o u s n o n - d i m e n s i o n a l f o r m s ; one p o s s i b i l i t y , u s i n g  terms  to Equation 5.2 i s  similar  " •»* ^ V r '  ...  5.10b  or, i f the concept of a formative d i s c h a r g e i s r e t a i n e d b  f-  A  ( §—:)  ...  V'  D  Either version i s suitable basic similitude  5.10C  f o r comparison w i t h the  c r i t e r i o n , Equation 5-2.  The p a r a m e t e r s o f  t h e s t e a d y f l o w e q u a t i o n ( a ^ ' , A^, b^) c a n be c o n s i d e r e d " r e s u l t a n t measures" of the channel f o r m i n g p r o c e s s , s i m i l a r t o c h a n n e l width,W^, depth,and forms  of the s i m i l i t u d e Q  ,f  (  D  -S  '  5 / 3  ,  r o u g h n e s s , D.  criterion '  S ,  K  -|-  5.2  Two  possible  are t h e r e f o r e ,  b  )  = 0  ...  5.2a  101  1/3  f  which as  (  >  shows t h a t  possibility  Some  c a n be assumed  i n detail  by Q  constant.  i s obviously not a " r e a d i l y  D  0  =  A  ...  5 • 2b  and S,  D  Exploring  i s t h e main o b j e c t i v e  available"  o f Day  (1969).  here. parameter,  i n a r e g i o n w i t h r e a s o n a b l y homogeneous c l i m a t e t h e c o n -  tributing  drainage area o f a channel  instead.  As t h e r e i s v i r t u a l l y  physics  area  of a  A  segment, DA, c a n be u s e d  n o t h i n g known about t h e  e x p r e s s e d by E q u a t i o n 5 . 2 , m u l t i p l e  o f the process  regressions  and b  on t h e i n d e p e n d e n t  A  ( i n km ) , and s l o p e were t r i e d ,  ations  of transformed For  ing  a ' )  o f h i s f i n d i n g s w i l l be summarized b r i e f l y Q  but  ,  a ^ and b ^ s h o u l d be d e t e r m i n e d  a l l other v a r i a b l e s  this  > ' gf  s  the test  variables  including  drainage  various  combin-  data.  reaches  i n the mountainous  t h e lower F r a s e r V a l l e y  the following  areas  surround-  two e q u a t i o n s  give  best f i t  They e x p l a i n With  a  A  = 1.738 , D A  b  A  = 0.28:88  S  - ° -  range  0  a  DA *  6  o f freedom, both  w e l l b e y o n d t h e 1% l e v e l .  Ashnola  1  ... 5 . 1 5  "  0  0 7 5 6  ... 5 . 1 6  '  9 6 . 1 % and 6 9 . 7 % o f t h e v a r i a n c e i n t h e d a t a .  11 degrees  interior  0 : 2 9 2 2  equations  The' 6 t e s t  o f ' B . C. ( J u n i p e r ,Creek, River, Tables  are s i g n i f i c a n t  reaches  Ewart  Creek  i n the dry and t h e  3 and 7 ) do n o t c o v e r a wide  of the independent  variables  to justify  enough  a meaningful  102  relationship In drainage is  f o rthat region.  generally applicable relations  a r e a c a n o b v i o u s l y n o t t a k e t h e p l a c e o f Q^'.  If i t  t o be u s e d i n t h e a n a l y s i s , some c o r r e c t i o n f a c t o r f o r  regional variations to  f o r a ^ and b ^  be a d d e d .  i n the drainage  An a l t e r n a t i v e  t o such a f a c t o r i s t h e use o f a  c o n s i s t e n t d i s c h a r g e v a l u e , such flood.  a r e a - r u n o f f r e l a t i o n has  A further possibility  as t h e e s t i m a t e d mean  which  may p r o v e  annual  interesting i n  areas w i t h sparse h y d r o - m e t e o r o l o g i c a l r e c o r d s , i s t o use w i d t h , W , a s an i n d e p e n d e n t  variable.  D  g i v e good f i t t o r e g i o n a l l y and  drainage  The d a t a o f t h i s  c o n s t a n t r e l a t i o n s between w i d t h  area, and t h e s e r e l a t i o n s  by m e a s u r i n g  a few c h a n n e l w i d t h s  i n the region of i n t e r e s t .  study  are easily e s t a b l i s h e d  on s t r e a m s  Slope  of various  sizes  a p p e a r s t o h a v e no e f f e c t on  width. W i t h W^  and S as i n d e p e n d e n t  the data from a l l areas for  a ^ and b  variables  and i n c l u d i n g  one o b t a i n s t h e f o l l o w i n g  relations  A  0 ii 7 p a b  A  A  = 0.943 8 W = 0,2519  W  D  D  ^'  ...  :  0.1368 •  S  _ Or: 0,82 2 '  ...  5.17 5.18  They e x p l a i n &6% a n d 6 3% o f t h e d a t a v a r i a n c e a n d a r e :  statistically of  freedom.  significant  ;  a t t h e 1% l e v e l , h a v i n g  I t i s n o t s u r p r i s i n g t h a t w i d t h and s l o p e d e t e r -  m i n e b. t o a l e s s e r d e g r e e t h a n a A  18 d e g r e e s  A >  The f a c t o r a , w h i c h i s A  3  i d e n t i c a l t o the flow area at Q = 1 m s  -1  can. v a r y o v e r -a •.  103  l a r g e r a n g e and of  n e e d s t o be p r e d i c t e d c l o s e l y . 0.25  b^ i s l i m i t e d to approximately  The  range  < 0.65,  < b^  so t h a t  a c c u r a t e p r e d i c t i o n o f b ^ i s n o t e s s e n t i a l as l o n g as t h e of  a r e o f t h e o r d e r o f 1 m^  interest  d i c t i v e equations 5.10c  by  c l o s e t o DA <*"  More g e n e r a l p r e -  2  and W  2  or  Equation  f o r the  f o u n d by  Q  Day  are  ) .  F r i c t i o n Concept A p p l i e d t o Tumbling Flow  Although concept  .  s h o u l d be p o s s i b l e on t h e b a s i s o f  ( t h e r e l a t i o n b e t w e e n DA  D  consistently The  - 1  s u b s t i t u t i n g m e a s u r e d v a l u e s o f DA  uncertain Q  5.4  s  flows  and  the present study  the data are l e s s than i d e a l l y  c a t i o n of g e n e r a l l y accepted a> b r i e f c o m p a r i s o n flow equation comparison  does n o t r e p l y  open c h a n n e l  between f r i c t i o n  (5-10)  may  be  with other studies.  suited  and  friction-  for appli-  friction  formulas  interesting  on t h e  formulas,  the  general  and may  facilitate  To•the w r i t e r ' s  knowledge, 2  all  p r e v i o u s w o r k on v e r y r o u g h c h a n n e l s  i s b a s e d on t h e f r i c t i o n  o r on t u m b l i n g  c o n c e p t , w h i c h , by  u n o b t a i n a b l e roughness d a t a , tends  to y i e l d  cannot  problems.  be  applied to h y d r o l o g i c a l  requiring results  flow virtually  that  ^Utah S t a t e U n i v e r s i t y appears t o have a c o n t i n u i n g r e s e a r c h p r o g r a m on t u m b l i n g f l o w . Some o f t h e r e s u l t s a r e p u b l i s h e d i n P e t e r s o n and M o h a n t y , I 9 6 0 and i n an e x t e n s i v e number o f M.Sc. and Ph.D. t h e s e s , s u c h as A l K a f a j i , 196l; Judd, 1963; Abdelsalam, 1956. O t h e r s t u d i e s on r o u g h , n a t u r a l c h a n n e l s a r e : L e o p o l d , B a g n o l d e_t a l / , I 9 6 0 ; M i r a j g a o k e r and C h a r l u , 1 9 6 3 ; J o h n s o n , 1 9 6 4 ; H e r b i c h , 1 9 6 4 ; A r g y r o p o u l o s , 1 9 6 5 ; K e l l e r h a l s , 1 9 6 7 ; H a r t u n g and S c h e u e r l e i n , 1967; S c h e u e r l e i n , 1968.  104  5.4.1  Open C h a n n e l F l o w F o r m u l a s The  formula  p r o b l e m t o be  i s of the v  radius  S,  s  i n which d  = A/W  %  (they  g,  ? w  replaces  flow  /i  ,  5.19  \ )  t h e more commonly u s e d h y d r a u l i c  and  r e c t i o n f a c t o r s which vanish s e c t i o n and  t h e X^  stream  are non-dimensional  i n the  a particular  ments o f d i a m e t e r D. the  ,  a r e a l m o s t i n d i s t i n g u i s h a b l e i n most  channels),^ is viscosity  channel  an open c h a n n e l  form  = f (D, d ,  m  s o l v e d by  case of a b r o a d  rectangular  shape o f t h e r o u g h n e s s  Assuming t h i s  t o be  the  cor-  case,one  eleobtains  5.19  commonly u s e d n o n - d i m e n s i o n a l f o r m o f E q u a t i o n 2  v  v d«  "PUTS- It  (S  >  —  c a n be  to the  formation  5.20  > d- )  neglected  as  l o n g as  steady  o f s u r f a c e waves and  side  f o r the  case of s t e e p ,  size.  of  f l o w does n o t  e i t h e r one  of the  p a r a m e t e r s on t h e r i g h t i s o f t e n n e g l i g i b l e  d e p e n d i n g on t h e i r r e l a t i v e 5.20^  ~  i s w e l l e s t a b l i s h e d t h a t S on t h e r i g h t  (5.20)  remaining  f  A f o r m u l a t i o n of  rough channels i s  lead two  also, Equation  (Keulegan,  1938)  |  A  W  w h i c h c a n be of the  form  = 6.25 fitted  + 5.75  approximately  log  1  0  (^)  with exponential  ...  5.21  functions  105  .  .3  .6 .8 1.0  FIGURE 1 8 .  VALUES OF  2  c  2  4  FOR  6 8 10  5.22  20  BEST F I T TO EQUATION  5.21  CA  I, -  The  commonly u s e d M a n n i n g E q u a t i o n assumes a c„ o f 1 / 6 , a,  p r o v i d e s good f i t t o E q u a t i o n 5-21 I t i s important t o note terms v d / u > m  %  over the range  t h a t E q u a t i o n 5-22  and S o f E q u a t i o n 5 . 2 0 .  While  7< —  which  <  130.  n e g l e c t s the  the theory  of  t u r b u l e n t b o u n d a r y l a y e r s j u s t i f i e s t h e f o r m e r , t h e r e i s no a priori justification  f o r the l a t t e r  i n c a s e s where  the  106  roughness 5.4.2  tial of  elements  free  s u r f a c e , as  the  The  data of t h i s  steady-flow  c o n s t a n t , but Equation regarding  and  unknown r o u g h n e s s ,  into  comparable  cross-sectional  should bracket  (i)  W  (ii)  W  v  study  s  =  the  form  shape.  consist  velocity constant  unknown c r o s s - s e c t i o n a l  5-22  i n tumbling  flow.  Data  between d i s c h a r g e  constant, but  v  the  Comparison w i t h  relations  which  affect  shape.  exponen-  for conditions known s l o p e , To  r e q u i r e s some Two  of  transform assumptions  assumptions w i l l  true s i t u a t i o n  and  be  used  (Section 5 . 2 . 1 ) .  c -3 3  Q° '  2  a  s Equation  5.22  and  1 -, c„ + 0 . 5 d„ <x v 2 * m Assumption (1) t h i s  with  can be  w r i t t e n as  leads  to  e +0.5 2  c +1.5 ?  v and  with  m  <* Q  Assumption(ii) i t leads  ...  5.23  ...  5.24  to  0.8(c +0.5) 2  c +1.5 p  «r Q  v m The to b  v  •  Q-exponents  of Equation ^  5.13,  of the '  and  b  last v  two  equations  i s related  correspond  to b, of Tables A  6  and  107  7 by  b. = 1 - b V  ( E q u a t i o n 5-14C). Jr\.  the range 0 . 4 < b  v  0.72.  <  The o b s e r v e d  FIGURE 1 9 .  On F i g u r e 1 9 , t h e e x p o n e n t s o f c.  against  0  EXPONENTS OF EQUATIONS 5 - 2 3 AND 5-24 v s . c  U s i n g F i g u r e 19 t o c o n v e r t t h e o b s e r v e d 18 t o c o n v e r t  Figure  cover  \f  5 . 2 3 a n d 5.24 h a v e b e e n p l o t t e d  Equations  b  c  2  t o apparent  b  2  t o c , and  y  2  roughness r a t i o s  (assuming  E q u a t i o n 5 . 2 i s v a l i d ) one c a n s e e t h a t t h e d a t a c o v e r t h e approximate  range o f roughness r a t i o s  from  0.4 t o 8 , w h i c h i s  compatible w i t h t h e appearance o f the channels. 5.18  one c a n o b t a i n an e x p l i c i t b  which,  y  i f used  that at a fixed  =  1  -  1  4  S " -  0  . . .  8  s l o p e , l a r g e channels  are rougher  with f i e l d  W D  are r e l a t i v e l y  and, f o r a g i v e n channel than f l a t  observations.  Equation  equation f o rb^  i n c o n j u n c t i o n w i t h F i g u r e s 18 a n d 19  than s m a l l channels channels  0.25  From  channels.  size,  This also  5.25  indicates smoother  steep agrees  108  In  c o n c l u s i o n , the data of t h i s  study appear to  c o m p a t i b l e w i t h t h e commonly a c c e p t e d l o g a r i t h m i c r o u g h c h a n n e l s , E q u a t i o n 5.21, r o u g h n e s s s i z e and  be  law f o r  b u t w i t h o u t i n f o r m a t i o n on  on s h a p e o f t h e f l o w s e c t i o n s , I t i s n o t  p o s s i b l e to decide whether t h i s  equation gives a  r e p r e s e n t a t i o n of flow i n extremely  rough  meaningful  channels.  109  6. _  UNSTEADY FLOW I N STEEP CHANNELS  6.1  K i n e m a t i c Waves and t h e S u r g e T e s t  6.1.1  Some F e a t u r e s o f K i n e m a t i c Waves and Whitham ( 1 9 5 5 )  Lighthill  Results  i n t r o d u c e d the  term  " k i n e m a t i c wave" f o r a c l a s s o f waves w h i c h a r i s e I n d i m e n s i o n a l f l o w systems relation  i f there i s a unique  one-  functional  between:  ( i ) the flow (ii) (iii)  Q,  t h e p o s i t i o n x,  and  the q u a n t i t y per u n i t d i s t a n c e  (A i n t h e c a s e o f  a stream). The wave m o t i o n s tinuity  a r e t h e n g o v e r n e d by t h e e q u a t i o n o f c o n -  a l o n e . I t has  l o n g b e e n r e c o g n i z e d t h a t t h e movement  o f a f l o o d down a l o n g r i v e r o f wave ( S e d d o n , The  1900;  c a n be a p p r o x i m a t e d by t h i s  type  Masse', 1 9 3 5 ) .  e q u a t i o n of c o n t i n u i t y  f o r unsteady flow i n a long  channel i s AR  = o  + AA  w h i c h c a n a l s o be w r i t t e n o t  b Q/d  d  A  6 i  as d  x  A has d i m e n s i o n s o f a v e l o c i t y  and  can only' depend  on  Q and o n t h e p o s i t i o n x i f t h e a s s u m p t i o n s f o r ' k i n e m a t i c waves are s a t i s f i e d .  An o b s e r v e r m o v i n g a l o n g x a t s p e e d 6Q/6  A  110  will  then  which  observe  no  change I n a r e a o r d i s c h a r g e  d  =  Q  6 A being  the  Henderson  celerity  matic  (1966)  waves can  equation  8 and  the  _  Q  i n w h i c h S„ i s t h e f Manning E q u a t i o n Terms  1  c o n d i t i o n s under which  the  -Q  dd  2  3.  v - dv m . . m '  slope ^  (e.g. n m  flow,  non-uniform on  uniform and  v m  c u ••  2  /d« *  4/3  i f the  the r i g h t  channels  o f magnitude the  the  4 however, may  be  I f S i s much  s i d e of  flood  5th  term  the  S i n a few  Equation  Henderson steep,  rise. i s always  averaged  places  to  equation  in a relatively  rapid  s m a l l e r than  local  complete  kinematic.  even d u r i n g a very flow  the  1  flow,' terms  conditions.  alluvial  3 and  2  &  condition i s satisfied  Terms  m 5  2 define steady,  3 o t h e r terms  comparable w i t h  <Sv 1  h  shows t h a t t h i s  more o r d e r s  w r i t t e n as '•  non-uniform  In tumbling  can be  The  8.5)  t h e wave m o t i o n i s a p p r o x i m a t e l y  river,  kine-  applicable).  to un-steady, than  flow,  t h e movement o f f l o o d waves.  friction  is  and  4 define steady,  be  open c h a n n e l  of motion f o r a p r i s m a t i c channel  ,  6.3  waves.  9 o f h i s book on  examines  1  larger  kinematic  approximate  ,  with  ...  of these  (Henderson's E q u a t i o n  applies  d e f i n e s a wave m o t i o n  c(x,Q)  In Chapters  6.4,  6.2  shows t h a t E q u a t i o n  0),  (DA/Dt =  S but  one  or  may  (big pools).  o f o r d e r S o r more and,  like  S,  Ill  they  are h i g h l y  and u n p r e d i c t a b l y v a r i a b l e w i t h  6.4  does n o t , t h e r e f o r e , p e r m i t any d e f i n i t e  ing  the a p p l i c a b i l i t y  flow.  Only The  location,  evidence  t o tumbling  c a n do t h i s .  e q u a t i o n f o r t h e k i n e m a t i c wave c e l e r i t y  at a f i x e d  c = dQ/dA, c a n a l s o be s t a t e d as  C  which  conclusions regard-  o f k i n e m a t i c wave t h e o r y  experimental  x. E q u a t i o n  =  d(vA) ~dA  . .dv =  dA  v  shows t h a t c I n c r e a s e s w i t h d i s c h a r g e i n n a t u r a l  channels. unique  In a t r u l y  and i n c r e a s i n g  kinematic function  a k i n e m a t i c wave c a n n o t  channel,  river  c(x) , i s t h e r e f o r e a  o f A o r Q.  As a c o n s e q u e n c e ,  d i s p e r s e but the h i g h e r p a r t s of the  wave w i l l  tend t o overrun  the lower  gradually  s t e e p e n i n g wave f r o n t  parts,  resulting i n a  of positive  waves.  I n S e c t i o n 5 . 2 i t was shown t h a t c h a n n e l r e a c h e s tumbling b  A = a^Q  f l o w r e g i m e obey e q u a t i o n s  i n the  o f the form  A (5.10).  Kinematic  waves i n s u c h  t h e r e f o r e have t h e c e l e r i t y dq i = iiS. = ± dA 1/b . a A b  '  c  c  channels  ,. y A•r -" Ab  R  A  A  should  6 5 ...DO  A  o r , i n terms o f d i s c h a r g e n  ° Substituting b  1-bA  ~ A°A  . . . 6 . 6  a  = 1 - b v b  m A  and a  = 1/a. i n t o E q u a t i o n  6.6 gives . . . 6 . 7  112  w h i c h shows t h a t t h e k i n e m a t i c  wave c e l e r i t y  i sproportional  to v • m 6.1.2  I n d i c a t i o n s from The  able  three  comparison with  the steepening  (ii)  Results  features of kinematic  f o r immediate (i)  t h e Surge T e s t  waves w h i c h a r e s u i t -  the f i e l d  of positive  the non-dispersive nature  wave  data are: fronts,  of kinematic  waves,  and (iii) All  t h e wave c e l e r i t y  surge  of p o s i t i v e  facts  are clear  test  line.  reaches,  based The  m  evidence  to Equation  as a s t r a i g h t  the Q - v  line  6.7,  to  the kinematic  16 and 17  together with  show t h e s e  the observed  celerities  shown I n F i g u r e s 16 and 1 7 .  Symmetrical  higher than tests,  celerity  f o r two  celerities rise  or  fall.  and t h e o b s e r v e d  to the s i t u a t i o n  and k i n e m a t i c  c l o s e b u t a t low f l o w s , t h e o b s e r v e d  t o be s i g n i f i c a n t l y  lines  At i n t e r m e d i a t e t o h i g h  agreement between o b s e r v e d  always  similar  direction.  p a r a l l e l to  ( o v e r Q) o f t h e o b s e r v e d  i s consistently  towards  surge  surge  line  flattening  effects.  on l o g a r i t h m i c p a p e r ,  Figures  on t h e m i d - p o i n t s  f o r dispersive  agreement between t h e t h e o r e t i c a l  surge  the  and a t e n d e n c y  smooth Q ( t ) - - c u r v e s i n t h e downstream  According plots  show a c o n s i s t e n t downstream  and n e g a t i v e wave f r o n t s  increasingly Both  tests  c = v/b .  flows  celerities i s celerities  tend  kinematic.  consisting  o f an u p - s u r g e  followed  113  by  a similar  instructive The  time  surges  (or vice  being  and w i t h  gradually  closely  constant  close to kinematic  the sharp  channels with  The  comparisons  a certain  channel  propagate  effect  kinematic  \/g d  pools  , which w i l l  ponding  kinematic  added.  large parts of  are occupied by;.relatively  deep and  according t o the  Changes i n d i s c h a r g e  a t t h e dynamic wave  g e n e r a l l y be much l a r g e r wave c e l e r i t y .  flows  c o n d i t i o n s a t low f l o w s  a t low s t a g e  stated In Section 6 . 1 . 1 .  through  that the  flow regime i s e s s e n t i a l l y  slow-moving p o o l s , which a r e not k i n e m a t i c assumptions  becoming  at intermediate to high  dispersive  can be e x p l a i n e d as f o l l o w s : flow  of these  at a l l but the lowest  one c a n c o n c l u d e  i n the tumbling  d i g r e s s i o n from  tumbling  the c e l e r i t y  t o the  above.  mechanism-' o f wave p r o p a g a t i o n  any  and i d e n t i c a l  changes i n d i s c h a r g e ,  s m o o t h e r as n o t e d  From t h e s e  kinematic  (Figure 1 5 ) .  o f t h e up and down-  l a g at the lake o u t l e t , with  mid-points  are p a r t i c u l a r l y  on t h e mechanism o f wave p r o p a g a t i o n  remains very  through  versa)  l a g between t h e m i d - p o i n t s  original  flows  down-surge  celerity than  the c o r r e s -  F o r example, a t a f l o w o f  3 —1 0.01  m s  Brockton  with  depth  o f more t h a n  Creek  (Figure 16)  contained  a few p o o l s  0 . 3 m and a l a r g e number o f p o o l s  with  d e p t h s between 0 . 1 and 0 . 3 m. The k i n e m a t i c wave c e l e r i t y a t t h i s f l o w i s 0 . 1 8 ms and t h e dynamic c e l e r i t i e s f o r 0 . 1 m -1 -1 and 0 . 3 m d e p t h a r e 1 ms and 1 . 7 ms . The e f f e c t s o f pools w i l l  be examined i n g r e a t e r d e t a i l  i n Section 6 . 3 .  114  6.2  Kinematic  6.2.1  Waves w i t h  D i s p e r s i o n through In  channels  t h e case  kinematic introduced  some d i s p e r s i v e  relatively prismatic i t has l o n g b e e n  o f f l o o d waves i s m a i n l y effects  ^ j n b_k _ 2 dx  4t  this  type  of kinematic  Equation  6.2,  with  according  Effects  added.  (1951)  Hayami  the equation  d A  for  with  flow throughout,  that the propagation with  Dispersion  S e c o n d a r y Dynamic  of long r i v e r s  and s u b - c r i t i c a l  recognized  Storage  <^ A £ 2 2  c  wave.  3v /2 being  ...  x  t o t h e Che'zy f r i c t i o n  o.r  This corresponds t o  t h e k i n e m a t i c wave  m  r „  formula  and D  celerity  b e i n g an c  undetermined Equation  dispersion coefficient.  6 . 7 by a d d i n g  s l o p e , which  occurs  the e f f e c t  he  claims  further  o f t h e changed water  d u r i n g the passage  t h e b a s i c f l o o d wave e q u a t i o n  (6.2).  other accounting  such  as p o o l s  solution tions  f o r Equation  o f constant  6.7,  based  v and c o n s t a n t m  between computed and o b s e r v e d produced  Without  detailed  symmetrical  f o r t h e s l o p e e f f e c t and  banks.  elements,  He g i v e s an e x p l i c i t  on t h e l i n e a r i z i n g D , and f o u n d c' .  propagation  f l o o d wave.  argument  consists of  f o r wave d i s p e r s i o n i n s t o r a g e  o r permeable stream  surface  o f a f l o o d wave, t o  that the dispersion c o e f f i c i e n t  a sum o f two t e r m s , one a c c o u n t i n g the  Hayami a r r i v e d a t  good  assumpagreement  o f an a r t i f i c i a l l y  The main d i f f i c u l t i e s  with  115  Hayami's s o l u t i o n s a r e t h e n o r m a l l y D  c  and  unpredictable size  v . m Lighthill  and  Witham d i s c u s s s e v e r a l d i f f e r e n t  of the d i s p e r s i o n term i n the k i n e m a t i c  compared w i t h t h e t e r m s on t h e  b A  b x  c  b  A/b  forms:  x b t  be more e a s i l y  .  b k/bx , The  1/c  2  2  e s t a b l i s h e d f o r one  2  A/Jt ,  Two  form than  (which  t h e d i s p e r s i o n t e r m may  n o t be  others,  In tumbling  flow  so t h a t t h e above t r a n s f o r m a t i o n  also discusses  transformed 6.7,  of  the d i s p e r s i o n of  motion (6.4)  of Hayami, E q u a t i o n  the  justified.  shows t h a t h i s f o r m o f t h e e q u a t i o n  equation  the  rating  k i n e m a t i c waves and can be  the  s m a l l because of  the term c o n t a i n i n g second d e r i v a t i o n i s not Henderson (1966)  may  t o measure)  i n stage-discharge  d u r i n g t h e p a s s a g e o f a f l o o d wave.  extensive pool storage,  f o r the  i s r a r e l y p o s s i b l e ) , and  h y s t e r e s i s e f f e c t , which occurs  channels  or  2  b a s e d on o b s e r v e d f l o o d  o t h e r b a s e d on t h e w e l l - k n o w n ( b u t d i f f i c u l t  curves  one  methods f o r d e t e r m i n i n g  d i s p e r s i o n c o e f f i c i e n t a r e g i v e n , one at f i x e d times  b  2  s t a t e d i n any  d i s p e r s i o n c o e f f i c i e n t , however,  d e p e n d i n g on c i r c u m s t a n c e s .  profiles  s m a l l , when 6.7  of Equation  t h e d i s p e r s i o n t e r m c a n t h e r e f o r e be  of the t h r e e  They  _b_k  ^  "ST  1/c  left  forms  wave e q u a t i o n .  c l a i m t h a t , s i n c e the d i s p e r s i v e term i s p r o b a b l y  and  of  i n t o the kinematic i f t e r m s 4 and  of  wave  5 are  neglected.  116  In c o n c l u s i o n i t appears body  o f knowledge on d i s p e r s i v e k i n e m a t i c  based  waves, b u t i t i s  i n which the d i s p e r s i o n i s mainly  differences resulting Tumbling  least  between s t e a d y . and u n s t e a d y  flow  to s u p e r c r i t i c a l  depths,  and t h e  relations. transitions  s e c t i o n , the stage-discharge  The c o n s e q u e n c e s  investigated  Storage  solely to  do n o t a p p e a r t o have b e e n  Equation  of Kinematic  Waves  with  Dispersion  A channel,  I n which the r e l a t i o n between Q  at regularly  spaced  discrete  the f o l l o w i n g Q - A r e l a t i o n  x. , < x < x . l-l I  relation i s  before.  The D i f f e r e n t i a l  unique  of this  from  w h i c h means t h a t , a t  The d i s p e r s i o n i s t h e r e f o r e a t t r i b u t a b l e  storage.  6.2.2  the r e s u l t of  slopes  i s c h a r a c t e r i z e d by f r e q u e n t  at the c r i t i c a l  unique.  prismatic  h y s t e r e s i s i n the stage-discharge  sub-critical  has  i s a considerable  on, and a p p l i c a b l e t o l o n g , r e l a t i v e l y  channels,  only  that there  and A i s ;  locations  at intermediate  ,  points  (see Figure 20) &  Q = f (A) I 1  +  ,<?W  D  -|-|  ... 6 . 8  x. I  since, into  at r i s i n g  storage  stage,  some o f t h e d i s c h a r g e  b e t w e e n x and x..  at x w i l l  go  117  FIGURE 2 0 .  D E F I N I T I O N SKETCH FOR EQUATION 6 . 8  The c o e f f i c i e n t o f  b A/b t has d i m e n s i o n  being the only l e n g t h r e a d i l y (Section 5 . 3 ) ,  available  L, and w i t h  Wp  i n the present  problem  i t i s convenient  t o use i t i n E q u a t i o n  6.8,  together with a non-dimensional  c o e f f i c i e n t fi , whose  value  w i l l h a v e t o be d e t e r m i n e d ft W  D  1963).  Physically,  the  i s a l e n g t h measure i n d i r e c t i o n x, r e l a t e d  average s i z e of p o o l s . riffle  l a t e r on.  D  i n (6.8)  t i o n holds i n tumbling flow  channels.  substitute  equation of continuity  (6.1),  (Leopold et a l . ,  one assumes t h a t a s i m i l a r r e l a -  Assuming a l o n g channel w i t h densely s e c t i o n s x^ , one may  to the  I n some a l l u v i a l r i v e r s , p o o l -  sequences s c a l e a p p r o x i m a t e l y w i t h w i d t h By u s i n g W  +  AR 6 A  AA bx  +  *  A  Q t  control  6.8 i n t o the  Equation  at l e a s t  spaced  as an  approximation,  giving AA i t  factor  bA 2  <*xdt  _  "  n  u  118  i n which  stands f o r & A/ 6t.  Noting that d Q / d A = c  and, a c c o r d i n g t o E q u a t i o n 6 . 8 , b Q / d A^ =  W^,  one o b t a i n s  o  d  t  d  x  " D o  xdt  T h i s i s t h e b a s i c e q u a t i o n f o r k i n e m a t i c waves w i t h s t o r a g e dispersion.  L i g h t h i l l and Whitham ( 1 9 5 5 ) a r r i v e a t t h e same  e q u a t i o n by c o n s i d e r i n g t h e e f f e c t o f h y s t e r e s i s i n a s t a g e d i s c h a r g e r a t i n g c u r v e , a p p l i c a b l e t o t h e whole r e a c h . Equation 6 . 8 a l s o defines a h y s t e r e s i s e f f e c t i n the Q - A r e l a t i o n , b u t i n a n a t u r a l t u m b l i n g f l o w channel t h i s i s p r o b a b l y h i g h l y v a r i a b l e and c o u l d c e r t a i n l y not l e a d t o a p r a c t i c a l method f o r . e s t i m a t i n g /? , t h e one r e m a i n i n g parameter. for  An a l t e r n a t i v e i s t o o b t a i n an e x p l i c i t  Equation 6 . 9 , w i t h the r e l a t i v e l y simple I n i t i a l  d i t i o n s o f t h e surge t e s t s , and then t o o b t a i n / ^ by the s o l u t i o n t o t h e observed s u r g e s .  free  solution confitting  T h i s w i l l be done i n  the f o l l o w i n g two s e c t i o n s . 6.2.3  A Solution forStep-like  Input  An e x p l i c i t s o l u t i o n o f E q u a t i o n 6 . 9 i s o n l y o b t a i n a b l e w i t h the l i n e a r i z i n g assumptions  o f c o n s t a n t c and c o n s t a n t A ,  which i s j u s t i f i a b l e f o r t h e surge t e s t s , s i n c e A Q < < Q . With these assumptions-  E q u a t i o n 6 . 9 becomes a l i n e a r , homo-  geneous, p a r t i a l d i f f e r e n t i a l e q u a t i o n o f second o r d e r . substitution  The  119  F = A e  ct  /S w D  /3  transforms the equation  W  D  6. 10  i n t o the compact, f i r s t  canonical  form  aF  cF  2  ^ wD  dxd.t w h i c h has  2  surge t e s t  initial  6.11  = 0 2  the c h a r a c t e r i s t i c s  The  x = const,  c o n d i t i o n s and b o u n d a r y  c a n be a p p r o x i m a t e d A ( x k 0,0)  =  A(0,0)  = A  A(0, t > 0) After  r  and t =  const.  c o n d i t i o n s of a  as: .  A  o = (1 + <* ) A  t h e above t r a n s f o r m a t i o n F(x^0,0)  = A  F(0,0)  = A  o  <* «  6.13  1.0  t h e y become x  6.12a  e  ct F ( 0 , t > 0) Since  = (1  the i n i t i a l  Goursat problem. solution method.  (Mikhlin,  + °<)A e  6.13a D  o  oc  «  1-0  c o n d i t i o n s d e f i n e F on two  c h a r a c t e r i s t i c s , the problem  6.12  t o be s o l v e d i s a  so-called  U n d e r t h e above c o n d i t i o n s i t has 1966), w h i c h c a n be  f o u n d by  of i t s  a  unique  Riemann's  12.0  The  Riemann F u n c t i o n  B is  B = I [-v/4V xt ] i n which Kind  I  o  (u) i s t h e " M o d i f i e d  of Order  Zero".  The  Bessel Function  solution  of  (6.9)  i s o f the  c  x F(x,t)  =  F(0,0)B(0,0)  +  j  '  B  d  F  ^ | >  0)  dj  of the  First form  dF(0,r)  +J  dr  dr  6.14  i n which  J and  coordinates evaluated is  T a r e dummy v a r i a b l e s i n l e n g t h and  respectively.  The  i n t h e above f o r m  u n d e f i n e d at  Y'=  0.  last  term  of"(6.14)  time cannot  s i n c e the d e r i v a t i v e d F ( 0 T ) / d T " 5  Partial  i n t e g r a t i o n of t h i s  x  F(x,t)  =  F ( O , O ) B ( O , O )  CB  +  be  term  gives  j  r=t. d  F  ^  ?  0  )  d/ + B(o,r)P(o,r) r=o  Q'  t - / Since  dI (u)/du = I Q  Function B.  and  (u) and  # 1  of the F i r s t  the s t a r t i n g  f| P ( . o , r ) d r  Kind  ...  (-u) i s t h e " M o d i f i e d  of Order  One",  conditions of F i n 6.15  6.15  Bessel  substituting for gives  121  0  D  t  cr 2  J  W&  1  MM V ,  1cl(t-rt7-  1/2  6.16  With A ( l , t ) solution  = F exp(-l//?W  I^( ) u  i t c a n be s i m p l i f i e d  For  l a r g e -arguments  tend  asymptotically  According  t o Jahnke  5% a t u = 9 . surge data, so t h a t  - ct^Wp)  6.9 f o r a reach  of Equation  circumstances  D  of length  will  functions  easily  computed  asymptote.  (6.16)  i s negligible,  d a t a a r e i n meters  !  0  \/l/2Tu  t h e agreement  exp(u)  i s within  of the present than 1 0 ,  c a n be r e p l a c e d by t h e i r more The m i d d l e t e r m on t h e l e f t o f with  t h e two  integral  given i n minutes, while  and s e c o n d s .  6 . 1 6 becomes  normal  l ( u ) and  a l w a y s be much l a r g e r  when compared  t e r m s . Time l a g i s g e n e r a l l y  Under  functions  the f u n c t i o n  and Emde ( 1 9 4 5 ) -  t h e arguments  1.  considerably.  u the B e s s e l towards  i s the e x p l i c i t  W i t h t h e 1 - v a l u e s and t i m e l a g s  the B e s s e l  Equation  this  a l l other  With these assumptions,  122 1  A  h / — — - ^ = r ^ P ( P V ^ sf? * f  ^ ^ i r  +  EX  0  60ct  ) dx  120(1 +<*) A C I 5 p —  +  /9^IAL/  ^  60cT  ^  J  0  J  :  •  =  / „ _  /TT;—ZTT"  exp (p v / l V t -  V2TPV^TT  60ct  1_  /?W  +  f—  / -i /  x ,  /?W  j  a  ^ ,„  •' •  r  D / i n which p tional  2  2*" .  = ^/2k0o./fi  E q u a t i o n 6.17  poses.no  computa-  problems. The  F o r t r a n IVG p r o g r a m fi,  v a l u e s o f Q ,o<, Q  W^,  1,  "PD" computes A ( l , t )  f o r given  a ^ , a n d b ^ u s i n g E q u a t i o n 5.10a  to  c o n v e r t d i s c h a r g e t o a r e a a n d v i c e v e r s a a n d E q u a t i o n 6.6  to  compute c.  (6.17).  On o u t p u t , t h e p r o g r a m  t o p e r m i t an a s s e s s m e n t  two t e r m s  on t h e r i g h t .  t i o n s / and sample  several parts of  of the contribution of the  The p r o g r a m , w i t h  operating  output, i s l i s t e d  i n the Appendix.  During the period of rapidly  changing A ( l , t ) ,  t e r m s o f (6.17)  a r e o f s i m i l a r magnitude.  dominates b e f o r e that,when A ( 1 , t ) ~ dominates  t h e p e r i o d when A ( l , t ) ~  t = 1/c, t h e d o m i n a n t to  lists  t = 0, t h e s o l u t i o n  asymptotic  The f i r s t  A ,and t h e s e c o n d (1+ <xr ) A .  as a r e s u l t  f u n c t i o n f o r t h e two B e s s e l  both term term  Away f r o m  t e r m s become t i m e i n d e p e n d e n t . fails  instruc-  Close  o f s u b s t i t u t i n g an  functions.  123  0.8 10  12  14  16  Time  18  20  22  24  in  Minutes  26  28  30  EFFECT OF J9 ON THE SOLUTION OF THE KINEMATIC WAVE EQUATION WITH  STORAGE DISPERSION Fig. 21  124  6.2.4  Comparison w i t h F i e l d To  e v a l u a t e the probable  free parameter i n Equation pared  Data r a n g e o f ft , w h i c h i s t h e only-  6.17,  a few  w i t h computed Q ( l , t ) c u r v e s  Figure  2 1 shows a t y p i c a l  c of that t e s t  surge  c o v e r i n g a wide range of  comparison.  Obviously  i s somewhat t o o s m a l l as The  b e t w e e n 0.5  1, w i t h t h e g r e a t e r v a l u e s  larger discharges. least  squares  F i t was  values  determined  f i t of E q u a t i o n  o f /3 , o r /? and  6.17  of  by  fall  "PD",  but  in  consistently  inspection.  width  noted  A  to evaluate optimal  values  "NLIN2"  i t would i n v o l v e e x c e s s i v e  i n S e c t i o n 5.2.1  of n a t u r a l channels,  functions  of the  w i t h the f a c t o r i n the  com-  that W  W  the  a c t u a l water  surface  , i s generally related  to W  z probably  falling  i n t o t h e r a n g e 0.1''" t o  flow channels  m i g h t be  (Miller,  a good e s t i m a t e  1958).  of^W  n  22a  and  22b  taken  show a few 6.17  and  typical results  6.19,  as t h e e s t i m a t e d mean a n n u a l  with  0.2  This  ...  on t h e b a s i s o f E q u a t i o n s D  by  or  A Figures  n  form  case of t u m b l i n g  suggests  Q  the  time. As  and  .  computed  o c c u r r i n g at  c i s f e a s i b l e , u s i n g the programs  ( S e c t i o n 3 . 3 . 1 ) and puter  fitting  the  . p o i n t e d out  S e c t i o n 6.1.2. and  best  t e s t s were com-  z taken  peak f l o w  6.19  obtained as  (Table  0.2 2).  125  J300  15  30  45  14OO  15  30  45  ^00  Time  Phyllis  Creek,  June  22,  1968.  /? = 0.54  -2.8  \n  -2.7  T=  -2.6  •—  -2.5  8.  -2.4  1  o  Q  ,  1500  ,  15  Phyllis  ,  30 Creek,  ,  45  !  |g00  ,  15  Sept. 17, 1968.  ,  30 jS = 0.69  COMPARISON BETWEEN FIELD OBSERVATIONS AND KINEMATIC WAVES WITH STORAGE DISPERSION Fig. 22a  126  'w 0.08"  10  -GI  E  ro  G3, observed-^/  L*-G3, computed fi =0.25  CD  TJ 0.07c o  (5 o  0.06 0  10  Blaney  20  n 30 40 50 60 70 80 Time in minutes  Creek, Upsurge  1 90  1 11r0 100  GI-G3, June 9,1967 1.2  1.0  /  W IO  CO  /  E  /  G 3,observed-^  A-*-G3,  / / fi  a O  /  computed =0.6  /  ro j 1.1 ^ CD  1.0  0.8 10 20 30 Time in minutes  +o O  40  Blaney Creek , Upsurge GI-G3, Nov. 30,1968 h2.2 _ ro E  G 3 .computed fi =0.725  CD  ° o  2.0 0  Blaney  "v>  G3, observed  -GI  2  4  -21  1 0  o O  6 8 10 12 14 Time in minutes  Creek, Downsurge  ro E  GI-G3,  16  18 20  March 5,1968  COMPARISON BETWEEN FIELD OBSERVATIONS AND KINEMATIC WAVES WITH STORAGE DISPERSION Fjg.22b  127  Only reaches immediately p a r i s o n , because the initial  s u r g e s on  c o n d i t i o n s , as  w r i t e r knows o f no parable  b e l o w l a k e s can be  6.17  having  to evaluate  i s not  r o u t i n e h y d r o l o g i c a l work. dispersion coefficient circumstances To  permit  The  numerical  some f r e e p a r a m e t e r s  beforehand.  a p r a c t i c a l routing equation I t i s a means o f o b t a i n i n g  the  (6.9)  i f  c r e a t i o n of a s m a l l , s t e p - l i k e  surge 6.  considered  n o n - l i n e a r and  programmed f o r  Whitham ( 1 9 5 5 )  by  (1966).  or Henderson  A P r a c t i c a l Approach to Unsteady, Tumbling Flow As  an a l t e r n a t i v e t o t h e r o u t i n g method o f t h e  s e c t i o n , which considers sequence of s t o r a g e  the  tumbling  flow  channel  e l e m e n t s w i t h u n i q u e Q-A  as  s e q u e n c e o f a few tumbling  flow.  r e s e r v o i r s and  The  b a s i c steady  s a t i s f i e d p h y s i c a l l y e i t h e r by appropriate  channels could flow Equation  channel  following 3 sections w i l l  a  large at  a  represent 5.10  can  be  an i n c l i n e d r o u g h c h a n n e l  r o u g h n e s s e l e m e n t s o r by  horizontal reservoir-like  last  relations  t h e i r outlets-, i t appears worth i n v e s t i g a t i n g whether  The  for  s o l u t i o n , p o s s i b l y u s i n g t h e methods d i s c u s s e d  L i g h t h i l l and  the  com-  o b t a i n an o p e r a t i o n a l f l o w f o r e c a s t i n g s y s t e m , E q u a t i o n  w o u l d have t o be  6.3  (6.13).  and  o f t h e b a s i c wave e q u a t i o n  the  f i t the  r o u t i n g method w h i c h c o u l d g i v e  from other- u n s t e a d y f l o w d a t a Equation  r e a c h e s do n o t  stated i n (6.12)  other  f i t without  lower  u s e d f o r com-  a smooth, almost  with a weir-like  explore  the  with  outlet.  consequences  of  128  assuming t h a t represented and  a channel  reach  i n the tumbling  regime  by a r e l a t i v e l y s m a l l number o f a l t e r n a t i n g  channels,  both  meeting the steady b  flow  A ...5.10  A  6.3.1''  Unsteady Unsteady  reservoirs  equation  A = a Q  length A  c a n be  Flow t h r o u g h  flow  through  a Non-linear  Reservoir  a prismatic reservoir  of  and a r e a A has t o s a t i s f y t h e c o n t i n u i t y ' r e l a t i o n Q (t)  -  u  Q(t)  =  -||  ... 6.20  i n w h i c h Q ( t ) i s t h e i n f l o w , and Q ( t ) t h e o u t f l o w . E v a l u a t i n g u  the of  derivative  dA/dt w i t h  the steady  charges  flow  =  dt  c  b  of  the  to other  less  constant  than  D  A  q Q^), leads t o  q  -  2-b Q  }  ... 6.21  }  but n o n - l i n e a r d i f f e r e n t i a l  into  (6.21) i s p u r e l y  systems  of u n i t s ;  f ,. J dt =  v  q-  i t does n o t l i m i t  u  solution  (6.21) as f o l l o w s 1  q - q—  +  equation.  The  f o r ease i n c o n v e r t i n g  To o b t a i n an e x p l i c i t  q , one c a n w r i t e  D AA b  (Q =  l-b \  A  introduction  values  D  (  which i s a separable  formulas  of Q  _ ! 5 H  form  e q u a t i o n ' 5•10b and r e p r e s e n t i n g a l l d i s -  as f r a c t i o n s  da  t h e d i m e n s i o n a l l y homogeneous  constant  for a  Q to  129  Substituting  (q D  integral  values  of b  widely, is  1  /r dk j —^— J k(l+k)- A  A  = -q  U  J  B  ki  explicit  solutions  (b^ = i / j ) ,  but  the  of the  i and  suitable  j  form  for applications  A Routing If  Figure  -at-  flow  channels  23,. E q u a t i o n  dq.(t)  method, s u c h  M o d e l B a s e d on  a tumbling  of kinematic  This  lecting  may  and  6.21  as  to solve Equation Runge-Kutta.  time  non-linear reservoirs,  as  shown i n  by  assuming  at  a l l times.  further 1  cascade  becomes 2-b  ^  l a g b e t w e e n a p o o l and  assuming t h a t the  Pools  a  l a g b e t w e e n p o o l s , T^,  by  and  as  A  time  6.21  i s represented  * i A ° b <*i-i - V the  A  a Cascade of Channels  channel  (t  The  vary  approach  i n which b  nQ  =  can  wide r a n g e o f v a l u e s .  a standard numerical  6.3-2  for rational  solution  (Edwards, 1 9 2 1 ) .  I n g e n e r a l i t i s most e f f i c i e n t by  , . constant  +  has  d e p e n d i n g on  a fairly  gives  right  t h e r e f o r e not  take  V  on t h e  A  = k  t  V A  A  The  - q)/q  channels  ~^  > ••• -  A  i s e v a l u a t e d by the  are kinematic  21a  neg-  f o l l o w i n g channel, flow  t h a t the p o o l w a t e r - s u r f a c e  W i t h t h i s , T^  6  systems,and is horizontal  becomes  "'"This i s i d e n t i c a l w i t h t h e a s s u m p t i o n o f an i n f i n i t e dynamic wave c e l e r i t y i n t h e p o o l s . The wave c e l e r i t i e s quoted i n • S e c t i o n . 6 . 1 . 1 would appear to j u s t i f y t h i s .  130  m  L  and  (l  =  - oO -i n c.(t) l  with a s u b s t i t u t i o n f o r c , according  °0  to Equation  6.6  Channel i Pool i  FIGURE 23.  DEFINITION SKETCH FOR THE CASCADE OF CHANNELS RESERVOIRS  ( 1 -dQ  =  1 A  b  p  AND  A  ..  6.22  'D (6.21a) and (6.22)  The two e q u a t i o n s  system s u i t a b l e f o r numerical  define a channel  evaluation.  A Fortran IV G  p r o g r a m "SNLR'-' - w r i t t e n f o r t h i s p u r p o s e i s l i s t e d Appendix. -  -  I n '-"SNLR" t h e p a r a m e t e r ;  routing  -  i s c a l l e d o< .  i n the  131  S u i t a b l e assumptions  f o r the f r e e parameters  w i l l be d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n . siderations  of computing  computations  impose f a i r l y  Stability ditions  economics  are  T  on b o t h p a r a m e t e r s .  i s a s s u r e d as l o n g as t h e f o l l o w i n g two  >>  ±  L ( J 1) +  g r a t i o n of ( 6 . 2 1 a ) ,  <  T  L(J)  +  A  •••  t  and t h e s u b s c r i p t j r e f e r s  exact f o r m u l a t i o n of I n e q u a l i t y  or s m a l l time i n t e r v a l s , i t c e r t a i n l y p o s s i b l e cf and  n  values.  would i n d i c a t e a tendency  6  '  2 4  t o these time  6.23 large  narrows  depends on t h e reservoirs  the range  towards  of  6.24  V i o l a t i o n of I n e q u a l i t y  the f o r m a t i o n of a bore.  be a r a t h e r r e m o t e p o s s i b i l i t y , s i n c e  surges o f . t h i s  6.23  time step i n the n u m e r i c a l i n t e -  i n t e g r a t i n g method, but b y - r e q u i r i n g e i t h e r  T h i s may  con-  ...  Qj_ A t  i n which A t Is the f i n i t e  The  limits  of the  met.. R  steps.  However, con-  and s t a b i l i t y  narrow  d  n and  even the  s t u d y do n o t come c l o s e t o v i o l a t i n g  largest  the  inequality. 6.3.3  E v a l u a t i o n of the Free Parameters  from F i e l d  Data  F i g u r e 23 shows t h a t t h e p a r a m e t e r n i s a s c a l e p a r a meter, which s h o u l d express whether "long"  or "short".  With the r a t i o  a reach i s r e l a t i v e l y 1/W^  a b l e and p r a c t i c a l m e a s u r e o f r e l a t i v e  b e i n g t h e most r e a s o n length, n w i l l  be  132  assumed a p r i o r i important ficult  at  t o change n i n t h e c o u r s e parameter  i s acting like  of a  a reservoir.  Since pools  Prom a p r a c t i c a l p o i n t o f v i e w t h i s boundary between a channel  channel  are prominent  d u r i n g f l o o d s , i t seems  i s a feasible  Q/Q^.  assumption.  segment and t h e a d j o i n i n g  c a n be s h i f t e d d u r i n g a s u r g e  h a v e i d e n t i c a l A-Q  dif-  computation.  t o e x p e c t d t o be an d e c r e a s i n g f u n c t i o n o f  reasonable  reservoir  It is  i n d i c a t e s how much o f a g i v e n  l o w f l o w s and t e n d t o d i s a p p e a r  The  alone.  t h a t n be i n d e p e n d e n t o f Q b e c a u s e i t w o u l d be  The reach  t o be a f u n c t i o n o f 1/W^  computation  as t h e y  relations.  c o m b i n e d e f f e c t o f I n e q u a l i t y 6 . 2 3 a n d t h e above  The  a s s u m p t i o n on t h e r e l a t i o n b e t w e e n 6 a n d Q i s somewhat u n f o r t u n a t e , s i n c e (6.23) i n d i c a t e s a need f o r l a r g e r r e s e r of d  v o i r s w i t h i n c r e a s i n g flow while the proposed decrease w i t h Q has t h e o p p o s i t e e f f e c t . met  The two c o n d i t i o n s c a n be  s i m u l t a n e o u s l y by d e c r e a s i n g t h e t i m e  step of the  n u m e r i c a l i n t e g r a t i o n as -Q i n c r e a s e s . To  gain a c l e a r e r p i c t u r e of the e f f e c t s  o f changes  i n n a n d i n d on t h e computed d o w n s t r e a m f l o w , t h e s u r g e test  shown i n F i g u r e 15 was r o u t e d t h r o u g h  Creek reaches The  results  the three  w i t h v a r i o u s assumed c o m b i n a t i o n s  a r e shown o n F i g u r e s 24 a , b , and c.  Blaney  o f n and d . They  i n d i c a t e t h a t g o o d f i t c a n be a c h i e v e d w i t h a w i d e r a n g e o f n- d  combinations.  I f the reach  i s d i v i d e d i n t o many  133 1200  | 00  13°°  4  r  Gauge I (ft)  •  1.25-  observed N oooo  N  R  R  = L/(40 = L/(IO  W ) D  W) D  1.2  15.3 Ip  If  1/  Gauge 3 (ft) 15.25  jj © I  1°  0  1  Vo \  o  /  15.2 time  12 00 Blaney  1400  1300 Creek,  Oct. 13,1968.  Q approx. I m s '  VARIABLE NUMBER OF RESERVOIRS  3  -  AT <J = 0.1 Fig. 24a  134  1400  I300  1200  r Gauge I (ft)  -  1.25  observed n = L/(40W ) + n = L/(20 W ) o9oo n = L/(IOW )  1.2  15.3 Gauge 3 (ft) 15.25  \ 0 \\ \\  7°  \  '9 /o  15.2 time  —  4.9 /+/© */  —-"\Y n  Gauge 4 (ft)  ©  v  V  o  u o  \\°  4.8 1200 Blaney  r A,  f° h  /A «°  I300  Creek,  Oct. 13,1968.  I400  Q approx.  Im3s-'  VARIABLE NUMBER OF RESERVOIRS AT (J = 0.28 Fig. 24b  135  1.3  r  Gauge 1  (ft) 1.25  observed - — - n = L/(40W ) D  OGGO  n  =  L/(|  0  W [ )  )  1.2  15.3 —vOO©  Gauge 3  \  (ft) 15.25  \  ' sT  \ b ^ v.  / /  7  15.2 time  Gauge 4 (ft)  oo  l oo  j2  Blaney  I400  3  Creek,  Oct. 13,1968.  Q approx. I m  VARIABLE NUMBER OF RESERVOIRS  3  s  -1  AT (p = 0.7 Fig. 24c  136  reservoirs length  (n l a r g e ) ' they  (cf l a r g e )  have t o cover  and v i c e v e r s a .  Since  a large part computing  of the  time  i n c r e a s e s more than, l i n e a r l y w i t h n due t o (6.23) a n d t h e increase  i n computing time w i t h  small, i t i s obviously possible.  The p r a c t i c a l  a "1/Wp" c r i t e r i o n  d i s relatively  a d v a n t a g e o u s t o keep n as s m a l l as  The s u r g e t e s t d a t a  lower l i m i t .  decreasing  forn  g i v e no c l e a r i n d i c a t i o n o f a  s o l u t i o n a p p e a r s t o be t o s e l e c t  that r e s u l t s i n a single r e s e r v o i r  f o r the s h o r t e s t reaches o f i n t e r e s t , which w i l l s c a l e a t w h i c h one i s w o r k i n g .  n = 1/40W is  As c a n be s e e n f r o m T a b l e 2  ... 6.25  D  a s u i t a b l e assumption f o r the present  s e to f data.  The s e c o n d p a r a m e t e r , 6 , was e s t i m a t e d error, using resulting  be  d - q r e l a t i o n i s n a t u r a l l y only  but  storage  obtained  valid  The i n combin-  As i n t h e c a s e o f t h e k i n e m a t i c  waves  d i s p e r s i o n , the free parameter d could  again  with a non-linear  l e a s t s q u a r e s f i t ( S e c t i o n 6.2.4),.  t h e amount o f c o m p u t i n g t i m e r e q u i r e d w o u l d be e v e n  greater here. not  by t r i a l a n d  a l l t h e surge t e s t s o f Blaney Creek.  a t i o n w i t h '(6.25). with  d e p e n d on t h e  A s i m u l t a n e o u s f i t o f n and d would  lead to significant  results,  s i n c e t h e minimum, o f t h e  s q u a r e d r e s i d u a l s a p p e a r s t o be a n e l o n g a t e d more o r l e s s i n a d i a g o n a l  probably  d i r e c t i o n across  valley,  lying  t h e d -n p l a n e .  137  .3 .2.1.001  .1  .01  1.0  q FIGURE 25.  Figures  THE ROUTING PARAMETER  26 a, b , and c show s e v e r a l  between computed and o b s e r v e d other streams,  The  Since  o f observed  o f t h e gauge r a t i n g  are the r e s u l t  to the r e s u l t the surge  and f o r  t h e 6 -q  3  out i n S e c t i o n 6 . 1 . 2 , neglecting  and com-  t h a n o f any d e f i -  this  At v e r y  i s again underestimated. to achieve a correct  l e a d s t o e x c e s s i v e damping.  dynamic waves.  evidence, p a r t i c u l a r l y  between o b s e r v e d  obtained with Equation 6.17.  celerity  this  are not too w e l l  The c l o s e n e s s o f f i t i s com-  an i n c r e a s e i n 6 i t i s p o s s i b l e time but  curves  of t h i s , rather  i n t h e r o u t i n g method.  stage  arrival  for deriving  Creek  and computed H - T c u r v e s .  some o f t h e d i f f e r e n c e s  surges  parable  f o r Blaney  comparisons  p r o g r a m "SNLR" c o n v e r t s d i s c h a r g e t o s t a g e f o r  several  ciency  low  w h i c h were n o t u s e d  comparison  defined, puted  surges  typical  D  of Figure 25.  relation  direct  FOR n = 1/40W  effect There  i s probably  of Brockton  surge  As p o i n t e d  the r e s u l t of  i s , however, some  i n the case  With  slight  Creek  (Figure  16)  13.8  9.80  A/1  9.78 9.76 9.74 9.72 Gauge I (ft) 4.06 4.04 4.02 4.00 3.98 3.96 Gauge 2 (ft) 4.8 4.6 4.4 4.2 30  40 50  15OO  10 20  30 40 Gauge  August Q^O.OI m  3  15, 1 9 6 7  s" , A Q - 0 . 0 0 1 1  40 50 £ 0 0 10 3 (ft)  Sept. 14, 1968  0.05, A Q — 0 . 0 1  COMPUTED AND OBSERVED SURGES, BROCKTON CREEK Fig. 26a  139  1.4  .55 .50]  .45  1.3  .40 Gauge I (ft) 12.33 observed  15.30  12.31  15.28  12.29  15.26  /^computed  15.24  12.27 _j  15.22-1  12.25  -T  r  Gauge 3 (ft) 4.60 4.9  4.58 4.56  4.8  4.54 4.52-1 IO  II  00  00  j oo I 3  00  2  -T  r-  20 30 40 50 j^oo 10 20 30 Gauge 4 (ft)  May Q~0.I2 m  19, 1967 3  s" , A Q-0.05 1  October 13, 1968 Q ~ 1.2, A Q -0.15  COMPUTED AND OBSERVED SURGES, BLANEY CREEK Fig. 26b  mo .34  2.4  .33  2.2  K32 1  -|  1  1  1  r  ~i  2.0  r-  - i — . — • — • — i — - — r  Discharge at outlet of Marion  Lake  (m s ) 3  _l  .30 .29  computed^  .28 "  I  1  Gauge  2 (ft)  1.90  .38-  1  l oo  1.854  ''  .371  1  1  1  1  I5  4  1 0 0  1  1  1  1  1  r-  , 00 6  1.80-1 n  50  Gauge  1  •  | | 0 0 10  3  30  '  40  '  50  1  |200  6 (ft) Nov. 29, 1968  July 28, 1967 Q~0.33m s-', A Q - O . O I  20  '  Q  ~ 2.2 ,  AQ  -0.3  COMPUTED AND OBSERVED SURGES, PHYLLIS  CREEK Fig 26 c  141 that  the t r u e Q - A r e l a t i o n  paper,  probably  would r e s u l t small  due  i n higher values  major d i f f e r e n c e  cn  channels  and  is  t h a t the  former  reservoirs  area at  log  zero  flow,and  this  f o r the k i n e m a t i c  celerity  c at  inflow.  case  between, t h e and  makes no  i n p u t to the r e a c h  which,In the local  to a r e s i d u a l  on d o u b l e  discharges. The  surge  i s somewhat c u r v e d  and  r o u t i n g method based,  r o u t i n g based  assumption proceeds  about with  of a r u n o f f model,permits  on E q u a t i o n  6.17  the  the  shape o f  finite the  time  steps,,  addition  of  142  7  CONCLUSIONS  7.1  The  H y d r a u l i c s of Tumbling  The  objectives  the I n t r o d u c t i o n as: steady  and  unsteady  of t h i s  tumbling  basin data.  ficant  has  i n a r u n o f f model,are  functions  A = f  The  data i n d i c a t e  field  (Q)  which  stated govern  can be  related  to  limitations,  basis  simple  channel  flow,which  completely  these  e x p o n e n t i a l s of the  of s i m i l a r i t y  parameters  a  considered  "readily  highly  A  and  significant  r e g r e s s i o n models. which i s i m p l i c i t The equations  two  b  are  available".  The  channel  network.  f u n c t i o n s can be  approxi-  A = a  A  A  Q  .  On  the  can  T h i s i s c o n f i r m e d by  the  appearing  methods f o r e x t e n d i n g  forming  flow r o u t i n g  are  the  process,  shown t o be  i n f l o w s can be  shapes except  i n those  capable  unknown.  steady  flow  capable  t h e downstream p r o p a g a t i o n o f s t e p - l i k e channel  be  (1969)  i n Day's  channel  the  two  which  o f s t e p s , b o t h methods a r e  hydrograph  form  p h y s i c s of the  proposed  S i n c e more c o m p l i c a t e d a series  the  i n Day's r e g r e s s i o n e q u a t i o n s , r e m a i n s  to unsteady  reproducing  be  signi-  d e s c r i b e d by  depend on b a s i n p a r a m e t e r s  correlations  readily to  c o n s i d e r a t i o n s I t i s shown t h a t A  these  accomplished.  b  mated by  in  ( i i ) expressing  f o r a l l segments.of the that  are  laws t h a t  certain  been  aspects of steady  the  f l o w , and  Within  d i s c u s s e d below, t h i s The  investigation  (i) finding  laws i n terms o f p a r a m e t e r s available  Flow  of  surges.  approximated  by  of r o u t i n g a l l  c a s e s where t h e  non-linearity  143  of  the channel response The  d a t a impose  None o f t h e t e s t reaches Placid because  reaches  Their  Brockton  is a first  steady  Creek  The r e s u l t s  application  appear  on l a r g e  Figure  2.  Brockton  t o almost  such  as t h e 1:2400 map  of  The f i r s t  s t u d y may be a p p l i e d .  channels The  have t o be i n c l u d e d  conclusions are f u r t h e r  large  streams  it  i s q u e s t i o n a b l e whether the unsteady the r u l e s  (i)  "tumbling"  turbulent  i s a twofold regional The r e l a t i o n s  relations  channel performance  field  work and may  over  by t h e l a c k o f The f l o w  flow models,  channel  and & ,  on t h e d a t a : and d r a i n -  T h i s c a n be overcome by  between DA and W-^, from  parti-  flow.  limitation  factors.  regime  l o n g r e a c h e s and  between c h a n n e l p a r a m e t e r s  a r e a depend on c l i m a t i c  establishing  streams.  second  phase.  f o r determining the parameters  t o o r d i n a r y , rough There  the  i s rarely  o r d e r and most  limited  in  age  used i n  t o which the r e s u l t s  i n the land  flow t e s t s  apply  on t h e l a r g e r  limit  unsteady  cularly  as t h e y  The c h a n n e l n e t w o r k s a p p e a r i n g on 1:50,000 NTS lower  order  by l o g g i n g  channel networks  maps r e p r e s e n t t h e a p p r o x i m a t e this  choked  are t h e r e f o r e not s u i t a b l e  complete  s c a l e maps  markedly  and i s e s s e n t i a l l y  i s severely  o f the study  and o n l y t h r e e  1-2 and 2-3, and differs  at t r e e - l i n e  Creek  on the. c o n c l u s i o n s .  order channel  flow behaviour  lies  free while P l a c i d  slash. for  a number o f l i m i t a t i o n s  r e p r e s e n t s m a l l streams; 1-2.  debris  leads to the formation of a bore.  and S.  t h e r e f o r e n o t always  and t h e n  predicting  This requires be  feasible.  some  144  (ii) ing  Climate  vegetation  on  and c a n t h e r e f o r e have a c o n s i d e r a b l e  the performance  logging 7 •2  and e l e v a t i o n a r e t h e m a i n f a c t o r s  of the smaller  and c l e a r i n g o p e r a t i o n s  Basin  effect  streams. . I t f o l l o w s  are of s i m i l a r  that  importance.  Linearity  B o t h r o u t i n g models d e v e l o p e d the  determin-  non-linear  response  6 show t h a t  i n Section  o f a c h a n n e l segment i s l a r g e l y  a  c o n s e q u e n c e o f t h e dependency between c and Q, w h i c h , f o r the  kinematic  approximation,is p o s i t i v e exponential since b c = dQ/dA «x v and v •= a Q . The s u r g e t e s t s do however m m v &  indicate dQ/dA  a c o n s i s t e n t tendency  (Figures  interpreted  towards  c values  26 a, b and c) a t low f l o w s ,  as a t r e n d  towards  linear  l a r g e r than  w h i c h may be  response  of the channel  s y s t e m a t low f l o w s . That is  flows  show no t e n d e n c y  not s u r p r i s i n g s i n c e the only  advanced as  the high  f o r such a t r e n d ,  the stream  applicable  i n steep  One may degrading  channels  overflow  mountainous  i n flow  the f l o o d  plain,  area i s rarely  basins.  even a r g u e t h a t , s i n c e t h e b e d m a t e r i a l o f  tumbling  flow  c h a n n e l s moves o.nly u n d e r extreme  and s i n c e  resistance  t o the f l o w i n g water  stronger  onto  linearity  which i s g e n e r a l l y  the r a p i d i n c r e a s e  conditions  be  reason  towards  a m o b i l e bed would p r o b a b l y  non-linear  trends  (Kellerhals, during  offer  1967),  lower  there  extreme r u n o f f  flood  could  events.  145 7.3  Towards an O p e r a t i v e  be  an o p e r a t i v e  considered  channel r u n o f f model, but both can  as b u i l d i n g b l o c k s  model c a n now be a s s e m b l e d . this  after  completion  what r e m a i n s  like  (6.17)  choose a p u r e l y  all  the  A mathematical  have t o be d e v i s e d channel parameters  (iv)  6.9 i s t o be  s o l u t i o n f o r step-  s h a p e s o r one m i g h t approxi-  on t h e x - t p l a n e s  of  (1969)  i n t h e program formulation  i n a computer. appears  b i n a t i o n with  areas  "SNLR".  The model r e c e n t l y  t o be a d a p t a b l e  to t h i s  network  pro-  purpose.  o f the land-phase  may be a c c e p t a b l e , records.  with  representation of  have t o be f o u n d .  meteorological  change i n d  f o r the drainage  proper  A suitable representation  source  on n o n - l i n e a r r e s e r v o i r s  The g r a d u a l  to permit  t h e channel system w i l l  a few s m a l l  grid  operational.  t o be i n c o r p o r a t e d  p o s e d by S u r k a n  to  n o t e on  s o l u t i o n b a s e d on s u c c e s s i v e  The r o u t i n g method b a s e d  (iii) will  the present  to unspecified input  numerical  c l o s e r to being  Q remains  a brief  segments.  (ii) is  study,  runoff  to pursue  programming p r o b l e m r e m a i n s  to Q (x,t) i n a f i n i t e  channel  the w r i t e r plans  I f t h e r o u t i n g method b a s e d on E q u a t i o n  One c a n e i t h e r a d o p t  input  mations  Since  of the present  be u s e d , a c o n s i d e r a b l e  solved.  out o f which a channel  t o be done may be i n o r d e r .  (i) to  Model  o f t h e two r o u t i n g methods o f S e c t i o n 6  Neither represents  Channel Runoff  input  Hydrographs o f p o s s i b l y i n com-  146 (v) W i t h dominant extend  increasing basin size,  over the  I t i s important,  t h e r o u t i n g methods t o l a r g e r  sidered  i n the p r e s e n t It  will  A(Q)-equation  streams  from  have t o be  therefore,  than those  to  con-  study.  p r o b a b l y become n e c e s s a r y  t r a c e r methods. will  land phase.  t h e c h a n n e l p h a s e becomes  extensive r i v e r  surveys  Dispersion coefficients established  through  t o o b t a i n the rather  and wave  controlled  than  basic with  celerities  releases  from  s e v e r a l m a j o r dams. Only to  pass  approach leave  after  a final  completion of a l l t h i s  judgement  to r u n o f f .  little  will  i t be  on t h e u s e f u l n e s s o f t h e  However, t h e r e s u l t s  room f o r doubt  that  i t will  presented be  possible two-phase here  positive.  147  8.  BIBLIOGRAPHY  A a s t a d j J . and Sdgnen, R. 1 9 5 4 . " D i s c h a r g e Measurements byMeans o f a S a l t S o l u t i o n . , ' t h e R e l a t i v e S a l t D i l u t i o n Method'," I n t e r n a t i o n a l A s s o c i a t i o n o f S c i e n t i f i c Hydrology. P u b l i c a t i o n No. 3 8 . Assemble I n t e r n a t i o n a l e d ' H y d r o l o g l e de Rome. Tome I I I . A b d e l s a l a m , W. W. , 1 9 6 5 . Flume S t u d y o f t h e E f f e c t o f Conc e n t r a t i o n and S i z e o f Roughness E l e m e n t s on Flow i n H i g h Gradient N a t u r a l Channels. Ph.D. T h e s i s , U t a h S t a t e University. Ackers, Peter, 1 9 5 8 . "Resistance of F l u i d s Flowing i n C h a n n e l s and P i p e s , " D e p a r t m e n t o f S c i e n t i f i c and I n d u s t r i a l R e s e a r c h , Hydr. R e s e a r c h S t a t i o n , Hydr. R e s e a r c h P a p e r No. 1 , London. Al  K h a f a j i , Abbas N a s s e r , 1 9 6 1 . The Dynamics o f T w c - D l m e n s i o n a l Flow i n S t e e p N a t u r a l S t r e a m s . Ph.D. T h e s i s , U t a h State University.  Amorocho, J . , and H a r t , W. E . 1 9 6 4 . "A C r i t i q u e o f C u r r e n t Methods i n H y d r o l o g i c Systems I n v e s t i g a t i o n s , " A m e r i c a n G e o p h y s i c a l U n i o n , T r a n s a c t i o n s V o l . 4 5 , No. 2 , pp. 307-321. ?  A r g y r c p o u l o s , P r a x i t e l i s A., 1 9 6 5 - " H i g h V e l o c i t y Flow i n I r r e g u l a r N a t u r a l Streams," I n t e r . Assoc. f o r H y d r a u l i c . Research, 1 1 t h Meeting, L e n i n g r a d , Paper 1 - 2 6 . Barr,  D a v i d I . H. - 1 9 6 8 . "Discriminating Formulation of n-term N o n - D i m e n s i o n a l F u n c t i o n a l E q u a t i o n s f r o m ( n + 1 ) t e r m D i m e n s i o n a l l y Homogeneous E q u a t i o n s w i t h P a r t i c u l a r R e f e r e n c e t o I n c o m p r e s s i b l e V i s c o u s Flow," I n s t i t u t i o n o f C i v i l E n g i n e e r s , P r o c . , V o l . 3 9 , pp. 3 0 5 - 3 1 2 .  Barr,  D a v i d 1. H., and H e r b e r t s o n , J o h n G. 1968. " S i m i l i t u d e T h e o r y A p p l i e d t o C o r r e l a t i o n o f Flume Sediment T r a n s p o r t D a t a , " Water R e s o u r c e s R e s e a r c h , Vol. 4, No.2,p.307.  Church,Michael.1967. "Observations of Turbulent D i f f u s i o n i n a N a t u r a l Channel," Canadian J o u r n a l o f E a r t h S c i e n c e s , V o l . 14. Church,: M. . and K e l l e r h a l s , R. 1 9 6 9 . 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" H i g h M o u n t a i n .Streams ^ E f f e c t s o f Geol o g y on C h a n n e l C h a r a c t e r i s t i c s and Bed M a t e r i a l , " New M e x i c o , S t a t e B u r e a u o f M i n e s and M i n e r a l R e s o u r c e s , Memoir No. 4 . M i r a j g a o k e r , A. G., and C h a r l u , K.L.N., S e p t . 1 9 6 3 . "Natural Roughness E f f e c t s i n R i g i d Open C h a n n e l s , " J o u r n a l o f t h e H y d r a u l i c s D i v i s i o n , ASCE, V o l . 8 9 , No. H Y 5 , P r o c . P a p e r 3630~ pp. 2 9 - 4 4 . M o r i s a w a , M. 1957"Accuracy of D e t e r m i n a t i o n of Stream L e n g t h s f r o m T o p o g r a p h i c Maps," A m e r i c a n G e o p h y s i c a l U n i o n T r a n s a c t i o n s , V o l . 3 8 , No. 1. 0 s t r e m , G., 1 9 6 4 . "A Method o f M e a s u r i n g Water D i s c h a r g e i n T u r b u l e n t S t r e a m s , " G e o g r a p h i c a l B u l l e t i n No. 2 1 , G e o g r a p h i c a l B r a n c h , D e p t . o f Mines and T e c h n i c a l S u r v e y s , Ottawa.  150  O v e r t o n , D. E . , 1 9 6 7 . " A n a l y t i c a l S i m u l a t i o n of Watershed Hydrographs from R a i n f a l l , " P r o c e e d i n g s of the I n t e r n a t i o n a l H y d r o l o g y Symposium, F o r t C o l l i n s , V o l . 1. P e t e r s o n , D. F. and Mohanty, P. K., i 9 6 0 . "Flume S t u d i e s i n S t e e p , Rough C h a n n e l s , " J o u r n a l o f t h e H y d r a u l i c s D i v i s i o n , P r o c e e d i n g s of the American S o c i e t y of C i v i l E n g i n e e r s , V o l . 8 6 , No. HY9, pp. 5 5 - 7 6 . P i l g r i m , D. H., 1 9 6 6 . " R a d i o a c t i v e T r a c i n g of Storm R u n o f f on a S m a l l C a t c h m e n t , " J o u r n a l o f H y d r o l o g y . Vol. 4, pp. 2 8 9 - 3 2 6 . R e p l o g l e , J . A. e t a l . , 1 9 6 6 . "Flow Measurements w i t h F l u o r e s c e n t T r a c e r s , " J o u r n a l of the H y d r a u l i c s Division, American S o c i e t y of C i v i l E n g i n e e r s , V o l . No. HY5, P r o c . P a p e r 4 8 9 5 , pp. 1-15.  92,  S c h e i d e g g e r , A. E . , 1 9 6 6 . " E f f e c t o f Map S c a l e on S t r e a m Orders," B u l l e t i n of the I n t e r n a t i o n a l A s s o c i a t i o n of S c i e n t i f i c Hydrology, V o l . 11, No. 3. S c h e u e r l e i n , Helmut, 1 9 6 8 . "Der R a u h g e r i n n e a b f l u s s , " Bericht No. 14 der V e r s u c h s a n s t a l t f u r Wasserbau der T e c h n i s c h e n H o c h s c h u l e Munchen, O s k a r V. M i l l e r I n s t i t u t . Seddon, J . A., 1 9 0 0 . American S o c i e t y  "River Hydraulics," Transactions, o f C i v i l E n g i n e e r s , V o l . 4 3 , pp. 179-  S t e w a r t , J o h n H., and L a M a r c h e , V a l m o r e , C., 1967. " E r o s i o n and D e p o s i t i o n P r o d u c e d by t h e F l o o d o f December 1 9 6 4 on C o f f e e C r e e k , T r i n i t y C o u n t y , C a l i f o r n i a , " United States G e o l o g i c a l Survey, P r o f e s s i o n a l P a p e r , No. 422-K. Sugaware, M., 1 9 6 7 . " R u n o f f A n a l y s i s and Water B a l a n c e A n a l y s i s By a S e r i e s S t o r a g e Type M o d e l , " P r o c e e d i n g s o f t h e I n t e r n a t i o n a l H y d r o l o g y Symposium, F o r t C o l l i n s , Vol. 1. S u r k a n , A. J . 1969. " S y n t h e t i c Hydrographs: E f f e c t s of Network Geometry." Water R e s o u r c e s R e s e a r c h , V o l . 5 , No. 1 , pp. 1 1 2 - 1 2 8 . . T a y l o r , G. I . , 1 9 5 4 . "The D i s p e r s i o n Flow Through a P i p e , " P r o c e e d i n g s o f London, V o l . 2 2 3 -  of Matter i n Turbulent of the Royal S o c i e t y  T h a c k s t o n , E. L. et_ a l . , 1 9 6 7 . "Least Squares E s t i m a t i o n of M i x i n g C o e f f i c i e n t s , " J o u r n a l of the S a n i t a r y E n g i n e e r i n g D i v i s i o n , American S o c i e t y of C i v i l E n g i n e e r s , Proceedings, Vol. 9 3 , No. SA 3 , PP47-58.  151 T h a c k s t o n , E . L. and K r e n k e l , P. A., 1 9 6 7 . "Longitudinal M i x i n g i n N a t u r a l Streams," J o u r n a l of the S a n i t a r y E n g i n e e r i n g D i v i s i o n , American S o c i e t y o f C i v i l E n g i n e e r s , V o l . 9 3 , No. SA 5 , pp. 6 7 - 9 0 . W i l s o n , J . P., 1 9 6 8 . " F l u o r o m e t r i c P r o c e d u r e s f o r Dye T r a c i n g , i n T e c h n i q u e s o f Water R e s o u r c e s I n v e s t i g a t i o n s o f t h e U. S. G e o l o g i c a l S u r v e y , C h a p t e r A 1 2 , Book 3 . Y a l i n , M. S., J a n . 1 9 6 6 . "A T h e o r e t i c a l Study o f S t a b l e A l l u v i a l Systems," G o l d e n J u b i l e e Symposium, C e n t r a l Water and Power R e s e a r c h S t a t i o n , Poona.  152 PHOTOGRAPHS  PHOTOGRAPH 2. PLACID CREEK, ALONG REACH P I 3 - 4, LOOKING DOWNSTREAM. TYPICAL LOG JAM IN FOREGROUND.  PHOTOGRAPH 4. BLANEY CREEK, AT B l GAUGE 4, LOOKING UPSTREAM FROM BRIDGE,  PHOTOGRAPH 5. PHYLLIS CREEK, AT PH GAUGE 2, LOOKING DOWNSTREAM. STAGE RECORDER AT RIGHT.  PHOTOGRAPH 6. PHYLLIS CREEK, AT PH GAUGE 4, LOOKING UPSTREAM.  PHOTOGRAPH 7. BARNSTEAD CONDUCTIVITY BRIDGE.  155  PHOTOGRAPH 8. VOLUMETRIC GLASS WARE FOR SALT DILUTION TESTS.  PHOTOGRAPH 9 . VATS, P A I L , AND STIRRING ROD FOR SALT DILUTION TESTS.  156  PHOTOGRAPH 10 EQUIPMENT FOR RHODAMINE WT SLUG INJECTION TEST  PHOTOGRAPH 1 1 . RECORDING CONDUCTIVITY BRIDGE, WITH ELECTRONIC INTERVAL TIMER.  PHOTOGRAPH 12. CONTROL STRUCTURE AT THE OUTLET OF BLANEY THREE FLASHBOARDS IN PLACE.  LAKE.  PHOTOGRAPH 1 3 . TIMBER CRIB DAM AT OUTLET OF MARION LAKE, WITH TWO ADDITIONS IN PLACE FOR A DOWN-SURGE.  158  159  i  f  -  160  APPENDIX COMPUTER PROGRAMS WITH OPERATING INDSTRUCTIONS PRINTOUT, AND PLOTS.  L I S T OP CONTENTS NACL  Source l i s t i n g Sample p l o t o f r a t i n g Sample p r i n t o u t  161 curve  DQV  Source Sample  listing printout  TAILEX  Source l i s t i n g Sample p r i n t o u t Sample p l o t s w i t h e x a m p l e f o r d e t e r m i n a t i o n o f A, B, and D  QVEL .  Source l i s t i n g , i n c l u d i n g numerical integration Three sample outputs  PLOTGA  Source l i s t i n g Sample p l o t s , w i t h a n d w i t h o u t  168  subroutines f o r  -extension  170  176  185  LOGRE  Source l i s t i n g , i n c l u d i n g three s u b r o u t i n e s P r i n t o u t and p l o t s f o r a l l 13 t e s t r e a c h e s  189  PD  Source l i s t i n g , i n c l u d i n g Sample p r i n t o u t  two s u b r o u t i n e s  249  SNLR  Source l i s t i n g , i n c l u d i n g Sample p r i n t o u t  one s u b r o u t i n e  253  C C C C C C C C C _£ C C C . C C C C C C C C _C C C C C C _C C C C C C  FORTRAN /360 MAIN PROGRAM CALLED NACL ', WHICH CONVERTS TIME-CONDUCTIVITY DATA TO TIME-CONCENTRATION DATA. TIME IN MINUTES AND SECONDS I S CONVERTED T O MINUTES AND DECIMALS. INPUT CONTRQL . CARDS _ „ . I ONE CARD PER RUN, NO. OF DATA SETS, KTOT, ( 1 2 ) 2 ONE PER DATA SFT . NO OF DATA POINTS, K, 1 1 3 J ARRIVAL TIME OF TRACER WAVE, T S T , ( F 7 . 2 ) TITLE_OR RUN I DENRIFICAT I ON NO. (7A4 L _ ,„. PARAMETERS OF GAMMA EXTENSION, I F DESIRED, LOG A, B, D , ( 2 X , 3 E 1 0 . 5 ) . LOG A I S CONVERTED TO A. 3 ONE PER $TET OF DATA. ; NO. OF POINTS ON THE RATING CURVE, N, ( 1 3 ) DILUTION RESULTING FROM 10 CC OF SECONDARY SOLUTION , IN RATING ...TANK , D l L 1 0 , ( F10.0) RATING TANK TEMPERATURE, TEMP, ( F 1 0 . 0 ) BACKGROUD READING AT START OF TEST, BACKST, ( F 1 0 . 0 ) BACKGROUND READING AT END OF TEST OR BLANCK I F IT IS EQUAL TO BACKST, BACKND, ( F 1 0 . 0 ) PARAMETER NPLO, WHICH SHOULD BE .GT. 0, I F NO PLOT . . DESIRED, j 13) .' .... PARAMETER NPUNCH, TO BE SET .GT. 0, IF NO PUNCHED OUTPUT DESIRED, ( 1 3 ) DATA CARDS OF STREAM MEASUREMENTS, K CARDS PER DATA SET. CONDUCTIVITY READINGS YC,TIME IN MINUTES AND SECONDS FROM I N J E C T I O N , XT, ( 2 F 9 . 3 ) DATA CARDS OF RATING CURVE, N CARDS PER SET AMOUNT OF SECONDARY SOLUTION IN RATING TANK IN CC, CC, CONDUCTIVITY READING, READ, ( 2 F 9 . 3 ) :  C C  OUTPUT P R I N T O U T OF I N P U T DATA P R I N T O U T . O F C O N V E R T E D D A T A , W I T H C O N C E N T R A T I O N . I N ..PPM OF T H E P R I M A R Y S O L U T I O N . OPTIONAL, P U N C H E D DATA C A R O S C O N T A I N I N G C O N C E N T R A T I O N Y C , AND T I M E X T , AS R E Q U I R E D F O R P R O G R A M DQV, (2F9.3), PLOT OF R A T I N G C U R V E .  c c c c c c 1 2 '  ;  > "-3  5  7 16 19  '  CALL PLOTS DIMENSION XT ( 2 0 0 ) , YC ( 2 0 0 ) , . T I T L E FORMAT ( 1 3 , F 7 . 2 , 7 A 4 , 2 X , 3 E 1 0 . 5 ) FORMAT ( 2 F 9 . 3 ) FORMAT ( 1 3 , 4 F 1 0 . 0 , 2 1 3 )  (7) ,  CC(20)  ,R FAD  (20)  FORMAT!. 8 H 0 R A T I N G , 4 X , 4HSTEP, 9X ,2HCC, 8X,. THREADING ,/ K13X , 12 , 7X, F 6 . 0 , 4 X , F9.4 ) ) FORMAT ( 1 2 ) FORMAT (18H1C0NTR0L CARD 1 = / I X , 1 3 , 2X, F 7 . 2 , 7A4, 1 2X, 3E12.6 / 18H0C0NTR0L CARD 2 = / . I X , 1 2 , 2X, 4 F 1 2 . 2 , 2 3X, 1 2 , 3X, 12 ) FORMAT ( 22H0CONVERTED FINAL DATA . .. ).  32  c  V, C  c C  r  c  f  c 9  FORMAT(5H0DATA , 4X,2HN0,8X,2HXT , 7X , 7HREA0ING • / 1( 9X , 12 ,5X, F7.2 , 2X ,F10.4 ) ) LOOP FOR SETS READ ( 5 , 7 ) KTOT DO 8 KSET = 1, KTOT READ DATA READ(5,1) K IF ( A .NE. READ(5,3) N IF ( BACKND READ ( 5 , 2 ) READ (5,2)  , TST, T I T L E , A, B, D 0.0 ) A = EXP (A) » OIL 10 , TEMP , BACKST, BACKND, NPLOT, NPUNCH . L E . 0.0 ) BACKND = BACKST ( YC ( I ) , XT ( I ) , I = I , K ) . . .. . (CC ( I ) , R E A D d ) , I = 1,N)  PRINT DATA WRITE (6,16) K, TST, T I T L E ,A,B,D, N, DIL10, TEMP, 1 BACKST, BACKND, NPLOT, NPUNCH WRITE (6,32) (I , XT ( I) , YC ( I ) , I = 1, K ) WRITE ( 6 , 5) ( I , C C ( I ) , R E A D d ) , 1 = 1 , N ) CONVERT SECONDS TO MINUTES DO 9 I =1 , K IXT =XTd) . TMIN .... =IXT . X T ( I ) =TMIN + ( X T ( I ) - T M I N ) / 0.6  C  CONCENTRATION RATING CURVE  10  CONVERT C C ( I ) TO CONCENTRATION IN PPM RI = R E A D d ) DO 10 I = 1 , N READ ( I ) = READ(I) - RI CCd) = ( C C d ) /(10.0 * OIL 1 0 ) ) * 10.0E+5  c c. c c  12 C C  11  L...  .  COMPUTE B OF REGRESSION LINE = o.o . ;. : .. = 0.0 00 12 I = It N SYX = C C d ) * REAO(I) + SYX SXX =READ(I)**2 + SXX BB = SYX / SXX . ' TION ADJUST Y C d ) TO A ZERO BACKGROUND AND CONVERT TO CONCEMTRADBACK =(BACKST - BACKND ) / (XT(K) - T S T ) OD 11 1 = 1 , K IF ( X T U ) . L E . TST ) Y C d ) =0.0 * DBACK IF ( X T ( I ) .GT. TST ) Y C d ) = Y C d ) - BACKST + ( ( X T d ) - T S T ) YCd ) = BB* Y C d ) ,. WRITE ( 6 , 19 ) WRITE (6,32) (I XT(I).3, YC ( I ) , I = 1, K ) IF ( NPLOT .NE. 0 ) GO TO 17  SYX SXX  C  c  PLOT RATING CURVE ; . CCMAX =8B* READ(N)  1  ....  163 C A L L S C A L E ( R E A D , N , 7 . 0 , R X M I N , R D X , 1) C A L L S C A L E { CC , N , 9 . 0 ,CYMIN , C D Y , 1) CCMAX = (CCMAX - CYMIN) / CDY CALL AXIS ( 0 . 0 , 0 . 0 , 7HREADING , - 7 , 7.0 , 0 . 0 , RXMIN,RDX ) CALL A X I S I 0 . 0 , 0 . 0 , 2 0 H C O N C E N T R A T I O N I N P P M , + 2 0 , 9 . 0 , 9 0 . 0 , 1 CYMIN, CDY) CALL .SYMBOL..:.(. 1 . 0 , 9 . 5 , 0 . 2 1 , T I T L E . , 0 . 0 , . . 2 8 ) CALL S Y M B O L ( 1 . 0 , 9 . 0 , 0 . 2 1 , 7 H T E M P . = , 0 . 0 , 7 ) CALL N U M B E R ( 2 . 4 , 9 . 0 , 0 . 2 1 , T E M P , 0 . 0 , 1 )  CALL  SYMBOL ( 3 . 5 , 9 . 0 , 0 . 2 1 , 4HB8 = , 0 . 0 , 3 C A L L NUMBER ( 4 . 6 , 9 . 0 , 0.21 ,BB , 0 . 0 , 4 ) DO 1 3 I = 1 " N " • CALL...SYMBOL... i READ( I ) , C C C I ) , 0 . 14 . . , 4 , 0 . 0 CALL P L O T ( 0 . 0 « 0 . 0 , + 3 ) CALL PLOT { R E A D { N ) , C C M A X , + 2 )  )  .  t  v  CALL PLOT t 9.6 , 0 . 0 , - 3 CONTINUE  -1  )  )  PUNCH'. DATA .CARDS .. ... _ IF .< NPUNCH <, N E . 0 ) GO T O 1 8 WRITE « 7 » 1 J K » 1 S T , T I T L E , A , , B , D WRITE < '7,2) ( Y C U ) , X T ( I ) , 1= 1,K ) CONTINUE  CALLS _ T n _ FITTING. AND P L O T T I N G . R O U T I N E S . ... _ THE CALL CARDS FOR N U M E R I C A L I N T E G R A T I O N O F T H E C - T C U R V E FOfl PITTING A G A M M A - D I S T R I B U T I O N E X T E N S I O N G O I N H E R E , f.A\L.JJSJ. LEX I K ; TST, X T , Y C , T I T L E ) CONTINUE C A L ( PLOT NO STOP END  _  ......  AND  CONCENTRATION 24. Q 32.Q  IN PPM 40.0  46. Q _J  56.Q  64. Q  72. Q _J  >  -o r m  > o  m TQ  o CO  4 ^  LU I 4^  I  CO •J-  CD  X  LO  m LU LH  cu CD  *  CD  CONTROL CARD 1 = .• . 63 15.00PH R 28, 3-4-6X, SEPT. 17, 6 CONTROL CARD 2 ' = 6 83333.25 > r  DATA  . . _._  ...  _  NO 1 —_ 2 _ 3 4 5 6 7 8 ' 9 10 11 12 13 ... 14 15 16 17 18 19 - 20__21 22 23 24 25 ......26 27 28 29 30 31 32 33 34 35 36 37 .38. 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53  11.40  XT 14.30 15.30 . 16.00 16.30 17.00 17.30 . 18. 10 .18.30^ 19.00 19.30 20.00 20.35 21.00 21.30 22.00 22.30 23.00 23.30 24.00 .24. 30... 25.00 25.30 26.05 26.30 27.00 27.30 28.30 29.00 29.30 30.00 30.30 .31...00_ 31.30 32.00 32.30 33.00 33.35 .34.00_ 34.30 35.00 35.30 36.00 36.40 37.00 37.30 38.05 38.30 39.10 39.30 40.00 41.00 42.00 43.00  1.62  READING 1.6150 1.6190 1.6240 1.6360 1.6610 1.7090 1.7900 ' 1.8640.* 1.9800 2.0610 2.1610 2.2510 2.3000 2.3290 . 2.3340 2.3210 2.2900 2.2550 2.2020 2. 1440 2.0930 2.0390 1.9970 1.9640 1.9250 1.8840 1.8210 " 1.7900 1.7730 1.7540 1.7420 1.7270 . 1.7150 1.7060 1.6950 1.6880 1.6800 1.6760. . 1.6730 1.6690 1.6650 1.6610 1.6590 1.6580 . 1.6560 1.6530 1.6510 1.6490 1.6480 1.6470 _ 1.6450 1.6420 1*6490  0.0  0.0 1.62  10  10  „  'NI A P I V SAMPLE  _  ,._  PRINTOUT -  (  5  44.00  4  55 56  46.00  57  59 60 61 62 63  RATING  1.6320  1.6300  0.  10. .20. 30. 40. 50.  5 6  FINAL  1. 6 3 0 0 , 1.6280 CC  2 3 4  CONVERTED  1.6360 1.6350 1.6340  .55.00 6 0 . 15 STEP 1  166  1.6370  47.00 48.00 49.00 51.00 53.00  58  L'  1.6390 1.6380  45.00  READING 1.5970 1.8790 2.1460 2.4170 . 2.7000 2.9780  DATA . . . .  DATA  NO 1 2 3 4  .  5 6  7 8 9 10  11 12 13 14 15 16 17 18 19 20  21 22 23. 24  25 26 27 28  29 30 31 32  .  t  33 34  35 36 37 38  XT  14.50 15.50 16.00 16.50 17.0.0.. 17.50 1 8 . 17 18.50  19.00 19.50 20.00 20.58 21.00 21.50 22.00 22.50  ;" R E A D I N G  0.0 0.0402 0.2545 0.7737 . 1.8589 3.9456  7.4681 10.6881 15.7357 19.2594 23.6103 27.5252 29.6560 30.9154 31.1298 30.5603  _23.00 23.50 24.00 24.50  29.2072 27.6797 25.3686  25.00 25.50 26.08  20.6157 18.2610  26.50 27.00 27.50 28.50 29.00  29.50 30.00  30.50 31.00  31.50 32.00  . 32.50... 33.00 33.58 34.00  22.8397  16.4282 14.9885 13.2869 11.4983  8.7483 7.3952  6.6515 5.8208 5.2950  4.6384 4.1125 3.7173 3 . 2 3 5 0 .. 2.9268 2.5745 2.3975  .  39 40 41 42 43 44 45 46 ... 47. 48 49 50 51 52 53 _ 54 55 56 57 58 59 .._ 60 61 62 63  34.50 2.2635 35.00 2.0860. 35.50 1.9085 36.00 1.7309 36.67 1.6393 37.00 1.5936 37.50 1.5031 38.08 1.3685 38.50 1.2786 39.17 1.1870 39.50 1.1413 40.00 1.0943 41.00 1.0005 42.00 0.8631 43.00 ... 0. 7693 44.00 0.7191 45.00 0.6688 46.00 0.6185 47.00 0.5682 0.5179 48.00 ,. _ 49.00 „ ... . 0.4677 51.00 0.3671 53.00 0.2665 55.00 0.2530 60.25 0.1306 .  167  c c c c c c c c c c c c c c c c c c c c c c c  c  1 2 7 16 32  C C  c c  r  c c  8 100  D QV  ;  -  FORTRAN /360 MAIN PROGRAM, CALLED DQV, FOR READING TIME CONCENTRATION DATA INTO ARRAYS SUITABLE FOR FURTHER PROCESSING BY SUBROUTINES 9V, PLOTGA, AND TAILEX. INPUT CONTROL CARDS 1 ONE CARD PER RUN* NO. OF DATA SETS, KTOT, (12) 2 ONE PER DATA SET. NO OF DATA POINTS, K, (13) ARRIVAL TIME OF TRACER WAVE, TST, (F7.2) TITLE OR RUN IDENRIFICATION NO. (7A4) PARAMETERS OF GAMMA EXTENSION, IF DESIRED, LOG A, B, D,(2X,3E10.5). LOG A IS CONVERTED TO A. DATA CARDS TRACER CONCENTRATION, YC,IN PPB,TIME FROM INJECTION, XT, IN MINUTES AND DECIMAL FRACTIONS, (2F9.3) OUTPUT PRINTOUT OF DATA CALL PLOTS DIMENSION  XT(50) ,YC(50) , TITLE (7)  FORMAT (13 , F7.2,7A4,2X, 3E10.5) FORMAT (2F9.3) FORMAT (12) FORMAT (13H1CONTROL CARD ,5X , 13 , F7.2, 7A4./15H A, B, AND> 1 , 3E10.5) FORMAT (5H0DATA ,4X , 2HN0 , 8X, 2HXT ,9X , 2HYC ,/ 1 (9X, 12, 5X, F7.2, 2X, F9.3) ) LOOP FOR SETS READ (5,7) KTOT DO 8 KSET = 1 , KTOT READ AND WRITE DATA READ (5,1) K , TST ,TITLE , A, B , D IF ( A .NE. 0.0 ) A = EXP (A) READ (5,2)(YC (I), XTU), I = 1 ,K ) WRITE (6,16) K , TST , TITLE , A, B, D WRITE (6, 32) ( I, XTU) , YCd) , I = 1, K) CALLS TO SUBROUTINES GO HERE CALL TAILEX (K, TST, XT, YC, TITLE ) CALL TAILEX (K, TST, XT, YC, TITLE ) CONTINUE CALL PLOTND WRITE (6,100) FORMAT (1H1) STOP  169 r  CONTROL CARD A» B , AND D = DATA  NO  1 2  \ I  3 4 5 .... 6 7 8 9  .  10  11 12 13 14 15 16 17  17 .16323E  1 4 . OOBR R 2 G1UP- i - 2 X t AUG 0 1 . 10000E 01.86000E-01  XT 12.00 15.00  YC 0.0 0.100  18.00 21.00  24.00 27.00  29.00 31.00 33.00 35.00 37.00  41.00 45.00  49.00 54.00 59.00 .69.00 .  15,67  0.600 12.100 . 38.000 50.500 47.000 38.000 27.800  20.200 14.100 7.300 4.500 3.100 2.400 1. 8 0 0  ._ -  1.000  _L  nQ  V  . S A M P . L E .. P R I N T O U T  170  TAILEX SUBROUTINE  c c c  TAILEX  (  K  ,  TST  ,  XTIN.YC  ,  TITLE  )  THIS FORTRAN / 3 6 0 SUBROUTINE IS C A L L E D B Y D Q V OR B Y IF A GAMMA E X T E N S I O N I S TO BE F I T T E D . I T P L O T S T H E C - T DARA IN THE FORM ( L O G C - B * L O G T ) V S . (T), FOR B - V A L U E S OF - 1 , 0 , 1, 2 , 3 , AND4.  C C C  1  DIMENSION X T 1 2 0 0 ) , YC(200), XTIN(200), XTPL01200) DO 1 J = 1 , K XT(J) = XTIN(J) - TST XTPLO IJ) = XT (J ) IF ( X T P L O <J) . L T . 0.0 ) IF (YC(J> . L E . 0.0) YL(J) IF ( YC(J> . G T . 0.0) YL(J) CONTINUE  BXL(200),  YL(200),  NACL,  T ITLEl7 f ,  XTPLO(J) * 0.0 = - 1 0 . 0 = ALOG ( YC(J))  UUM I I inut  .XTMIN,  CALL SCALE (XTPLO , K , 1 4 . 0 , X T M I N , DXT , 1 ) N 0XIS C A L=L 0 . A ( 0 . 0 , 7.0 ,15HXT - T S T , (MIN),-13 , 1 4 . 0 1 DOD X2 T J) = 1 , K YDIFF = YC (J+l) YC(J) IF (YDIFF . L T . 0 . 0 ) N = N+l IF (N . E Q . 3 ) GO T O 3 CONTINUE  <XTIV  , 0 The parameters, A, B,^ and  D, of 'TAILEX' correspond  to YI.YZ.and Y3  2 .... 4  WRITE ( 6 , 4 ) TITLE , TST , J , XT(J) FORMAT ( 1 8 H 1 S U B R O U T I N E T A I L E X , / 9 H RUN N O . , 7A4, 1 18H STARTING TIME , F7.2 , / "2 2 8 H T A I L E X S T A R T S A T P O I N T NO ,I 2 , 1 0 X , 7 H X T I M E = L O O P FOR DIFFERENT B VALUES DO 6 J5 = 0 , 5 _ _ J2 B  =  =  DO 7 A X = IF IF  ( (  Y(J3) IF ( IWRITE  2  J5 J2  -  ,F8.2)  K  .GT.0.01 ) . L E . 0.01  =-BXL(J3)  ( 6 , 8 )  BXL (J3) = B * ) BXL (J3) = -  +  TST  YL(J3)  ALOG 10.0  J2 . E Q . 1 . O R . J2 , B , ( M ,YC(M) ,  , M = J , K ) FORMAT (16H0INITIAL TIME = 1 5 4 H NO CONC. LOG C  2  2X,  ]  J3 = J XT(J3)  AX AX  of text.  ,  F7.2 B*LOG  , / T  (AX)  .EQ. 4 ) Y U M ) , B X L (M) 5H Y  B  =  ,  ,  NXT(M) Y(MT>  F6.2, / XT - T I N  , /  (IX, 12 , F 8 . 2 , F 9 . 4 , F 1 0 . 4 , F 1 0 . 4 , F 9 . 2 )) JNC.) ELIMINATION OF D A T A P O I N T S T O S E C O N D P O I N T B E Y O N D P E A K ( N O T " > IF (J2 . N E . ( - l ) )G0 TO 10 •__ YMAX = 4 . * A L O G (AX) IF (YL(K) . L E . 0 . 0 .AND. YL(K) . G T . ( - 9 . ) ) Y M A X = YMAX + Y L ( K ) DY = 0 . 5  IF (YMAX . IF (YMAX . IF (YMAX . IF (YMAX . YLMAX = Y IF ( Y(K)  GT. GT. GT. GT. (J) .GT  3.5) 7.0) 14.) 35.0) .  Y(J))  DY = 1 . 0 DY = 2 . 0 DY = 5 . 0 DY = 1 0 . 0 YLMAX  =  Y(K)  171 DX IF IF  = 0 . 5 ( YLMAX ( YLMAX  IF ( IF ( YMIN YMAX  =*3.0*  )  (  )  DX DX  = =  1.0 2.0  ) DX = 5 . 0 DY = DX  DY  .  0.0,0.0,15HL0G C  C A L L SYMBOL ( 1 . CALL SYMBOL (1. CALL NUMBER( 4. 00 12 J4 = J ~Y(J4) = Y ( J 4 ) / CALL S Y M B O L ( X T K S = J +1 DO 1 1 M = KS IF (YL(M) .LT.  13  1.5) 3.0  YLMAX . G T . 6 . 0 DX . G T . DY ) = - 7 . 0 * DY  CALL AXIS 1 Y M I N , OY  10 12  -GT. .GT.  0, 1.0, 0 0, 0.5, 0 0, 0.5, 0 , K DY + PL0(J)»Y(J , K (-9.0V)  .21, .21, .21,  ),  -  T  ,  ,  ,  3  ,  ,  10.0,  0.0,  -1  ,  11  CONTINUE  CONTINUE CALL PLOT RETURN END  90.0,  0.0,  (  16.0  ,  0.0  ,  )  11  7 5  , .  (_2) 0.0 0.0 ^2)  . -3  15  )  IF ( Y(M).GT.10.0 .OR. Y(M).LT. 0.0 )G0 TO 13 CALL SYMBOL(XTPL0(M) ,Y(M) ,0.14 , 3 , 0 . 0 , -2 ) GO T O 11 IF ( Y(M).GT.IO.O) C A L L SYMBOL ( X T P L O ( M ) , 1 0 . , 0 . 14 , IF ( Y(M).LT. 0.0 )CALLSYMBOL(XTPLO(M),0.0,0.14 ,  6^ _  ;  ;  +15  TITLE, 0 . 0 , 28 ) 15HSTARTING TIME = TST, 0.0, 2 )  7.0 0.14  GOTO  B.LOG  )  .  ,) • ,)  SUBROUTINE TAILEX RUN NO. BR R2 G1UP-1-2X, AUG 15,67 TAILEX STARTS AT POINT NO 8 V  I N I T I A L TIME R = i .no NO CONC. 8 38.00 9.__ 2 7 - 8 0 _ _ 10 20.20 11 14.10 1? 7.^0 13 4.50 14 3.10 15 2.40 16 1.80 17 1.00  =  STARTING TIME XTIME = 17.00  14.00  14.00  LOG C 3.6376 3.3250 3.0057 2.6462 1-9879 1.5041 1.1314 0.8755 0.5878 0.0  B*LOG T 2.8332 2.9444 3.0445 3.1355 3.7958 3.4340 3.5553 3.6889 3.8067 4.0073  XT - T I N Y 0.8044 17.00 .. .0.3806. 19.00 21.00 -0.0388 23.00 -0.4893 -1.3080 27.00 -1.9299 31.00 -2.4239 35.00 -2.8134 _ 40.00 -3.2189 45.00 -4.0073 55.00  I N I T I A L TIME 14.00 B = 4.00 y_ NO '..CONC. - LOG. C _ B $ L O G _ T _ _ 8 11.3329 3.6376 -7.6953 38.00 9 . 27.80 3.3250 11.7778 -8.4527 10 20.20 3.0057 12.1781 -9.1724 12.5420 -9.8958 11 14. 10 2.6462 13.1833 - 1 1 . 1 9 5 5 12 7.30 1.9879 50 13.7359_._ -12.2319. _1.5C41 1314.2214 - 1 3 . 0 9 0 0 14 1.1314 3. 10 15 2.40 14.7555 -13.8800 0.8755 16 1 .80 0.5878 15.2267 -14.6 389 17 0.0 16.0293 - 1 6 . 0 2 9 3 1.00  „  XT„.-...TIN 17.00 19.00 21.00 23.00 27.00 31.00 35.00 40.00 45.00 55.00  •  ...  1 • -  T A I L EX "...  S A M PI  F  PRINT-OUT  .  --•  ...  -  174  o  in I  sL  'TAILEX' S A M P L E  PLOT  BL R 29. 3-5-4X. JUNE 13. 68 STARTING TIME = 115.00  CD I  o  SAMPLE a  m CM-  BR R2 G1UP-1-2X- AUG STARTING TIME =  14-00  15.67  PLOT  176  QVEl C C C C C C C C  SUBROUTINE  £  C . C C C C C  INPUT  KK IS T S T IS X...AND TITLE A , B, NRWT 0 1 2 NIGA, 0 1  9  10  11  C C.  KK,  TST  ,  X  ,  Y  ,  TITLE,  A,  B,  0  ,NRWT,  NIGA)  [  T H E NUMBER OF D A T A P O I N T S , C A L L E D K I N N A C L AND D Q V , S T A R T I N G T I M E , AS B E F O R E , „Y. A R E . T H E T - C D A T A , . . C A L L E D . X T A N D . . Y C . I N N A C L AND DQV , IS AS BEFORE, A N D D A R E T H E P A R A M E T E R S O F T H E GAMMA E X T E N S I O N , " I F RHWT T E S T I F NA C L T E S T , 5 0 L I T E R TANK I F NA C L . J P S T , . 1 6 L L T E R T A N K J. _ IF IF  A, A,  B, B,  D ARE D ARE  NOT G I V E N A V A I L A B L E FOR  EXTENSION  TO  INF.  OUTPUT I N T E G R A L S . . A N D . F I R S T MOM. OVER T H E D A T A . POI N T S , USING F I R S T AND S E C O N D ORDER M E T H O D S . MEAN T I M E I S ( F I R S T MOMENT S STARTING TIME, TST ). OPTIONAL, W I T H N I G A = 1, I N T E G R A L S AND M O M E N T S W I T H E X T E N S I O N T O INFINITE TIME. * TNT TO X T ( K ) « I S T H E N E G L E C T E D PART OF  _  T H E . . I N T E G R A L O V E R T H E GAMMA D I S T R I B U T I O N , UP TO _.. TIME X T ( K ) . ' F A C T O R F A M • IS T H E A D J U S T M E N T TO A , T O A C H I E V E C L O S E S T F I T TO THE L A S T 3 DATA POIMTS. * FACTOR A' IS T H E C O R R E C T E D V A L U E OF A . A * F A M . W I T H NRWT = 1 OR 2 , THE PROGRAM COMPUTES T H E D I S C H A R G E .  1  C C  (  S U B R O U T I N E FOR N U M E R I C A L I N T E G R A T I O N AND N U M E R I C A L E V A L U A T I O N O F F I R S T M O M E N T S O F T I M E - C O N C E N T R A T I O N C U R V E S « E X T E N S I ON T O I N F I N I T E T I M E , B A S E D ON A D E C L I N E O F C S I M I L A R T O A GAMMA DISTRIBUTION,IS OPTIONAL. T H I S PROGRAM R E Q U I R E S .4.. S U B R O U T I N E S , GAUSS1, GAUSS2, AUX1, AND A U X 2  ..  C C C C C C C C C C C C C C C..„ C C C C C  Q VEL  DIMENSI0N_XT(260I.,_„YC.(200),„X(2a) , . Y ( 2 0 ) ..,_II.TLE(7.),YC0(3), FACT0R(3) DOUBLE P R E C I S I O N DGAMMA , G X , G Y REAL M T , MEAN T I , MEAN T 2 ,MEAN T 3 ; E L I M I N A T I O N OF SUPERFLUOS DO . 9 . . . J _ = _ 1 _ ^ _ _ K _ K IF <X(J) .GT. TST) G O TO CONTINUE K = KK-J + 2 DO 1 1 Jl = 1 , K  I =J1 + J XT ( J 1-H) Y C ( J l + 1) XT ( 1 ) YC ( 1 ) INTEGRAL  -1 = X = Y  DATA  POINTS  10  ( I) .-..TST. "(I)  =0.0 0.0  = OF  DATA  POINTS  ,  FIRST  AND S E C O N D ORDER  METHODS  ._  177  C 1  F I R S T ORDER C T MT 1 = 0 . 0 CT INT1 = 0 . 0 DO  4  J  TRAPEZ CT INT1  =  2  K  T  = = CT  UYC(J-1) TRAPEZ  INT1+  YC(J))*  (XT(J)-  X T U - U J I /  2.0  - CT~MT_l....=._.C.T-MT-_.l„+__T.RA.P..E2._*_(-_XT.(.J^.l.) +„.„(.(.2 . * Y.C ( J ) + YC(J-l)) 1 (3.0 *(YC(J-1)+ YC(J)))) * ( XT(J) - X T ( J - i ) ) ) CONTINUE F I R S T M = C T MT 1 / C T I NT 1 MEAN T l = F I R S T M + TST  4  C C  SECOND-ORDER KTEST =(K / K L IM = K CT INT2 a 0 . 0  1 2)* 1  .._  2  _  = XT ( J - l ) XT(J-2) = XT (J) XTU-2) =((((DT2**?)*0Tl)/2.)  F2  = (UDT2**3)/ ... * . D T 2 ) )...  F l = 1 ( D T 2 * * 3 ) / ( ~ 6 . 0 ) 3.0)  - (PT2**3)/6.0) / (DT1*DT2) p T I )/ ((DT1**2) - (DT1*DT2)) -(((DT2**2)*DTI) / 2.0)) /((DT2**2V  t-  D INT = FO * YC ( J - 2 ) + FI CT INT2 = CT INT 2 + D INT U =. YC( J - 2 ) / (DTI * DT2)  1 ? 3  = =  YC(J-l) YC(J)  / /  ...  = K ..  DTI DT2 FO  V W  ^  (DT1**2 (DT2**2  -  *  YC  (J-l)  + F2  .NE.  K  )  GO  TO  *  YC(J)  DT1*DT2) DT1*0T2)  CT. .MT_2—=_CT_MT_.2- .+..D I N T . * ( XT ( J - 2 ) +( ((U*V+W)*(DT2**4))/ + ( V * D T 2 ) +(W * D T D ) * ( O T 2 * * 3 ) ( D T 2 « * 3) ) / 2 . 0 ) / D I N T ) CONTINUE IF (KTEST  /  ;  C T MT 2 = 0 . 0 IF (KTEST . N E . K ) KLIM DO 5 J_=_3_,_.KLI M » 2  „  5  +  (±DT_2)) (DTl) DTI*  4.0 - ((U* / 3.0 +(U* ,  6  TRAPEZ CT INT C T MT  6  =_(.{y.C-<K-l.J*„yC.(K)..l*UX.T..-.(.Kl==_XT-(K-=l)).).../-_2.0 2 = TRAPEZ + CT INT 2 2 = C T MT 2 + T R A P E Z * ( X T ( K - l ) + (2.0*YC(K) +YC(K-1))/ 1 ( 3 . 0 * (YC(K) + YC(K-H)) * (XT(K) - XT(K-I))) FIRST N = C T MT2 / C T I N T 2 MEAN T2 = TST + FIRST N  (MEANT2  C  WRITE  7  WRITE ( 6 , 7) C T INT 1 • F I R S T M » MEAN T l , F O R M A T ( 3 2 H 1 1 N T E G R A T I O N OF M E A S U R E D P O I N T S  C  RESULTS  19H0INTEGRAL CT1 1 t 1 9 H F I R S T MOMENT (1)= 2 t . ..... 3 .. ... 1 9 H _M EAN_t.IJM.E_.' (1 ) = —- • ? 4 19H I N T E G R A L C T 2 t 1 9 H F I R S T MOMENT (2)= 5 t 19H MF AN T I M F (?) t. 6 INTEGRATION  IF  (NIGA  OF  .EQ.  DATA  0  )  POINTS  GO  TO  3  F15.5 F15.5  -F15.5 F15.5 F15.5  t  10HPPB  4HMIN 4HMIN  * »  •  F15.5 t COMBINED  10HPPB 4HMIN  CTINT2,FIRSTN,) . / *  t  /  T  /  ... f  „  * MIN  4HMTN  WITH  MIN  FITTED  f/ t  V  / /  1  EXTENSION  (INF. TO)  178  C  CORRECTION FACTOR K3 = K - 3 DO 8 J = 1 , 3 I  =  K3  +  J  YCO (J) = A*(Xt(I)**B) FACTOR(J) = YCIII /  8  - F A M_=JJj? A C.TO.R_.  * EXP< YCO(J)  -D*XT(I))  . ).„_+.„ 2...0„JL., J£A C T OR ( 2 ) _ t _ 3 . . 0 _ * F A C T OR ( 3 I . )  /  6.0  C C  INTEGRATION R = B + GX = R  FIRST3 XINT= CTINT3  12  = 0.0 XT I K ) / =0.0.  J = 1 = J = XT(K)  XLL  =  G  20.0 ._  -  XINT  XINT  XLL  ,  *  XUL  (COUNT ,  DB,  A,  CT INT FIR m  4  = CTINT1 =(CTMT1  + DINT3 + DFM03  CT  5  =  + DINT3  WRITE  CTINT2  =(CTMT2 = FIR M5  +  + DFM03 TST  B  * *  FAM A))  )  /  CT  INT  .4  )  /  CT  INT  5  *  FAM  RESULTS "  WRITE(6,13) DINT 3 , DFMO 1 , MEAN T 3 , D E B C T , FAM FORMAT ( 4 5 H 0 I N T E G R A T I O N OF  3  ,  CTINT4  ,  FIRM4  ,  CTINT5,  DATA POINT WITH F I T T E D EXT. , F 1 5 . 5 , 7HPPB*MIN , / 18H0AREA CORR. 18H_.FIR.SX_.MaM.-.C0RR.=_ , . F 1 5 . 5 , . 15H M I N * * . 2 ^ * „ P P B 1 8 H A R E A BY T R A P E Z = , F 1 5 . 5 , 7HPPB*MIN , /  4  18H  FIRST  =  ,  F15.5,  5 6  18H 18H  A R E A BY P A R A B . = F I R S T M O . BY PA.=  ,  F15.5,  7  18H  MEAN  ,  F15.5  9  , D)  I NT  ;  -1.0)  D.)  8 ... A  18H  =  18H  INT.  FAM  WRITE  C  /  ,20  -  GAUSSK  )  ,  I 2 3  3  XUL  __  (D**R)  C A L L. . G A U S S 2 (._ X L . L _ i _ X U L _ _ t _ D A.t..A B, CTINT3 = C T I N T 3 + DB FIRST3 = F I R S T 3 + DA CONTINUE ; DEBCT = ( CTINT3 * A ) / GAMMA D INT3 =(GAMMA - C T I N T 3* A ) DFM03 = ( ( X M O l * GAMMA) (FIRST3  FIR M5 MEAN T 3  C  DISTRIBUTION  1  DO 1 2 COUNT XUL CALL  16  GAMMA  GY = D G A M M A ( G X ) G = GY _I GAMMA = A * G / XMOl = R / D C T I N T F = (D * * " . *  ..  13  OF  1.0  FORMAT  TIME  TO  *  {  18H  3  ,  F15.5,  =.. , F 1 5 . 5  FAM  A  (6,16)  (TR)  XT(K)  FACTOR  CONTINUE _  MOM.  ,  7HMIN  7HPPB*MIN  7HMIN ,  7HMIN  __../_  F15.5  )  _..  A FACTOR  A  =  , F15.5  )  , ,  / / / //  FIRM5 , ,//  /  179  COMPUTE DISCHARGE OF SALT T E S T S . IF ( NRWT .EQ. 0 ) RETURN DISCH = 0.0 IF ( NRWT . F Q . 1 .AND. NIGA .EQ. 0 10ISCH = 833.3 / C T I N T 2 IF { NRWT .EQ. 2 .AND. NIGA .EQ. 0 JDISCH = 833.3 / ( 3 . * C T I N T 2 ) IF ( NRWT .EQ. 1 .AND. NIGA .GT.O ) DISCH = 833.3 / C T I N T 5 ~ . I F _ J N R W.T__. E Q. ..1.2—. AN D. __N J G A„... GT... 0....J _DJ.S.C H _.= „8 3 3 . 3_ 11 3 .*CTINT5 I F ( DISCH .GT. 0.0 ) WRITE ( 6 , 1 5 ) DISCH FORMAT ( 18H0DISCHARGE = , F 1 5 . 5 , 17H CUBIC M PER S E C . ) RFTURN ; ; ; END  .'  SUBROUTINE  C  C C  GAUSS1  SUBROUTINE  IN  (A,  B,  FORTRAN  DIMENSION A X I 4 ) , DOUBLE P R E C I S I O N  AREA,  /360  AX{2) AX(3) AXt4)  H Q )  H(4) AX, H  X  30  =  _  CALL AUXl (X, Y, XA, Z ' = Y X = P-R CALL AUXl (X, Y, XA, _SUM_j=.„.SUM_+_H ( J ) * ( Z+Y )  CALLED =  RETURN END  QVEL.  _  XB,  XD)  XB,  XD) J  "  BY  AUXl  (  X,  Y,A,  B,  D)  G A U S S 1. :  Y  SUBROUTINE  -  0*SUM  SUBROUTINE  C  _ _ _  P+R  AREA = RETURN END  C C  XD)  0.101228536290376  = AX(J)*Q  =  BY  XB,  180  = 0.796666477413627 = 0.525532409916329 •= 0 . 1 8 3 4 3 4 6 4 2 4 9 5 6 5 0  H(2) =0.222381034453374 H(3) =„0.313706645877887 H(4) = 0.362683783378362 P = (B+A)*0.5 Q = (B-A)*0.5 SUM = 0 . 0 DO 3 0 J = 1,4  R  XA,  CALLED  AXi.l)_.^Jl..a6Q2B9_8.56.49753^  .  '  ..  ( X  **  Bl'  *  EXP(  (-  D)*  X  )  J  :  _.  -•  "  '•  SUBROUTINE  -  "  GAUSS2 (A, B,  • '•• AREA, XA, XB,  181  XO)  C C  SUBROUTINE  _c  IN FORTRAN /360 CALLED BY SUBROUTINE  1  DTMENSIGN AXC4), H(4) DOUBLE PRECISION AX, H A XXI .)._=_0..9 60.285.8 56 4973 3.6 AX(2) = 0.796666477413627 AX(3) = 0.525532409916329 AX(4) = 0.183434642495650 H I D = 0. 101228536290376 H(2) =' 0.222381034453374 _ _ H.C3.)_S--Q^313706.645.877 887. H(4) =0.362683783378362 P = (B+A)*0.5 0 = IB-A)*0.5 SUM = 0.0 DO 30 J = 1,4 R_ = . AX( j)#o. ;j . X = P+R CALL AUX2 (X, Y, XA, XB, XD) i = Y : ; X = P-R CALL AUX2 (X, Y, XA, XB, XD) .30 ... - SUW_=_SUM._+_.H.U.)-*XZ*Y.)._, AREA = Q*SUM RETURN  EMU  :  ;  AUX2 ( X , Y , A , B , D )  CALLED BY GAUSS2. Y = ....  ( X **(B+1.0)) * EXP <(-D)* X )  RETURN END _  —  _1  QVEL.  : _  1  SUBROUTINE C C  ;  .  182 INTEGRATION INTEGRAL  FIRST MEAN  X  FIRST MEAN  CT1  MOMENT  TIME  INTEGRAL  MEASURED  OF  (1)  (2)=  (2)  INTEGRATION AREA CORR. F I R S T MOM.  17.41537MIN 31.41537MIN 674.12207PPB 17.38902MIN  =  MOMENT  TIME  678.49805PPB  (11=  CT2  TIME  I NT J O FACTOR FACTOR  *  MIN  *  MIN  31.38902MIN  OF  DATA  POINT  WITH  FITTED  EXT.  13.54708PPB*MIN 930.09424 MIN#*2.*  CORR.=  A R E A BY.__TRAP.EZ i F I R S T MOM. (TR) A R E A BY PARAB. F I R S T M O . BY PA.MEAN  POINTS  PPB  .6.9 2 . 0 4 4 9 2 P_PB*_M I N. 18.41844MIN 687.66895PPB*MIN 18.39899MIN  3  32.39899MIN  JKTtK). FAM A  .0.94942. 1.21365 1.98106  1  QVE L  SAMPLE FOR 'B R  1  PRINTOUT  R 2 , GI UP  I - 2X'  J83 INTEGRATION  OF  MEASURED  INTEGRAL CT1 F I R S T MOMENT ( 1 ) = MEAN T I M E (1) INTEGRAL CT2 FIRST  MEAN  MOMENT  TIME  (2)  INTEGRATION AREA CORR. F I R S T MOM.  OF  TIME  INT TO FACTOR FACTOR  3  XT(K) FAM A  DISCHARGE  *  MIN  *  MIN  96.21269MIN  211.21269MIN  DATA  A R E A . BY. T R A P E Z F I R S T MOM. (TR) A R E A BY PARAB. F I R S T M O . BY PA. MEAN  6153.19922PPB 96.25470MIN 211.25470MIN 6149.38672PPB  (2)=  CORR.=  POINTS  POINT  WITH  FITTED  EXT.  459.59253PPB*MIN 176856.87500 MIN**2 .6612.78906PPB*MIN 116.30965MIN 6608.97656PPB*MIN 116.28214MIN  *  PPB  .  231.28214MIN .0.85202. 0.99531 0.44722 0.12609  CUBIC  M PER  Q V E L' SAMPLE FOR J BL. R 2 9,  PRINTOUT G 3 - 5 - 4X'  SEC,  184 INTEGRATION  OF  MEASURED  INTEGRAL CT1 F I R S T MOMENT < 1 ) : MEAN T I M E (1) INTEGRAL GT2 F I R S T MOMENT (2); MEAN T I M E (2) DISCHARGE  POINTS 268.61548PPB 9.89905MIN 24.89903MIN 268.43823PPB  *  MIN  *  MIN  9.90452MIN 24.90451MIN 3.10425  CUBIC  M PER  'Q V E L* SAMPI F FOR 'PH R2 8,  _..  PRINTOUT G 3 - 4 - 6X'  SEC  185  P I 0 T fi A SUBROUTINE  C C C C  (Kt  TST,XT IN,YCIN,A,  BE  C C  1  CALLED  AFTER  THE  SUBROUTINE  TITLE  )  QVEL  HAS  BEEN  CALLED,  AS  QVEL  DIMENSION X T ( 2 0 0 ) , Y C ( 2 0 0 ) , TITLE(7) , XTINI200), YCIN(200) DO 11 I =1 , 200 ' XT(I) = XTIN(I) YC(I) = YCINU) CALL. SCAL E ( X T , K, 10.0,.. XTMIN, DXT, 1 ) CALL SCALE ( Y C , K, 9 . 0 , YCMIN, DYC, 1 ) (DXT) CALL AXIS (0.0, 0.0, 1 5 H T I ME I N M I N U T E S , - 1 5 , 1 3 . 0 , 0 . 0 , X T M I N , ) CALL AXIS (0.0, 0.0, 2 0 H C 0 N C E N T R A T I O N IN P P B , »20 , 9.0,) YCMIN DO 1 J  , =  DYC ) 1, K  (90.0,  C A L L . S Y M B O L . ( X T . ( J ) , _ Y C ( J L . „ , . „ 0 . . 1 A . , 2 . ,. „ 0 . 0 , - 1 .) C A L L SYMBOL (6.0, 9.0, 0.28, TITLE, 0.0, 30 ) C A L L SYMBOL (6.0, 8.5 , 0.14 , 5HTST = , 0 . 0 , 5 C A L L NUMBER ( 7 . 5 , 8.5 , 0 . 1 4 , TST , 0 . 0 , 2) IF (A . E Q . 0 . 0 ) GO T O 6 C A L L PLOT (0.0 ,0.0, +3) ...YMAX__=.LY.CM.IN_£OYXJ_•__.9...0. 0 0 2 I = 1, 131 F = I1 X . = F / 10.0 T = XTMIN + X * DXT IF { T . L T . 0.0 ) T = 0.0  :  :  T  )  -YCMIN  , 0 . 0 ,  -2  )  /  DYC  )  GO T O 2 CALL PLOT ( X ,Y , + 2 ) CONTINUE C A L L S Y M 8 0 L . _ (...6 , 0 . . , _ 8 . 0 . . . , _ _ 0 . 14. .. 2 4 H G A M M A . . P A R A M . 1 0.0 , 24 ) C A L L NUMBER ( 9 . 0 , 8.0 , 0.14 , A , 0.0 , 6 ) CALL CALL  CALL  NUMBER NUMBER PLOT  RETURN END  ( (  10.3 11.6  (15.0,  , ,  0.0,  8.0 8.0  -3  , ,  )  TST  Y _ _ = ( {... A * ( _ t _ * * . . B l ) * . E X P ( - D * IF ( Y .LE. YMAX ) G O T O 5 C A L L SYMBOL ( X , 9 . 0 , 0 . 0 7 , 13  6  D,  IMPROVE.S__THE..ES_TIMAXE_OF_A.  11  5 2  B,  T H I S S U B R O U T I N E IN F O R T R A N / 3 6 0 IS C A L L E D BY T H E MAIN PROGRAMS N A C L AND DQV T O P L O T T H E C - T C U R V E S . OPTIONALLY IT W I L L A L S O P L O T T H E GAMMA E X T E N S I O N S . I N T H I S C A S E IT SHOULD  C  1  PLOTGA  )  0.14 0.14  , ,  B 0  , ,  0.0 0.0  , ,  2 6  A,  B,  D  =  ) ) •  PH R 2 8 . 3 - 4 - 6 X .  SEPT. 1 7 .  15.00  TST =  A A  A A  A  ' P L O T G A*  A  SAMPLE  PLOT  A A A A A  A A  10.0  18.0  26.0  I 34.0  ,A A A — , _ A 42.0  SO.O  58.0  , — 66.0  TIME IN MINUTES  -1  74.0  B2.0  90.0  I 9B.0  -r  106  BL R 2 9 . 3 - 5 - 4 X . TST =  SAMPLE  A A A A  A A  80.0  120.0  A  160.0  0.447722  'PL 0 T G A'  A A  A  280.0  320.0  1 3 . 68  115.00  GAMMA PARAM. A. B. D  A A  JUNE  360.0  TIME IN MINUTES  PLOT  1.00  0.012499  BR R 2 G 1 U P - 1 - 2 X . R U G TST =  14.00  GAMMA PARAM. A. B. D =  1.981554  ' P L 0 T G A* A  SAMPLE  A  A  15.67 J  PLOT  1.00  0.086499  189  L0GRE  '  r  c  J  C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C  T H I S FORTRAN / 3 6 0 PROGRAM COMPUTES THE L I N E A R R E G R E S S I O N S ON L O G Q ( D I S C H A R G E ) O F T H E F O L L O W I N G V A R I A B L E S= L O G TM (MEAN TRACER TRAVEL T I M E ) LOG A ( CROSSECTIONAL AREA) LOG V (VELOCITY) LOG TS _ ( S T A R T I N.G.TIME) . LOG TP (PEAK TIME) LOG T S S ( S T A R T I N G T I M E , BUT O M I T T I N G RUNS WITH T R A C E R I N J E C T I O N ABOVE THE REACH ) LOG T P P ( P E A K T I M E , O M I T T I N G R U N S AS FOR T S S ) T H E A C T U A L R E G R E S S I O N A N A L Y S I S I S D O N E BY A S U B R . • R E G R * . TWO P L O T T I N G . S U B R O U T I N E S ..CAN. A L S O . B E . C A L L E D _ F R O M T H I S P R O G R A M . INPUT F I R S T CONTROL CARD, ONE PER J O B S U B M I S S I O N , = NO. OF S E T S , ( 1 2 ) . SECOND C O N T R O L C A R D , ONE P E R DATA S E T , = TITLE, (6X, ?A4) DATA C A R D S , ONE P E R T E S T R U N , = R U N NO. (12) COL 1 £ 2 IDENTIFICATION ( I D COL 5 T H I S I S I F O R R U N S W I T H I N J E C T I O N OF T R A C E R A T UPSTREAM E N D OF T E S T R E A C H , 0 F O R O T H E R R U N S . DATA .._ . (6F6.0) COL 7 . £ ON, ( Q , T S , T P , TM , A , V ) Q I N L / S , T I M E S I N M I N . , A I N S O M, V I N M/S, 0 I S C O N V E R T E D TO CU M/S. OUTPUT P R I N T O U T OF D A T A , L I N E A R R E G R E S S I O N E Q U A T I O N S , S T A N D A R D ERROR OF E S T I M A T E , C O R R E L A T I O N C O E F F . , D E G R E E S OF F R E E D O M , F - R A T I O . CALL PLOTS DIMENSION NOI30), 1 A(30), V (30), 2,Q1 ( 3 0 )  C C. 1  C 3  5 4 6 7  LOOP FOR NUMBER OF READ ( 5 , 1) KTOT FORMAT ( 1 2 ) DO 2 KS=1, KTOT  ID ( 3 0 ) , Q ( 3 0 ) , T S ( 3 0 ) , T S S I 3 0 ) , TPP ( 3 0 ) , T I T .. SETS  TP (7  ( 3 0 ) , TM(30), ) ,QQ(30)  ,  R E A D I N G AND P R T N T I N G OF ~ D A T A ~ READ ( 5 , 3 ) T I T FORMAT ( 6 X , 7 A 4 ) DO 4 K - 1, 30 ~~ READ ( 5 , 5) NO(K), ID(K) , Q I K ) , TS(K), TP(K), FORMAT ( 1 2 , 2X . I I , I X , 12F. 6.0 ) i IF (NO.(K).LE. 0 ) GO TO 6 CONTINUE K = K -1 WRITE ( 6 , 7) TIT FORMAT ( 1 H 1 , 7 A 4 , / 1 5 8 H 0 N O . . I 0 . Q.J L / S ) TS TP_ TM.  (V(k)  TM ( K ) , A ( K ) ,)  T  •  A  v/)  190 1 8 1 r c  WRITE  (6,  ACID FORMAT  12, 13, KID = 0  10  11  12  13  14  r  L  C 18  T S ( I 2) TP(12) TM ( 1 2 ) A(12) VU2) KID  :  ' k  19  K  ,  3F9.2  =  KID  REGRESSIONS  ,  +  QN  ID  ORIGINAL  T P AND T S NID = 0  REGRESSIONS  (KID  15 (ID  =  DATA  .EQ.  0  )  TP  GO  1 5 = 1 , K (15 ) .LE.  NID  =  =  =  +  1  TS  115  TP (15 Q(15)  ,  0  K  TO  )  ,ATP 20  LOG  Q  (1H0  /  18H  BTM ) LOG Q  )  ,  BA LOG  )  ,  BV  ,  ,  Q  TO  21  )  BTS ) LOG Q BTP  )  )  __  GO  TO  )  15  . „  TSS  VS.  LOG  WRITE ( 6 , 1 7 ) '_ C A L L REGR ( Q Q , T S S , KID , ATSS , FORMAT (1H0 / 18H LOG TPP V S . LOG WRITE ( 6 , 19) C A L L REGR ( Q Q , T P P , KID , ATPP , GO  )  .  )  LOG  )  LOG  )  ,  Q  T M Q 1) »  )  ..  CONTINUE IF(NID .NE. KID ) WRITE ( 6 , 16) KS FORMAT (1H1, 17H NID ERROR IN S E T FORMAT  T P U 1 ) ,  (12)  14) ( Q ",  DO IF  T S U I ) ,  2F9.4  (TS(12)) (TP(I 2)) ( T M (1 2 ) ) (A(I 2)> (V(I 2))  WRITE ( 6 , C A L L REGR IF  Q U I ) ,  )  . . E V A L U A T I O N . . O F ._ . N 0 . . _ D £  T O . LOGS......  = AL0G10 = AL0G10 = ALOG10 = ALOG10 = AL0G10  TSS(NID)  17  1,  ALOG10 (QU2J/1000.) = Q(I2)  TPP(NID) QQ(NIO)  16  10(11),  =  . . F O R M A T „ ( 1 H 0 /._1_8H L O G T M . V S . WRITE (6,10) C A L L R E G R ( Q , TM , K , A T M FORMAT (1H0 / 18H LOG A VS. WRITE ( 6 , 11) C A L L REGR ( Q , A , K ,AA FORMAT J 1 H 0 / 18H LOG V VS. WRITE ( 6 , 12) C A L L REGR ( Q , V , K ,AV IF (KID .EQ. K ) GO T O 18 FORMAT (1H0 / 18H LOG TS V S . WRITE ( 6 , 13) C A L L REGR ( Q , T S , K ,ATS FORMAT (1H0 / 18H LOG TP V S .  NID  15  II  F10.2  TRANSFORMATION DO 9 12 = 1 , K Q( 1 2 ) = Q1U2)  9 C C  <N0(I1),  8)  , V(I1), (IH ,  _  Q  )  .  12  ,  8TSS Q ) BTPP  :  )  )  S I M P L E . RUNS  191 C C 20  CALLS  CONTINUE CALL TPLO  1 GO 21  22 C 2  TO P L O T T I N G  TIT,Q) TO  I  Q  ,  SUBROUTINES  TS  ,  TH  TP,  , K  ,  K  ,  ATS,  ATP,  ATM,  BTS,  (BTM, BTPT)  22  CONTINUE. CALL TPLO ( Q , 1 BTPP , BTM , CONTINUE C A L L H Y P L O IQ1, CONTINUE.• C A L L PLOTNO STOP END  _  TSS TIT  _ ,TPP, , QQ  A  V  ,  ,  K  TM )  ,  ,AA  ... . _ ... KID , A T S S ,  K  ,  ,  AV  ,  BA  ,  '  BV  . ATPP  ,  (BTSS, , A T M ,)  TIT  )  SUBROUTINE REGR  (X,Y,N  ,  A » B )  192  A SUBROUTINE IN FORTRAN /360 C A L L E D BY THE MAIN ROUTINE LOGRE IT COMPUTES THE REGRESSION OF Y ON X AND PRINTS THE RESULT DIMENSION X ( 1 0 0 ) , Y ( 1 0 0 ) . . SUMX=O.O _._ ._ SUMY=0.0 SUMX2=0.0 SUMY2=0.0 SUMP=0.0 DO 1 J=1,N SUMX = SUMX+X( J ) ... _. SUMY=SUMY+Y(J) SUMX2=SUMX2+X(J)**2 SUMY2=SUMY2+Y(J )**2 1 SUMP=SUMP+X(J)*Y(J) AN=N . SSX=SUMX2-{.SUMX**2)/AN •.. _ SSY=SUMY2—(SUMY**2)/AM SP=SUMP-(SUMX*SUMY)/AN B=SP/SSX A=(SUMY/AN)-(B*(SUMX/AN)) R=SP/(SQRT(SSX*SSY)) WRITE ( 6 , 4 ) SSX,SSY,SP 4 FORMAT (// 4H SSX,F12.4,4X,4H SSY,F12.4,4X,3H SP,F12.4 //) WRITE ( 6 , 5 ) A , B 5 FORMAT (26H REGRESSION EQUATION Y= ,F10.4,2H +, F I 0 . 4 , 2 H X) S = SQRT ( (SSY - SP*SP/SSX) / (AN - 2.0 ) ) WRITE ( 6 , 9 ) S 9 FORMAT (27H STANDARD ERROR.0F_ EST I MATE ,.F10.4 ) WRITE ( 6 , 6 ) R 6 FORMAT (24H CORRELATION C O E F F I C I E N T , F10.4 ) NDF = N - 1 WRITE ( 6 , 7) NDF 7 FORMAT ( 24H DEGREE OF FREEDOM ,110) F = ( R*R*( AN . - 2.0) ) / ( 1.0 R*R) _._ WRITE ( 6 , 8) F 8 FORMAT ( 4H F = , 20X, F 1 0 . 4 ) RETURN END  193 1  SUBROUTINE BTSS  ,  TPLO  BTPP  ,  THIS FORTRAN IT PLOTS THE DATA POINTS.  I  D I MENS I ON , QQ(30)  (  BTM  Q,  TSS,  ,  TIT  TPP, ,  ,  K  )  ,KID  ,  ATSS  ,  ATPP  ,ATM,  IS CALLED TSS, TPP,  (LOGRE F R O M T H E M A I N PROGRAM) TM ON Q , INCLUDING  TPP ( 3 0 ) " ,  TM  ( 3 0 ) , T  ,  TMIN  ,  DT  , 1  )  5.0 , KID  QMIN  ,  OQ  ,  / 3 6 0 SUBROUTIN R E G R E S S I O N S OF  ol 3 0 ) ,  TM  QQ  T S S ( 3 0 F,  ( 90 )  ,  T I T (7)  S C A L E OATA DO 1 I - 1, K T ( I ) . _ = T M .( I ) DO I O N = 1 , KID K5 = N + K  T( Nl K6  =  K5) = T P P ( N ) K + KID = N + Nl  T( K6_) = TSS(N)_ _ __. N2 =N1 + K I D CALL SCALE ( t , N2 , K7 = K + 2 * KID DO 100 J5 = 1 , K7 T(J5) = T( J5) + DO 2 J _ = 1 , K TM(J) = T (J) DO 11 Jl = 1, KID K7 = Jl + Nl TSS (Jl) = T ( K7 K8 = Jl + K TPP (Jl) = T ( . K8 CALL SCALE ( Q, K DO 200 JJ7 = 1 QQ(JJ7) DRAW  (  5.0  3.0  ) )  , ,  QQ(JJ7)  -  QMIN  )  /  )  DQ  AXIS  (DO)  CALL  AXIS  (  0.0,  3.0,16HQ  IN  CU  M /  CALL  AXIS  (  0.0,  3.0,12HTIME  IN  MIN.  PLOT  POINTS  DO 3 1 1 = 1 , C A L L SYMBOL DO 4 12 = C A L L SYMBOL C A L L SYMBOL  K  ( Q (II) 1 , KID ( QQ(I2) I QQ(12)  PLOT  REGRESSION  TM YB  VS =  Q LINE ( ( ( A T M + BTM*  IF YB XB YE XE  < YB . L E . = 8.0 = ( 5.0 = (((ATM = 5.0  XB  1  =  0.0  8.0  .  SEC  ,  ,  -16,  +12  ,  5 . 0 , 0 . , QMll^) 5.0  , 9 0 ^ (TMIN , DT)  ,  TM(I1),  , ,  TSS(I2), TPP(I2),  0.07,  2  ,  0.0,  0.07_, 0.07 ,  3 4  , ,  -I  0.0 0.0  ) , ,  -1 -1  ) )  LINES  )  QMIN). - . TMIN).. / GO T O  * DT + TMIN + BTM* (QMIN  101 -• A T M + 5.0*  DT)  +J3.0  : - Q M I N * BTM DQ)) - TMIN)  ) /  . - . / ( DQ * BTM) DT ) + 3 . 0  194  102 C  c  IF YE XE  CALL CALL TS YB XB IF  103  C  (  = =  VS = =  PLOT PLOT  GE -  < XB (XE  . 3 . 0 ATM  -  ,  ,  ,  YB YE  Q LINE . (((ATSS+BTSS* 0.0  ,  ) QMIN  +3 ) +2 )  QMIN)-  GO *  TO BTM  J  /  TMIN)  /  DT)  TP YB XB IF  =  106 C C  C C  (  DQ  +  *  BTM  VS Q L I N E = (UATPP + B T P P * QMIN) = 0.0 ( YB . L E . 8.0 ) GO T O 1 0 5  "3.0"  TMIN  )  /  DT  )  )  /  / ( DQ * BTSS  DT. »  BTSS  TITLE SYMBOL SYMBOL SYMBOL SYMBOL SYMBOL SYMBOL SYMBOL  COMPLETE C A L L PLOT C A L L PLOT C A L L PLOT C A L L PLOT RETURN END  AND LEGEND ( 0 . 5 , 9 . 0 , 0 . 2 1, T I T ( .1 . 0 . , 1 . 5 , .0.07 ( 1.0 ,1.0 , 0.07 ( 1.0 ,0.5 , 0.07 ( 1.5 ,1.5 , 0.14 ( 1.5 ,1.0 , 0.14 ( 1.5 ,0.5 , 0.14 : O U T L I N E , M O V E ON ( 0 . 0 , 8 . 0 , +3 ) ( 5.0, 8 . 0 , +2 ) ( 5 . 0 , 3 . 0 , +1 ) ( 1 1 . 0 , 0 . 0 , -3 ) .„.;„  )  + 3 . 0  )  +3.0  _ _  XB = ( 5.0 * DT + TMIN - ATPP - QMIN* BTPP ) / ( YE = IUATPP + BTPP* (QMIN + 5 . 0 * DQ)) - TMIN ) / XE = 5.0 IF { YE . GE . 3.0 ) GO T O 1 0 6 YE = 3.0 XE = ( T M I N . - . . A T P P - Q M I N .*... B T P P . . ) . . . / ( DQ * BTPP CALL PLOT (XB , YB , +3 ) C A L L PLOT (XE , YE , +2 ) WRITE CALL CALL CALL CALL CALL CALL CALL  )  YB  YB _„=.._8.0.  105  102  .LE. 8.0 ) GO T O 1 0 3 8.0 = ( 5.0 * DT + T M I N -r A T S S - Q M I N * B T S S = ( ( ( A T S S + B T S S * . ( Q M I N ..+ 5 . 0 * . D Q ) ) - T M I N ) = 5.0 ( YE . GE . 3.0 ) GO T O 1 0 4 YE = 3.0 XE = ( T M I N - A T S S - QMIN * B T S S ) / { DQ * C A L L PLOT (XB , YB , + 3 ) C A L L P L O T ( X E ... , Y E , + 2 ) . . .  YB XB YE XE IF  I  YE . 3.0 ( TMIN  , 0 . 0 , 28 ) , 2.., . 0 . 0 . , - 1 ) . , 4 , 0 . 0 , -I ) , 3 , 0 . 0 , -1 ) , 9HMEAN TIME , 0.0 , , 9HPEAK TIME , 0.0 , , 13HSTARTING TIME ,  DQ DT  .. .. ... * )  BTPP +3.0  )  9 ) 9 ) 0.0  ,  13)  )  195 SUBROUTINE  HYPLO  (Q  ,  A  ,  V  ,  K  ,  AA ,  A V , BA  ,  BV  C  C C C  T H I S F O R T R A N / 3 6 0 S U B R O U T I N E I S C A L L E D FROM T H E MAIN IT P L O T S T H E R E G R E S S I O N S OF A , A N D V t ON Q . DIMENSION  C C  C C  S C A L E DATA CALL SCALE CALL SCALE CALL ..  CALL  1 C C C C  101  102  c C  103  104  SCALE  AXIS  DQ ) CALL AXIS  CALL  1  C C  I ( (  DRAW.AXIS. 1  .  Q(30), _  1  DA )  AXIS  Q , V , A  ,  A(30)  K K K  , ,  ,  ,  V(30) .._  ,  TIT  5 . 0 , QMIN 5 . 0 , VMIN  , ,  OQ , 1 DV ,1  5 . 0 , AMIN  ,  0.0  TIT  (LOGRE PROGRAM )  ) )  DA ,1  )  (QMIN, ,  3.0  ,  1 6 H Q IN  CU M /  ( 0 . 0 ,  3.0  ,  14HAREA  ( 5 . 0 ,  3.0  ,  1 7 H V E L 0 C I T Y IN  IN  SEC  SQ M .  , - 1 6 , 5 . 0 , 0.0, I ,  M/SEC  (AMIN, ,5.0,90.0,;  H 4  (VMIN.  , — 1 7 , 5 . 0 , 9 U. U,)  0V..1 „ _ PLOT POINTS DO 1 I = 1 , K A(I) = A(I) + 3.0 V( I) V ( I) + 3.0 C A L L SYMBOL ("_Q( I )..,.. A ( I ) _ , 0 . 0 7 , C A L L SYMBOL ( Q(I) , V(I) , 0 . 0 7 , PLOT  REGRESSION  2 3  ,  0. 0_,_-1 0 . 0 , -1  ) )  LINE  Q VS. A LINE YB = ( ( ( A A . + B A * „ Q M I N ) - A M I N ) / O A ) + 3 . 0 _.. XB = 0 . 0 IF ( YB . G E . 3 . 0 ) GO TO 1 0 1 YB = 3 . 0 XB = (AM IN - AA - QMIN * BA) / (DQ * BA) XE = 5 . 0 YE = ( ( ( AA + B A * ( Q M I N + 5 . 0 * D Q ) ) - A M I N ) A OA ) + 3 . 0 IF ( YE .LE . 8.0 ) GO TO 1 0 2 YE = 8 . 0 XE = ( 5 . 0 * DA + A M I N - AA - Q M I N * B A ) / ( O Q * BA ) C A L L PLOT ( XB , YB , + 3 ) C A L L PLOT ( XE , YE , + 2 )  ..;„  Q VS XB = YB = IF ( YB = XB = XE = YE = IF ( YE = XE = CALL  )  (7)  _' (  ,  V LINE 0.0 ( < ( AV + BV*QMIN ) -VMIN) /DV ) + 3.0 YB . G E . 3 . 0 ) GO TO 1 0 3 3.0 ( VMIN - AV - QMIN * BV. ) / (DQ * BV) 5.0 ((( AV + BV * ( Q M I N + 5 . 0 * D Q ) ) - V M I N ) / DV ) + 3 . 0 YE . L E . 8 . 0 ) GO T O 1 0 4 8.0 ( 5 . 0 * DV + V M I N - A V - Q M I N * B V ) / ( DQ * B V ) P L O T ( XB:.,__YB . , + 3 . J >  3r9-6 CALL  r  c  TITLE  ... r C  CALL CALL CALL  CALL CALL  PLOT AND  SYMBOL SYMBOL SYMBOL  SYMBOL. SYMBOL  COMPLETE CALL  (  PLOT  XE  ,  YE  LEGEND  ( 0.5, ( 1.0, ( 1 . 0 ,  I (  1.5, 1.5,  OUTLINE  i  C A L L PLOT I . C A L L PLOT.. ( RETURN END  ,  ,  +2  9.0, 1.6, 1.1,  )  0.21, 0.14, 0.14,  TIT 2 3  , , ,  0.0 0.0 0.0  , , ,  28 ) -1 ) -1 ) A R E A . ., . .. 0 . 0 . , . 9  1 . 5 , . 0 . 1 4 , . ..9HFL0W 1.0, 0.14 , 9HVEL0CITY  MOVE  ON  0.0  ,  8.0  ,  +3  5.0 8.0  , ,  8.0 0.0  , ,  +2 ) -3.)  ) ...  ,  ,  9  .) )  >  BROCKTON  CK,  NO  (L/S)  2 4 7 9  ID 1 1  1 1  21 23  1 1  LOG  TM  SSX  1-2  110.00 350.00  __1...2.3 58.00 50.00 158.00  .7.0.00 4.90  30.10 44.50  180.00 540.00  193.00 560.00  l.l.7.._00_..'. 1159... 5.0. 8.10 9.08 11.60 5.00  12.58 5.40  7.30 5.50  8.33 6.97  SSY  4.5008  . A  SSX  VS.  LOG  EQUATION  D E G R E E_ O F „ F R E E DOM F =  V  SSX  VS.  LOG  _  SSY.  1. 1 8 5 6  SP  Y=  -0.0913  .  •+  SSX *  VS.  LOG  10.1903  .  .....  :L.0  3. 4399.  X  .9 379.7510  Q  10.1903  TS  X  COMPLETE  0.3376  0.0553 0.9896  SSY  4.5095  SP  REGRESSION EQUATION Y= 0.0934 + STANDARD ERROR OF E S T I M A T E 0.0561 CORRELATION COEFF.ICIENT. 0.9972 D E G R E E OF FREEDOM 9 F = 1423.0298  LOG  0.0125 0.2180 0 . 1580 0.3680 0 . 2 3 80 0.2850  ^6.7536  -0.6628  1439.3.098—  STANDARD ERROR OF E S T I M A T E CORRELATION COEFFICIENT  LOG  0.0660 0.0450 0.0103 0.0035  Q  1 0 * 15LQ.3  REGRESSION  0.1400 0.1260 0.0650 0.0450 - . 0 . . Q 9 9 Q ..._ 0.2660 0.3170 0.4300 0.3860 0.4810  SP  REGRESSION EQUATION Y= 0.2056 + STANDARD ERROR OF E S T I M A T E 0.0558 CORRELATION COEFFICIENT -0.9972 D E G R E E OF FREEDOM 9  LOG  V  Q  10.1903  .£,_.=  A  TM  25.50 37.30  7.20 2.50 4.20 3.20  92.00 137.00  LOG  TP  17.00 24.00  0.67 0.16  VS.  197  TS  9.20 5.60  0 0  ... . 1 0 ._ 1 16 1 18 19  0  REACH  0.6634  6.7599  X  _„  Q  SSY  4.7987  SP ,  -6.9778  G  R  E  PRINTOUT  198  r R E G R E S S I O N S T A N D A R D  E Q U A T I O N  E R R O R  C O R R E L A T I O N D E G R E E ^  F  OF  O F  Y=  - 0 . 1 1 7 3  E S T I M A T E  *  - 0 . 6 8 4 7  X  0 . 0 5 0 9  C O E F F I C I E N T  - 0 . 9 9 7 8  F R E E D O M  9  =  1 8 4 1 . 9 0 1 1  ? LOG  TP  V S .  L O G  Q  . S P  S S X  1 0 . 1 9 0 3  R E G R E S S I O N S T A N D A R D  E Q U A T I O N  E R R O R  C O R R E L A T I O N D E G R E E F  OF  S S Y  O F  - 6 . 7 8 4 0  4 . 5 4 1 9  Y=  0 . 1 3 9 0  E S T I M A T E  +  - 0 . 6 6 5 7  .X  0 . 0 5 6 6  C O E F F I C I E N T  - 0 . 9 9 7 2  F R E E D O M  9  =  1 4 1 2 . 1 2 7 9  L O 6 " Y S S ^ S 7 " L O G ~ Q "  S S X  4 . 0 3 4 9  S S Y  R E G R E S S I g^YoljATl O N S T A N D A R D  E R R O R  C O R R E L A T I O N D E G R E E F  O F  V-T""  E S T I M A T E  C O E F F I C I E N T  F R E E D O M  -076787 +  - 0 . 6 5 6 1  - 2 . 6 4 7 2  X  0 . 0 4 6 6 - 0 . 9 9 6 3 7 9 8 . 5 0 8 1  T P P  V S .  S S X  S T A N D A R D  Q  O F  S S Y  E Q U A T I O N  E R R O R  C O R R E L A T I O N D E G R E E  L O G  4 . 0 3 4 9  R E G R E S S I O N  =  S P  7  =  LOG  F  O F  1 . 7 4 9 8  O F  Y=  E S T I M A T E  C O E F F I C I E N T  F R E E D O M  _ _  1 . 6 0 3 9  0 . 1 8 9 6  S P  +  0 . 0 4 9 6 - 0 . 9 9 5 4 7  . „  646.0571...7  - 0 . 6 2 7 6  - 2 . 5 3 2 2  X  199  BROCKTON CK. REACH 1-2  A  MERN TIME' PEAK  +  TIME  STflRTING  TIME"  200  BROCKTON CK. REACH 1-2  Q IN CU M /  A  FLOW AREA  +  VELOCITY  SEC  BROCKTON  CK,  Q  REACH  NO  10  1 4  1 0 0  6.70  11 1.7.  1  1.20  8  20 22  LOG  TM  13.60  „,L  SSX  LOG  TM 35.00 3 4 . 17  0.1740 0.1720  172.00 119.80 8.5.0 5.39 4.53  0.0935 0.1065  33.00 34.50  27.00  34.00 89.00 110.00  VS.  TP  TS  (L/S) 6.80 0.73  _l. 1 1  2-3  76.00 53.00 3.00  160.00 97.00 7.20 4.70  2.20 1.80  4.00  SSY  2.4174  REGRESSION EQUATION Y= -0.0129 • ST ANDARD ERROR O F . E S T I M A T E 0.0179. CORRELATION COEFFICIENT -0.9997 DEGREE OF FREEDOM 6 F = 7506.9609  VS.  SSX  SSY  4.7054  -3.3716  -0.7165  X  0.3784  SP  1.3316  -0.1437 + 0.0179 0.9979 6  . 0 . 2 83.0  X  1182.4143  F = V  VS.  SSX  LOG  Q  SSY  4.7054  2.4167  REGRESSION EQUATION Y= STANDARD ERROR OF E S T I M A T E CORRELATION COEFFICIENT DEGREE F =  OF  LOG  VS.  SSX  SP  L.QJS_Q_  R E G R E S S I O N . E Q U A T I O N . . . Y= STANDARD ERROR OF E S T I M A T E CORRELATION COEFFICIENT D E G R E E OF F R E E D O M  LOG  0.3690  Q  4.7054  LOG...A  0.340.0. 0.3560  TS  FREEDOM  LOG  4.7054  0.1442 + 0.0185 0.9996  SP  0.7164  3.3710  X  7072.7969  Q  SSY  REGRESSION EQUATION Y= STANDARD ERROR O F E S T I M A T E  2.7562  -0.4422 + 0.1151  SP  -0.7561  -3.5577  X  0.0390 0.0400  0.0078 0.0113 0.1590 0.2500 0.2980  202 CORRELATION COEFFICIENT D E G R E E OF FREEDOM F =  LOG  TP  VS.  SSX  LOG  -0.9879 6 203.1117  Q  4.7054  SSY  2.4596  REGRESSION EQUATION Y= -0.0710 + STANDARD ERROR OF E S T I M A T E 0.0342 CORRELATION COEFFICIENT -0.9988 D E G R E E OF FREEDOM 6 F = 2102.5312  LOG  TSS  VS.  SSX  LOG  SSY  1.5750  REGRESSION EQUATION Y= -0.4533 + STANDARD ERROR O F E S T I M A T E 0.0194 CORRELATION COEFFICIENT -0.9996  LOG  TPP  SSX  OF  FREEDOM  VS.  SP  -0.7405  -2.1253  X  LOG Q  2.8700  --•  X  4 4198.3047  SSY  1.4477  REGRESSION EQUATION Y= -0.0606 + S T A N D A R D ERROR OF E S T I M A T E 0.0305 . CORRELATION COEFFICIENT -0.9990 D E G R E E OF F R E E D O M 4 F = 1557.8159  -  -0.7221  -3.3980  Q  2.8700  DEGREE F =  SP  SP  -0.7095  -2.0364  X  —  -  -  BROCKTON CK.'.REACH 2-3  Q IN CU M /  A  SEC  MEAN TIME . PEAK TIME  +  STARTING TIME  204  ^ ?  PLACID  CREEK,  NO  Q  ID  2 13 25 28  1 1 1 1  ICG  TM  SSX  REACH  (L/S) 50.30 35.40 64.60 95.90  VS.  LOG  20 5  1-2 TS  TP  TM  122.00 165.00 115.00 94.00  164.00 208.00 159.00  210.00 280.60 180.60  130.00  144.20  0.0997  A  SSX  VS.  LOG  SSY  0.0441  0.0997  0.0119  SSY  =  LOG  V  SSX  VS.  LOG  0.0997  SSX  I  0.2739 + 0.0141 0.9833 3 58.3338  0.0437  SSY  =  LOG  0.8630  SP  -0.0660  -0.6622  X  SP  0.0339  0.3403  X  Q  REGRESSION EQUATION Y= STANDARD ERROR OF ESTIMATE CORRELATION COEFFICIENT D E G R E E OF FREEDOM F  0.6600 0.6180 0.7280  Q  REGRESSION EQUATION Y= STANDARD ERROR OF ESTIMATE CORRELATION COEFFICIENT D E G R E E OF FREEDOM F  V  Q  REGRESSION EQUATION Y= 1.4758 + STANDARD ERROR OF ESTIMATE 0.0147 CORRELATION COEFFICIENT -0.9951 DEGREE OF FREEDOM 3 F = 203.3226  LOG  A  -0.2748 + 0.0147 0.9950 3  SP  0.6587  0.0656  X  199.5172  TSS  VS.  LOG  0.0997  Q  SSY  0.0307  1.4121 + REGRESSION EQUATION •Y= 0.0257 STANDARD ERROR OF ESTIMATE CORRELATION COEFFICIENT -0.9782 D E G R E E OF FREEDOM 3 F = 44.3011  SP  -0.5425  -0.0541  X  0.0763 0 .0573 0. 0890 0 . 1110  206  LOG TPP VS. LOG Q  SSX  0.0997  SSY  0.0210  SP  -0.0448  > REGRESSION EQUATION Y1.6546 + S T A N D A R D ERROR OF ESTIMATE _ 0.J3202 CORRELATION COEFFICIENT -6.9T04 "~ ~ DEGREE OF FREEDOM 3 F = 49.3988  -0.4498 X ~  ~~  ~~ ~ "  PLACID CREEK. REACH 1-2  .035  .04  Q IN CU M /  SEC  MEAN TIME PEAK TIME STARTING TIME  208  A  FLOW AREA  +  VELOCITY  PLACID  CREEK,  NO  Q  ID  5 10 r  REACH  (L/S) 15.40  18 24 27  1 1 1  LOG  TM  SSX  72.60 114.50 121.20 181.00  VS.  LOG  2-3 TS  TP  TM  160.00 62.00  236.00 94.00 71.00 74.00 54.80  351.30 121.40  48.00 47.50 36.10  83.30 92.10 62.10  0.6955  SSY  =  LOG  0.3363  A  VS.  0.6955  V  SSX  VS.  SSY  0.0674  SSY  0.3356  REGRESSION EQUATION Y= STANDARD ERROR OF E S T I M A T E  CORRELATION COEFFICIENT D E G R E E OF F R E E D O M F =  SSX  ,  -0.6932 X  VS.  SP  0.2131  0.3065 X  LOG Q  0.6955  TSS  -0;2868 + 0.0270  SP  0.4815  0.6924  0.9967 4 456.2595  LOG Q  0.6955  0.0289 0.0834  - 0 . 4 8 21  LOG Q  REGRESSION EQUATION Y= 0.2855 + S T A N D A R D ERROR O F E S T I M A T E 0.0266 CORRELATION COEFFICIENT 0.9842 D E G R E E OF FREEDOM 4 F = 92.4102  LOG  SP  477.4194  SSX  LOG  0^5340 0.8690 0.9390 I. 1 0 0 0 1. 1100  0  REGRESSION EQUATION Y= 1.2919 + STANDARD ERROR OF E S T I M A T E 0.0265 CORRELATION COEFFICIENT -0.9969 D E G R E E OF F R E E D O M 4 F  V  SSY  0.2499  REGRESSION EQUATION Y= 1.1170 + S T A N D A R D ERROR O F E S T I M A T E 0.0074 CORRELATION COEFFICIENT -0.9997 D E G R E E OF FREEDOM 4  SP  -0.4168  -Q.5993 X  0 . 1220 0 . 1100 0 . 1630  209  210 F  =  LOG  y  4588.8828  TPP  VS.  LOG  Q  0.6955  SSX  SSY  0.2397  REGRESSION EQUATION Y= 1.3101 + STANDARD ERROR OF E S T I M A T E 0.0146 CORRELATION COEFFICIENT -0.9987 DEGREE F  =  OF  FREEDOM  4 1118.6213  SP~  -0.5862  -0.4077  X  211  PLACID CREEK. REACH .2-3  \ K  MEAN TIME PEAK TIME STARTING TIME  PLACID CREEK. REACH 2-3  A  FLOW AREA  +  VELOCITY  <  ?  PLACID  CREEK,  NO  Q  ID  REACH  (L/S)  3-4 TS  17  1  14.50  674.00  18 19 21 _24 27  1 1 1 1. 1  245.00 268.00 70.00 2.67.00 404.00  188.00 162.00 302.00 157.50 121.00  LOG  TM  VS.  SSX  LOG  TP 1000.00 223.00 199.00 386.00 200.00 169.00  1200.00 255.30 238.90 481.60 254.00 209.00  1.4894  A  VS.  SSX  LOG  V  0.5650  2.0300 2.0000 1.0950 2.2000 2.7400  Q  SSY  0.4213  REGRESSION EQUATION Y= 2.0902 + STANDARD ERROR OF E S T I M A T E 0.0187 CORRELATION COEFFICIENT -0.9983 D E G R E E OF FREEDOM 5 F = 1203.0806  LOG  A  TM  SP  -0.7908  - 0 . 5310  X  SP  0.6934  Q  1.4894  SSY  0.3250  REGRESSION EQUATION Y= 0.5958+ STANDARD ERROR OF E S T I M A T E 0.0232 CORRELATION COEFFICIENT 0.9967 : -'• D E G R E E OF F R E E D O M F = 599.9749  0. 4656  X  5  LOG  V  VS.  SSX  LOG  Q  1.4894  SSY  0.4296  REGRESSION EQUATION Y= STANDARD ERROR OF E S T I M A T E  CORRELATION  COEFFICIENT  LOG  LOG  DEGREE F =  SSX  \—  TSS  OF  FREEDOM  VS.  1.4894  -0.5947 + 0.0230  SP  0. 5358  0.7980  X  0.9975  5 810.3389  Q  SSY  0.3661  REGRESSION EQUATION Y= 1.9227 + STANDARD ERROR OF E S T I M A T E 0.0312 CORRELATION COEFFICIENT -0.9947  SP  - 0 . 4931  -0.7345  X  0 .0256  0 . 1210 0.1340 0.0638 0.1210 0 . 1480  DEGREE F =  LOG  OF  FREEDOM  2T?  5 372.5400  TPP VS. LOG Q  SSX  i.4894  SSY  0.4252  SP  -0.7939  REGRESSION EQUATION Y= 2.0035 + -0.5330 X STANDARD ERROR OF E S T I M A T E 0.0226 . CORRELATION COEFFICIENT -0.9976 D E G R E E OF FREEDOM 5 F = _826.400?_ _____ PLOT T A P E S U C C E S S F U L L Y WRITTEN DONE STOP EXECUTION  $SIG  0 TERMINATED  PLACID" GREEK.REACH 3 - 4  4  MEAN T I M E PEAK TIME STARTING TIME  PLACID CREEK. REACH 3 - 4 o  Q IN CU M / SEC ~  A  FLOW AREA VELOCITY  B L A N E Y  C R E E K ,  NO  I D  Q  R E A C H  ( L / S )  1-3  T S  '>  A  TM  T P  v  1 1  1  5 0 0 . 0 0  3 0 . 0 0  4 4 . 5 0  5 4 . 7 0  2 . 3 9 0 0  0 . 2 0 9 0  V  12  1  1 7 5 0 . 0 0  1 7 . 0 0  2 3 . 5 0  2 7 . 4 8  4 . 2 2 0 0  0 . 4 1 6 0  R  15  1  1 1 5 0 0 . 0 0  7 . 5 0  1 0 . 6 0  1 2 . 1 0  1 2 . 1 5 0 0  0 . 9 4 7 0  16  1  1 6 3 0 . 0 0  1 9 . 5 0  2 6 . 4 0  3 0 . 1 6  4 . 3 2 0 0  0 . 3 8 0 0  17  1  1600.00  1 8 . 3 0  25-50  2 9 . 6 3  4 . 2 5 0 0  0 . 3 8 7 0  19  1  1 9 5 0 . 0 0  1 5 . 0 0  2 2 . 5 0  2  4 . 3 2 0 0  0 . 4 5 1 0  2 4  1  1 2 0 . 0 0  7 1 . 0 0  1 0 1 . 0 0  1 2 3 . 0 0  1 . 2 9 0 0  0 . 0 9 6 0  5 . 3 7  3 1  1  1 4 6 . 0 0  5 7 . 0 0  9 0 . 0 0  1 1 7 . 0 0  1 . 4 9 0 0  0 . 0 9 8 0  3 5  1  2 8 5 . 0 0  4 0 . 5 0  6 1 . 0 0  7 1 . 2 0  1 . 7 7 0 0  0 . 1 5 5 0  36  1  7 4 1 . 0 0  2 4 . 0 0  3 4 . 0 0  4 0 . 4 0  2 . 6 2 0 0  0 . 2 8 3 0  LOG  TM  V S .  S S X  L O G  3 . 2 5 3 7  R E G R E S S I O N S T A N D A R D  E Q U A T I O N  E R R O R  C O R R E L A T I O N D E G R E E F  OF  0 . 8 9 9 4  Y=  1 . 5 8 5 4  E S T I M A T E  A  V S .  C O E F F I C I E N T  L O G  X  S P  1 . 5 5 6 6  - 0 . 9 9 4 8  Q  D F G R F F  S S Y  E Q U A T I O N  E R R O R  C O R R E L A T I O N OF  OF  .  Y=  E S T I M A T E  C O E F F I C I E N T  F R E E D O M  . .  0 . 7 5 3 7  0 . 5 2 8 3  +  0 . 4 7 8 4  X  0 . 0 3 3 5 0 . 9 9 4 0 9  =  6 6 1 . 6 2 2 1  V  V S .  S S X  L O G  Q  3 . 2 5 3 7  R E G R E S S I O N S T A N D A R D  E Q U A T I O N  E R R O R  C O R R E L A T I O N D E G R E E  OF  O F  S S Y  0 . 8 9 4 5  Y=  - 0 . 5 2 7 0  E S T I M A T E  . C O E F F I C I E N T  F R E E D O M  S P  •  0 . 5 2 1 9  1 . 6 9 8 1  X  0 . 0 3 2 1 0 . 9 5 5 4 9  =  S S X  - 0 .5 2 3 0  9  3 . 2 5 3 7  S T A N D A R D  L O G  +  - 1 . 7 0 1 8  7 7 0 . 1 7 7 5  R E G R E S S I O N  L O G  S P  0 . 0 3 4 0  F R E E D O M  S S X  F  O F  S S Y  =  LOG  F  Q  8 5 8 . 6 0 8 4  T S S  V S .  L O G  3 . 2 5 3 7  Q  S S Y  0 . 7 6 4 2  SP.  - 1 . 5 6 7 8  217  218 REGRESSION EQUATION Y= 1.3558 + STANDARD ERROR OF ESTIMATE 0.0331 CORRELATION C O E F F I C I E N T -0.9943 DEGREE OF FREEDOM 9 F = 690.2686  LOG  SSX  -0.4819 X  TPP VS. LOG Q  3.2537  SSY  0.8187  REGRESSION EQUATION Y= . . 1 .5139 + STANDARD ERROR OF ESTIMATE 0.0287 CORRELATION C O E F F I C I E N T -0.9960 DEGREE OF FREEDOM 9 F = 985.6753  SP  -1.6255  -0.4996 X  •  BLANEY CREEK. REACH 1-3  220  BLANEY CREEK. REACH 1-3  Q IN CU M 7  A  FLOW AREA  +  VELOCITY  SEC  BLANEY CREEK, REACH 3-5 NO ID 8 10 11 12 13. 14 15 16 19 20 22 25 26 29 32 33 34  37  0 (L/S) 870.00 530.00 520.00 1820.00  0 0 J L J.XL4..0.Q....Q.Q. 1 11700.00 0 11700.00 0 1650.00 2050.00 0 530.00 1 1 60.. 0.0. 1_ 682.00 1 262.00 1 140.00 1 1 80.00 1 80.00 J L .. 748...00. 1 1350.00  221  TP 8.50 12.00 21.00 11.00 3.30. 3.20 4.00 12.00 11.00 10.00 2COO. 9.50 16.00 21.20 27.50 29.00 _8.90 7.50  1.6.20 20.5 0 23.00 15.00 5.60 5.50 5.00 14.00 12.00 18.20 3A..,.Q_0_. 16.60 26.00 38.50 53.0 0 54.50 15.00 12.70  TM  V  21.15 26. 31 22.5 5 15.67  3.3000 2.500 0 2.1400 5.0300  6. 24 13.0000 13.500 0 6.45 5.2100 17.62 12.62 4.630 0 24.78 2.3500 45.5.0... .:1_.3JQ0JL. 20. 85 2.5500 34.20 1.6000 4 7 . 85 1.200 0 71.43 1 .0200 71.45 1 .0200 2.6200 15.46 3.7300  0.26 40 0.2120 0.24 30 0. 35 3C _0_._7LQJQ0.9000 0.8700 0.3170 0.44 30 0.22 60 .0. 1 ? 3 0 6.2680 0.1640 0.1160 0.0780 0.0780 .Q..28 5C... 0.3620  LOG TM VS. LOG Q SSX  7.8009  SSY  1 .7186  REGRESSION EQUATION Y=. 1.2*62 + STANDARD ERROR OF ESTIMATE 0.0407 COR R..E.L AT I 0 N_ _C 0 JE F FJ CJ E_N T -0.9923 DEGREE OF FREEDOM 17 F •= 1023.4202 LOG A SSX  SSX  •3.633?  -0.4657 X  VS. LOG Q 7.8009  SSY  2.248 7  0.5391 + REGRESSION EQUATION Y= S T A N D A RD...E R R.OR__0 F__ ESTIMATE 0.0394 CORRELATION COEFFICIENT 0.9945 DEGRFE OF FREEDOM ' 17 F = 1433.6624 1.0G V  SP  SP  4.1651  0.5339 X  VS ....LOG. 0 7.8009  SSY  REGRESSION E.Q.UATI ON. v = STANDARD ERROR OF ESTIMATE CORRELATION COEFFICIENT OEGREF OF FREEDOM '  1 .6867 -0.5423 + 0.0437 0.9909 17  SP  3.5944  0.4608 X  222 F  =  LOG  687.9802  TS  VS.  SSX  LOG Q  7.5619  REGRESSION  SSY  EQUATION  1.4003  Y=  1.0047  SP  STANDARD ERROR OF E S T I M A T E 0.1061 CORRELATION COEFFICIENT -0.9334 DEGREE  F  =  LOG  OF  FREEDOM  X  17  TP  VS.  LOG  Q  7.5619  SSY  REGRESSION EQUATION Y= STANDARD ERROR O F E S T I M A T E  CORRELATION DEGREE =  LOG  -0.4017  108.3378  SSX  F  +  -3.0375  TSS  SSX.  OF  COEFFICIENT  FREEDOM  VS.  _  SP  1.2003 + 0.0493  -0.4541  -3.4337  X  -0.9878  17  64.1.9316.  LOG Q  .5.55.11  REGRESSION  .  1.5980  EQUATION  SSY.  .1.1274  Y=  0.9407  -2.4827  _S.P_  +  -0.4472  X  STANDARD ERROR OF E S T I M A T E 0.0394 CORRELATION COEFFICIENT -0.9924 0EGR.EE CF.. FREEDOM _1.2 1_ F = 716.6177  LOG  SSX  TPP  VS.  LOG Q  5.5511  SSY  REGRESSION EQUATION Y= STANDARD ERROR OF E S T I M A T E C 0 RR.E L A T I O N . C O E F F I C I E N J D E G R E E OF FREEDOM F =  1.2177  SP  1.1846 + 0.0461  -0.4638  ± 0 . . 9.904 12 561.8801  ,  -2.5748  .  X  BLANEY CREEK. REACH 3-5  A  MEAN  TIME  X  PEAK TIME  +  STARTING TIME  2 24  BLANEY CREEK. REACH 3-5 1  T  1—i—r  T  1—i—i  O  o  o CM  C3  o  J  CO  CE  cr o  cvi  .04 .06  .1  Q IN CU M /  A  FLOW AREA  +  VELOCITY  SEC  -A.  r  -i  r  BLANEY  CREEK,  NO  Q  ID 0 0  10 12  13 0 19 0 . 2 1 ... 1 23 1 28 1 29 0 37  0  LOG  TM  REACH  (L/S)  5-4 TS  570.00 1960.00  46.00 25.00  11000.00 22C0.00 .JULQ.JOXL 125.00 280.00 140.00  13.50 24.00 38.50 98.00 56.OC 93 . 80  1350.00  28.50  VS.  SSX  LOG  225 TP  TM  57.50 29.00 13.90 26.00 51.40 137.00 81.00 133.50  6 3 . 10 30.80 14.40 30.30 ...J5iu.6iL 165.00 93.90 158.00  _2....850.Q„ 1.3300 1.7000 1.4300  35.90  3.1300  32.70  3.1444  A  VS.  SSX  LOG  SSY  0.9987  3.1444  SSY  CORRELATION COEFFICIENT D E G R E E OF F R E E D O M _F_= :  V  VS.  . SSX  LOG  SP  0.6162  OF  LOG  SSY  VS.  SSX  v.  FREEDOM  X  SP  1.3802  0.4927 + 0.0386  0.4389  X  1 ...OjOi)7_  -0.4922 + 0.0387 0.9948  .  S_P_  0.5612  1.7646.  X  JL_  =  TS  -0.5606  0.9915 8 406.31.18...  REGRESSION EQUATION Y= STANDARD ERROR OF E S T I M A T E CORRELATION COEFFICIENT F  -1.7627  Q  3_, 1 4 4 4  DEGREE  662.0354  LOG  3.1444  0.4320  Q  REGRESSION EQUATION Y= STANDARD ERROR OF E S T I M A T E  LOG  0.2460 0.5030 1.0800 0.5120 .0.2740 0.0940 0 . 1650 0.0980  Q  REGRESSION EQUATION Y= 1.6828 + STANOARD ERROR OF E S T I M A T E 0.0389 CORRELATION COEFFICIENT -0.9947 DEGREE OF FREEDOM 8 F = 654.3979  LOG  2.3200 3.9000 10.2000 4.3000  Q  SSY  676478"  SP  -1.4164  (  869 .0930 LOG  226  TS VS. LOG Q  >- SSX  7.8009  SSY  1.4003  REGRESSION EQUATION Y= 1.0024 + STANDARD ERROR OF ESTIMATE 0.1055 CORRELATION COEFFICIENT -0.9343 DEGREE OF FREEDOM 17 F = 109.8279  SP  •3.0879  -0.3958 X  LOG TP VS. LOG Q SSX  7.8009  SSY  1.5980  REGRESSION EQUATION Y= 1.1977 +• STANDARD ERROR OF ESTIMATE 0.0457 CORRELATION COEFFICIENT -0.9895 DEGREE OF FREEDOM 17 F = 750.7678  LOG  -3.4937  -0.4479 X  TSS VS. LOG Q  SSX  5.7530  SSY  1.1274  REGRESSION EQUATION Y= 0.9382 + STANDARD ERROR OF ESTIMATE 0.0343 CORRELATION COEFFICIENT -0.9943 DEGRE.E O F F R E E D O M '  F =  LOG  SP  .  SP  •2.5322  -0.4401 X  12  948.2959  TPP VS. LOG Q  SSX  5.7530  SSY  1.2177  REGRESSION EQUATION Y= 1.1819 + STANDARD ERROR OF ESTIMATE 0.0394 .CORR EL AT. I 0 N JC.QE F FIX JIRI - - 0. 9.13.0 DEGREE OF FREEDOM 12 F = 772. 1868' PLOT TAPE SUCCESSFULLY WRITTEN DONE STOP EXFCUTTON  0 TERMINATED  SP  •2.6281  •0.4568 X  BLANEY CREEK. REACH 5 - 4  1  T  1  i  Q IN CU M /  A  1  r  SEC  MEAN TIME ' PERK TIME  +  STARTING TIME  1  1  r  228  BLANEY CREEK. REACH 5 - 4 d  Q IN CU "M /  A  FLOW AREA  +  VELOCITY  SEC  PHYLLIS NO  ID  CREEK, Q  REACH  <L/S)  TS  369.00 312.00 1470.00 2400.00 J.398.00. 945.00 945.00 826.00  38.50 43.50  21.25 16.50  OSL-.0JCL 24.00 22.50 23.00  3480.00  LOG  TM  SSX  VS.  LOG  1-2  14.50  TP 56.00 61.00  28.50 22.50 28.50 33.00 33.00 35.40 20.00  0.9355  A  SSX  VS.  LOG  SSY  0.2044  SSY  0.9355  V  SSX  VS.  LOG  0.2802  0...93.55  SSX  TSS  VS.  LOG  0.9355  36.19 27.79 36.66 39.80 38.75 46.39 25.81  1.9900 1.8300 4.1000 5.1500 .3...9600 2.9000 2.8300 2.9600 6.9400  SP  -0.4306  -0.4603  X  SP  0.5064  0.5413  X  Q  SSY.,  Q.. 2 0 . 3 2 .  REGRESSION EQUATION Y= -0.5133 + STANDARD ERROR OF E S T I M A T E 0.0294 CORRELATION COEFFICIENT 0.9850 D E G R E E OF F R E E D O M _ . _ 8 F = 228.4597  LOG  69.90 76.40  Q  REGRESSION EQUATION Y= 0.5135 + STANDARD ERROR OF E S T I M A T E 0.0294 CORRELATION COEFFICIENT 0.9891 D E G R E E OF F R E E D O M 8 F = _ 317. 0220.  LOG  V  Q  REGRESSION EQUATION Y= 1.6262 + STANDARD ERROR OF E S T I M A T E 0.0296 CORRELATION COEFFICIENT -0.9849 D E G R E E OF FREEDOM 8 F = 225.9623  LOG  TM  S.P  0.4591  .0.4295  X  Q  SSY  0.1958  SP  -0.4191  0.1850 0.1710  0.3580 0.4670 .0. 3540 0.3260 0.3340 0.2790 0.5020  REGRESSION EQUATION Y= 1.3751 + S T A N D A R D ERROR OF E S T I M A T E 0.0339 CORRELATION COEFFICIENT -0.9792 DEGREE OF FREEDOM 8 F = 162.9622 f LOG  TPP  SSX  VS.  SSY  0.2079  SP  REGRESSION EQUATION Y= 1.5288 + S T A N D A R D E R R O R O F E S T I.MAT E 0.0195 CORRELATION COEFFICIENT -0.9936 DEGREE OF FREEDOM 8 F = 538.0989  -  — ~  -  —  X  • )  LOG Q  0.9355  —  -0.4480  —  —  —  •  —  -0.4382  -0.4684  X  •.  _  —  „ —  —- -  —  PHYLLIS CREEK. REACH 1-2  Q IN CU M /  A  SEC  MEAN  TIME-  PERK  TIME  STARTING  TIME  232  PHYLLIS CREEK. REACH 1-2  Q IN CU M /  A  FLOW  +  VELOCITY  flREft  SEC  PHYLLIS NO  ID  CREEKt Q  REACH  (L/S)  .255.Q..JD.GL 2415.00 985.00 1880.00  840.00 1194.00 3610.00  TM  VS.  SSX.  LOG  233  TS  748.00 352.00 228.00 1590.00  LOG  2-3 TP  25.00 37.50  38.00 57.00  43.00 18.75 15.00 14.25 22.40 17.00 23.50 20.00 12.50  70.00 29.50 .21.00 21.20 33.50 24.00  87.62 28.05 23,43 24.15 40.00 26.78  35.50 31.20 .17.. 2 0 .  40.84 35.48 18.65  .1.3517  JSSAL  D E.GR EE_.OF__ERJE£.O.OM F =  A  VS.  SSX  LOG  .0.4005  LOG  VS.  V  SSY  SSX  FREEDOM  LOG  0.2844  0.5057 + 0.0115 0 .9979...  VS.  LOG  0.1362 0 . 4 0 50 .0.5100 0.4960 0.2980 0.4450 0.2840 0.3360 0.6410  SP  —0.7340  -0.5430  X  SP  0.6187  0.4577  X  Q  1.3517  TS  1.6720 3.9300 5..O000. 4.8700 3.3000 4.2200 2.9600 3.5500 5.6300  10 2144.6553  SSY  0.3986  REGRESSION EQUATION Y= -0.5055 + S T A N D A R D . E R R O R O F . E S T IM A T E 0 .012 2 CORRELATION COEFFICIENT 6.9983 D E G R E E OF FREEDOM 10 F = 2648.8000  LOG  0.2780 0.1840  10 1902.6912  REGRESSION EQUATION Y= STANDARD ERROR OF E S T I M A T E C O R R E L A T I O N . C Q E F F I C I E NT OF  2.7200 1.9100  Q  1.3517  DEGREE F =  43.52 64.76  Q  REGRESSION EQUATION Y= 1.5798 + STANDARD ERROR OF E S T I M A T E 0.0145 CORRELATION COEFFICIENT -0.9976  LOG  TM  Q  SP  0.5421  0.7327  X  f f"  L  REGRESSION EQUATION Y1.3481 • STANDARD ERROR O F E S T I M A T E 0.0135 CORRELATION COEFFICIENT -0.9971 DEGREE OF FREEDOM 10  ^  F  =  -0.4546  2 3 4  X  1522.2800  1LOG  TP  VS.  LOG Q  r SSX  f"  ;•"  f-  (  ( r  r ("..  1.3517  SSY  0.3411  SP  REGRESSION EQUATION Y= 1.5257 • STANDARD ERROR OF E S T I M A T E 0.0170 CORRELATION COEFFICIENT -0.9962 D E G R E E OF F R E E D O M 10 F  =  LOG  -0.5004  X  1166.0486  TSS  SSX  VS.  LOG  Q  1.0294  SSY  0.2185  SP  REGRESSION EQUATION Y= 1.3457 + STANDARD ERROR OF E S T I M A T E 0.0148 CORRELATION COEFFICIENT -0.9970 D E G R E E OF F R E E D O M 7 F = 985.6196  LOG  -0.6764  TPP  SSX  VS.  -0.4593  X  LOG Q  1.0294  REGRESSION  •0.4729  _  EQUATION  _SSY  Y=  0.2615  .  1.5219  +  S T A N D A R D ERROR O F E S T I M A T E 0.0071 CORRELATION COEFFICIENT -0.9994 DEGREE OF FREEDOM 7 F = 5139.0664  -0,5186  _SP  -0.5037  X  .  c,  (••  r  .  —-1::  ---  -—  -  PHYLLIS CREEK. REACH 2-3  MERN TIMEX  PERK  TIME  STARTING  TIME  PHYLLIS CREEK. REACH 2-3  Q IN CU M /  SEC  A  FLOW AREA .  +  VELOCITY  PHYLLIS NO  ID  CREEK, Q  (L/S)  3-4 TP  TS  TM  V  3  0  18.00  339.00  37.00  39.56  2.8800  1  32.00  45.00  1.7400  0.  6  0  338.00  52.46  39.50  47.00  53.34  1.7500  0.1930  11.50  64.00  64.70  -1J&-.JB.0.  .18.83  17.00  26.50  29.88  24.50  28.52  14.50  17.33  5.2200  0.5950  13.50  15.41  5.5300  0.6550  750.00  228.00  0  10  1070.00  1  27  1  LOG  TM  3100.00  10.30  3690.00  8.90  VS.  SSX  LOG  STANDARD  CORRELATION DEGREE =  OF  SSY  EQUATION  ERROR  OF  A  VS.  Y=  ESTIMATE  COEFFICIENT  LOG  3.3300  1.4903  0.0184  SP  +  -0.5147  -0.8211  X  -0.9972 8  Q  SSY  1.5952  REGRESSION  EQUATION  ERROR  CORRELATION DEGREE  OF  OF  0.3676  Y=  0.4801  ESTIMATE  COEFFICIENT  SP  +  0.4787  0.7636  X  0.0173 0.9971  FREEDOM  8  F..=  1219.084 5  V  VS.  SSX.  LOG  Q  .1,5952  REGRESSION STANDARD D E G R EE  OF  0,4183.  „__S5Y_.  EQUATION  ERROR  CORRELATION  OF  -0.4786  Y=  ESTIMATE  COEFFICIENT  F R E E DOM  SP  +  0.5106  0.8146  X  0.0182 0.9972 81  =  SSX  3.1200  1248.8062  STANDARD  LOG  0.4250  FREEDOM  SSX  LOG  1.4870  Jt.5600.  Q  1.5952  REGRESSION  LOG  19.00  1200.00  28 29  53.00  24.9il.00..  1  19  F  237  5  .13.  F  REACH  1260.8452  TS  VS.  LOG  1.5952  Q  SSY  0.5792  SP  -0.9452  0.2600 1950  0.1608 0.546Q. 6.3440 0.3610  238 r  REGRESSION  STANDARD  EQUATION  ERROR  CORRELATION DEGREE  >  F = LOG  TP  OF  Y=  ESTIMATE  COEFFICIENT  FREEDOM  VS.  SSX  OF  LOG  1.2809 + 0.0523 -0.9833 8  :  ;  Q  ;  SSY  1.5952  CORRELATION COEFFICIENT D E G R E E OF FREEDOM F =  TSS  VS.  SSX  :  0.4718 1.4390 + 0.0303 -0.9932 8 506.9019  STANDARD DEGREE F  =  LOG  SSY  EQUATION  ERROR  CORRELATION OF  TPP  SSX  STANDARD  COEFFICIENT  EQUATION OF  Y=  0.1959 "1.4235 + 0.0113 0 .9987 5 1521 .2705  ESTIMATE  COEFFICIENT  FREEDOM  DONE STOP  1.2698 + 0.0173 0 .9972 5 706 .3044  SSY  F = P L G T _ J A P _ E _ S U C C E S S . F UL L Y  EXECUTION  -0.5401  -0. 8616 X  SP  -0. 3982  .-0..532O._x_  LOG Q  ERROR  CORRELATION CF  Y=  0.2131  ESTIMATE  0.7485  REGRESSION  DEGREE  OF  FREEDOM  VS.  SP  LOG Q  0.7485  REGRESSION  X  204.5374  REGRESSION EQUATION Y= STANDARD ERROR OF ESTIMATE  LOG  -0.5925  0 TERMINATED  WR I T T E N _  SP  -o. 3825  -0.5109 ~x  :  ~- -  PHYLLIS CREEK. REACH 3 - 4  A  MEAN TIME PERK TIME  +  STARTING  TIME  PHYLLIS CREEK. REACH 3-4  PHYLLIS CREEK, REACH 4-6 NO  ID  5 0 8 1 10 0 12 1 . i s ....1 27 0 28 0 29 0  Q (L/S) 385.00 366.00 239.00 2370.00 ...1.1 CO.00 1200.00 3100.00 3720.00  TS 20.00 15.00 31.00 5.10 .8,00 9.00 4.70 5.60  2 i | 1  TP 28.00 26.00 35.00 8.40 12...8D 14.00 7.30 6.90  TM  A  29.44 31.49 35.00 9,54 14.43 16,23 7.57 7,79  V  2.2300 2.2700 1.6580 4.4500 3. 1300 3.8400 4.6200 5.7100  LOG _T.M._V.S.,_L.O.G_Q SSX  1.4633  SSY  0.5280  REGRESSION EQUATI.ON._Ys_ 1.2102 + STANDARD ERROR OF ESTIMATE 0.0345 CORRELATION COEFFICIENT -0.9932 DEGREE OF FREEDOM 7__ F = 437.0291 LOG A SSX  SSX  -0.8730  _-0.5966 X  VS. LOG Q 1.4633  SSY  0.2438  REGRESSION EQUATION Y= 0.5049 + STANDARD ERROR OF ESTIMATE 0.0341 CORRELATION COEFFICIENT 0.9856 DEGREE OF FREEDOM 7 F = 203.3331 LOG V  SP  SP  0.5887  0.4023 X  VS. LOG Q 1.4633  SSY  0.5279  REGRESSION EQUATION Y= -0.5044 + STANDARD ERROR OF ESTIMATE 0.0346 CORRELATION COEFFICIENT 0.9932 DEGREE OF FREEDOM 7 F = '_ . 435.2229 1  SP  0.8729  0.5965 X  LOG TS VS. LOG Q SSX „  1.46 33  REGRESSION EQUATION  SSY Y=  0.6307  SP  _ - 0 . 9286  1.0009 +  -0.6346 X  0. 1730 0.1610 0.1450 0.5330 0.3520 0.3130 0.6710 0.6510  242 STANDARD ERROR OF E S T I M A T E 0.0831 CORRELATION COEFFICIENT -0.9666 DEGREE OF FREEDOM 7 F = 85.3634  LOG  TP  SSX  VS.  LOG Q  1.4633  SSY  0.5447  SP  REGRESSION EQUATION Y= 1.1672 + STANDARD ERROR O F E S T I M A T E 0.0246 CORRELATION_COEFFICIENT -0.9967 _ _ DEGREE OF FREEDOM 7 F = 893.3013  LOG  TSS  SSX  VS.  0.3326  SSX  VS.  SSY  0.1108  SP  0.3326  SSY  Y=.  0.1230  1.1447  0.0152  STANDARD ERROR O F ESTIMATE CORRELATION COEFFICIENT -0.9991 D E G R E E OF F R E E O O M 2 =  -0.5771  -0.1919  X  LOG.  R E G R E S S 10N_ E . Q U A T I O N  F  X  LOG Q  REGRESSION EQUATION Y= 0.9250 + STANDARD ERROR_OF E S T I M A T E ^ . _0.0028_ CORRELATION COEFFICIENT -1.0000 DEGREE OF FREEDOM 2 F = 14613.2969  LOG.TPP  -0.6081  -0.8898  529.8909  SP  +  -0.6076  -0.2020  X  PHYLLIS CREEK. REACH 4-6  MEAN TIME PEAK TIME STARTING TIME  244  PHYLLIS CREEK. REACH 4-6  ft IN CU M /  A  FLOW AREA  +  VELOCITY  SEC  PHYLIS  LOWER  NO  Q  ID  10 20 30 40 LOG  245  CL/S)  TS  365.00 269.00 4358.00 3415.00 TM  SSX  V S . LOG  4.58 4.75 1.56 1.75  TP 10.33 12.00 2.55 3.00  TM  Q  1.2032  SSY  0.5027  REGRESSION EQUATION Y= 0.8764 + S T A N D A R D ERROR OF E S T I M A T E 0.0280 CORRELATION C O E F F I C I E N T -0.9984 D E G R E E OF F R E E D O M 3 F = 639.7966  LOG  A  SSX  VS.  1.203 2  V  SSY  V S . LOG  0.1489  SSY  0.5114  REGRESSION EQUATION Y= -0.5451 + S T A N D A R D ERROR OF E S T I M A T E 0.0309 CORR E L AT I ON „C0 E F F I C I ENT 0 . 9 9 8 1 __„._ D E G R E E OF F R E E D O M 3 F = 532.2039  SSX  TSS  -0.7765  -0.6454 X  V S . LOG  1.2032  S_P  Q .4206  0.3496  X  Q  'SS X " " 1 . 2 0 3 2  LOG  SP  LOG  REGRESSION EQUATION Y= 0.5449 + S T A N D A R D ERROR O F E S T I M A T E 0.0310 CORRELATION COEFFICIENT 0.9935 D E G R E E ^ O F FREEJDOM„ 3__I_ F = 152.6978  LOG  2.3300 2.3190 5.6140 5.6910  13.79 18.18 2.78 3.60  S P 0 . 7 8 2 9  0.6507  X  .  Q  SSY  0.2045  REGRESSION EQUATION Y= 0.4604 + STANDARD ERROR 0F_ E S T I M A T E 0.0197 _ CORRELATION "COEFFICIENT -0.9981 D E G R E E OF F R E E D O M 3 F = 525.7346  SP  -0.4951  -0.4115 X  0.1565 0.1159 0.7760 0.6000  -2-46LGG  >  SSX  TPP  VS.  LOG Q  1.2032  SSY  REGRESSION EQUATION Y= S T A N D A R D ERROR O F E S T I M A T E  CORRELATION COEFFICIENT DEGREE OF FREEDOM F  r-  =  0.3704  SP  0.7671 + 0.0073  -0.5548 __•  -0.9999 3  6927.8672  -0.6675  X  PHYL IS'. LOWER  STARTING TIME  248  PHYLIS LOWER  249  p. C C  FORTRAN /360. PROGRAM *PD* FOR SOLUTION OF THE DIFFERENTIAL EQUATION.OF UNSTEADY FLOW THROUGH A CASCADE OF'.RESERVOIRS.  C C C C C C  D:  CONTROL CARDS •  0  C  C  NO 1, Q 0 > NO 2, TO. = NO 3, W = NO 4 TIT=  .  (F6.0) (F6.Q) (F6.0)  •• •  .: ''/••••''  UNITS"ARE METERS ANO SECONDS EXCEPT'AS NOTED BELOW. BETA IS THE DISPERSION COEFFICIENT, WHICH CAN BE ESTIMATED AS (QO / QD1**0.2 . ALPHA IS THE RELATIVE CHANGE IN DISCHARGE, .. ( 0 ( END.) / Q( ST AR T) ) - 1.0.. .... THE COMPUTATIONS ARE PERFORMED FOR THE PERIOD TS - TE. TS AND TE ARE IN MINUTES FROM THE START OF THE TEST, TO IS THE STARTING TIME IN HOURS AND MINUTES(E.G. 1 4 2 0 . FOR »20 MINUTES PAST 2PM' ) WIDTH IS THE CHANNEL WIDTH, WD. LENG.NTH IS THE TOTAL LENGTH OF THE TEST REACH.  c C  . -  ;  .  C  v./,  Q AT START ,., AL..= ALPHA, .. BE = BETA STARTING T , TE = END T DT = TIME I NT START OF TIME. COUNT , v, y WIDTH , L '= LENGTH ' ' ' AA £ BA TITLE (20A4)  EXPLANATION OF TERMS:  C _C C C C C _C C C C  .  .-. •'  •• - ':• c  '  :  V  . OUTPUT::  r  "C C C  THE PROGRAM PRINTS THE.SOLUTION OF THE CASCADE EQUATION A(T) , THE CORRES PONDING Q ( T ) , AND SOME OF THE TERMS IN THE EQUATION FOR A ( T) .  c  •  DIMENSION TIT(20) COMMON L , P, W, C, T, EX1 , EX2, K EXTERNAL AUX1, BE, AUX2 REAL L , LS , LE  c. .. C  1 2  r.  C  ..J.  ... .  READ INITIAL DATA READ ( 5 , 1 ) QO, AL, BE READ (5,1 ) TS, T E , DT , TO READ ( 5 , 1 ) W, L , AA, BA FORMAT (12F6.0) READ (5,2) JIT. ; FORMAT (20A4) INITIALIZE AO = A A *(Q0 .** BA) .: ' AEND = A A * ( ( Q O * ( 1 . + A L ) ) *#BA ) AL = .( AEND - AO )/ AO S i :. C = ( QO ** ( l . - B A ) ) / (AA*BA )••',• P  ' .= S Q R T U 2 4 0 . * C)  / ((BE * ' W ) * * 2 M  •\ ' •."  COEFl = AO / (BE *W * SQRT (6.2 83 * P ) ) PI8=A0* ( 1. + A L ) / SQRT( 8. * 3.1416 ) C0EF2 = PI8 * ( ( ( 240. * C * L ) / HPv B E * W ) **2 ) ) * * 0 . 2 5 DL . = L/20. .  =  N  c c  4  5  c c  (TE  -  TS)  250  /DT  WRITE I N I T I A L DATA WRITE ( 6 , 3) TIT FORMAT( 1H 1, 2 0 A 4 ) I TO =TO  WR.I TE 1.6 , .4 1......Q0.. , . , . . . A L _ B E . , I TO , TS , TE , , ' DT 1 W , L , A A, BA , 2 AO , C y" " ' " CGEF1 , C O E F 2 ,P FORMAT ( * I N I T I A L C O N D I T I O N S ' / l » I N I T I A L 0 (QOI , ALPHA ( A L ) , BETA (BE) = 2 ' START OF T I M E COUNT ( I T O ) , T S , T E , DT = », 3». WIDTH ( W) .. , L E N G T H (i. ) , A A , BA 4« I N I T I A L AREA ( A O ) , C E L E R I T Y (C) 5« C O E F 1 , C O E F 2 , P WRITE (6,5) FORMAT ( 0 TIM E 1ST E X P O . 1ST I N T E G . 1ST 2ND TERM A(T) Q(T) '/) 12ND I NT E• . 1  DO LOOP FOR N V A L U E S OF DO 6 I = I, N T = TS+ ( 1 - 1 ) * DT  3F10.3 / 16, 3F8. 1 / / 4F10.3 // 2F10.3 3E14.5 ) TERM  2ND  AIT)  C  c  F I R S T I N T E G R A L OVER X A I NT I = 0.0,... LE = 0.0 DO 7 J= 1, 20 LS = LE IE = LS + DL K =1 All =. _ F G A U 1 6 ( L S , L E , A U X l A I NT 1 = A I N T 1 + A l l CONTINUE FT1 = C 0 E F 1 * A l N T 1 / (T  ) **0.25)  C C  SECOND  INTEGRAL  OVER  A l NT 2. TTE TO I F F DO 8 TT S  = 0.0 '.; = 0.0 = T / 20.0 J = 1 ,20 = TTE  TTE  = TTS +  K  _  = 1  T  TDIFF  TTE AT ? = FGAU16( T T S , A I N T 2 = A I N T 2 + AI2 CONTINUE FT2 = C0EF2 * AINT2 A = FT 1 + F T 2 0 . = ( A. / A A ) * * U . O  AUX2  )  /BA)  .  ;._  C C  WRITE  RESULTS  9 6  WRITE ( 6 , 9 ) FORMAT ( I X , CONTINUE STOP  T , E X 1 , A INT 1 , FT 1 , F4.0 , 8E12.4 )  EX2  ,  AINT2,  FT2  , A  EXPU  C C C  FUNCTION  • AUXl  {  X  F U N C T I O N C A L L E D BY  251  ) THE L I B R A R Y  PROGRAM F G A U 1 6  REAL L COMMON L» P» B E , H,. C , T , E X 1 , E X 2 , K . EX1 = P. *SQRT_( ( L - X ) * T ) + ( X - L - ( 6 0 . * ..C. * T) ) AUX1= EXP ( E X 1 ) /(( L-X}*# 0.25) K = 0 RETURN  /.(BE*  W )  •-' •- E N D  FUNCTION  AUX2  { Z)  c C  F U N C T I O N C A L L E D BY  THE  LIBRARY  PROGRAM  FGAU16  r _ _ L COMMON L , P EX 2 = P * AU X 2 = EXP K = 0 RE TURN END  T  B E , W, C , T, E X 1 , EX 2 ,K SORT ( L * ( T - I) ) + (60.*C*Z (EX?) / (( T - Z)**0.75)  - 60.*C*T - L ) I, ^ BE*W)  •p. D: SAMPLE P H Y L L I S  CREEK,  I N I T I A L I N I T I A L  OUTPUT  2 2 , 1 9 6 8 . DOWNSURGE  JUNE  CONDITIONS Q  START  OF  WIDTH  (W)  IQO) TIME ,  ,  TlMF  1ST  ALPHA  LENGTH  I N I T I A L * A R E A C0EF1  ,  COUNT ( A O ) ,  C 0 E F 2 ,  I A D ,  U T O » , ( L I ,  8ETA  T S ,  A A .  C E L E R I T Y  T E ,  (BE)  =  OT  =  - 0 . 0 6 5 1 2 . 0  1 1 . 5 0 0  BA t C )  0 . 1 4 0 0 5 E 1ST  I N T E G .  1ST  TERM  2 N D  EXPO.  0 . 5 4 0  6 0 . 0  7 7 7 . 0 0 0  2 . 9 1 8  ;  P  EXPO.  0 . 8 1 5 1300  2 . 0 3 . 2 6 0  0.541  0 . 5 1 6 0 0  0 . 3 8 4 8 4 E  2 N D INTE.  01 2 N D  0 . 1 7 9 1 9 F  01  Am  TERM  Q(T)  12.  - 0 . 3 4 6 1 E  02  C . 3 8 7 4 E  02  0 . 2 9 1 5 E  01  - 0 . 9 8 1 3 E  02  0 . 4 5 3 8 E - 0 6  0 . 1 7 4 6 E - 0 5  0 . 2 9 1 5 E  0 1  0 . 8 1 3 4 E  0 0  14.  - 0 . 4 2 2 9 E  02  0 . 4 0 2 7 F  02  0 . 2 9 1 5 E  01  - 0 . 9 6 1 1 E  02  0 . 2 5 7 2 E - 04  0 . 9 8 9 9 E - 04  0 . 2 9 1 6 E  01  0 . 8 1 3 6 E  00  - 0 . 5 0 1 2 E  02  0 . 4 1 6 1 E  02  0 . 2 9 1 4 E  01  - 0 . 9 4 2 5 E  02  16. 18. 2 0 . 2 2 .  _-_0...5m9.E__ Q 2 L _ - 0 . 6 6 1 6 E  02  - 0 . 7 4 3 3 E  02  0 . 4 . 2 . 5 . 3 E _ Q 2 _ —.0*23320.  _0_1_ - 0 . 9 2 5 1 E _ 0 2 _  0 . 5 7 2 7 E - 03  0 . 2 2 0 4 E - 02  0 . 2 9 1 6 E  01  0 . 8 1 3 7 E  00  C . 6 0 Q 9 E - 0?  0_._23.12Er 01  0 . 2 9 1 5 E  01  0 . 8 1 3 1 E  00  0 . 4 1 9 2 E  02  0 . 2 7 7 6 E  01  - 0 . 9 0 8 9 E  02  0 . 3 4 C 8 E - 01  0 . I 3 1 2 E  00  0 . 2 9 0 8 E  01  0 . 8 0 9 5 E  00  0 . 3 7 6 8 E  02  0 . 2 4 3 7 F  01  - 0 . 8 9 3 6 E  02  0 . 1 1 6 8 E  00  0 . 4 4 9 6 E  00  0 . 2 8 8 7 E  01  0 . 7 9 8 7 E  00  24..  - 0 . 8 2 5 7 E  02  0.2881E.  02  0 . 1 8 2 3 E  01  - 0 . 8 7 9 1 F  02  C . 2 6 6 4 E  00  0 . 1 0 2 5 E  01  0 . 2 8 4 8 E  01  0 . 7 7 9 2 E  00  2 6 .  - 0 . 9 0 8 9 E  02  0 . 1 7 7 5 F  02  0 . I 1 0 1 E  01  - 0 . 8 6 5 3 E  02  0 . 4 4 2 3 E  00  0 . 1 7 0 2 E  01  0 . 2 8 0 3 E  01  0 . 7 5 6 5 E  00  2 8 .  - 0 . 9 9 2 7 E  02  0 . 8 5 7 0 F  01  0 . 5 2 1 8 E  00  - 0 . 8 5 2 1 E  02  0 . 5 8 3 3 E  00  0 . 2 2 4 5 E  01  0 . 2 7 6 7 E  01  0 . 7 3 8 4 E  00  3 0 .  - 0 . 1 0 7 7 E  03  0 . 3 2 2 2 E  01  0 . 1 9 2 8 E  00  - 0 . 8 3 9 5 E  02  0 . 6 6 3 4 E  00  0 . 2 5 5 3 E  01  0 . 2 7 4 6 E  01  0 . 7 2 8 3 E  00  3 2 .  - 0 . 1 1 6 2 E  03  0 . 9 4 7 4 E  00  0 . 5 5 7 9 E - 0 1  - 0 . 8 2 7 4 E  02  0 . 6 9 6 8 E  00  0 . 2 6 8 1 E  01  0 . 2 7 3 7 E  01  0 . 7 2 4 0 E  00  3 4 .  - 0 . 1 2 4 7 E  03  0 . 2 2 0 2 E  00  0 . 1 2 7 7 E - 0 1  - 0 . 8 1 5 7 E  02  C . 7 0 7 3 E  00  0 . 2 7 2 2 E  01  0 . 2 7 3 5 E  oi  0 . 7 2 2 8 E  0 0  3 6 .  - 0 . 1 3 3 3 E  03  0 . 4 0 9 8 E - 0 1  0 . 2 3 4 3 E - 0 2  - 0 . 8 0 4 5 E  02  0 . 7 0 9 8 E  00  0 . 2 7 3 2 E  01  0 . 2 7 3 4 E  01  0 . 7 2 2 4 E  00  3 8 .  - 0 . 1 4 1 9 E  03  0 . 6 1 8 7 E - 0 2  0 . 3 4 9 0 E - 03  - 0 . 7 9 3 6 E  02  0 . 7 1 0 3 E  00  0 . 2 7 3 3 E  01  0 . 2 7 3 4 E  01  0 . 7 2 2 4 E  00  4 0 .  - 0 . 1 5 0 5 E  03  0 . 7 6 7 7 E - 0 3  0 . 4 2 7 5 E - 04  - 0 . 7 8 3 1 E  02  0 . 7 1 0 3 E  00  0 . 2 7 3 4 E  01  0 . 2 7  01  0 . 7 2 2 4 E  00  4 2 .  - 0 . 1 5 9 2 E  0 3  Q . 4 3 6 0 E - 03  00  4 4 .  - 0 . 1 6 7 9 E  03  0 . 6 8 8 5 E - 0 5  - 0 . 7 6 3 1 E  02  0 . 7 1 0 4 E  0 0  0 . 2 7 3 4 E  01  _0_^2J_34E_ 01  0 . 7 2 2 3 E  0 . 3 7 4 4 E - 06  - 0 . 7 7 . 2 9 E _ 0 . 2 _ __Q..J_LOAE__.0.Q_  0 . 2 7 3 4 E  01  0 . 7 2 2 3 E  00  4 6 .  - 0 . 1 7 6 7 E  03  0 . 5 0 8 6 E - 0 6  0 . 2 7 3 5 E - 07  - 0 . 7 5 3 4 E  02  0 . 7 1 0 4 E  00  0 . 2 7 3 4 E  01  0 . 2 7 3 4 E  01  0 . 7 2 2 3 E  00  4 8 .  - 0 . 1 8 5 4 E  03  0 . 3 2 2 4 E - C 7  0 . 1 7 1 6 E - 08  - 0 . 7 4 4 1 E  02  0 . 7 1 0 4 E  00  0 . 2 7 3 4 E  01  0 . 2 7 3 4 E  01  0 . 7 2 2 4 E  00  5 0 .  - 0. 1 9 4 2 F  03  0. 1770E-08  0 . 9 3 2 5 E - 1 0  -0.7351E  02  0 . 7 1 0 4 E  0 0  0  .  2734E  0 1 0  .  2 7 3 4 E  0 1  0 . 7 2 2 4 E  0 0  5 2 .  - 0. 2 0 3 0 E  0 3  0 . 4 4 2 6 E - 1 1  -0.7262S  02  0  .  2734E  0 1 0  .  2 7 3 4 E  0  5 4 .  - 0. . . 2 . L 1 2 . E _ 0 3 _  5 6 .  - 0. 2 2 0 7 E  5 8 .  - 0• 2 2 9 6 E  0 . 7 9 2 6 E - 0 4  0. 8 4 8 6 F - 1 0 JQ. 3 5 7 6 F - 1 1  J3_..1_8A8.E__LL2_  _i0_..J_l_76E_Q2.  0 3  0. 1334E-12  0 . 6 8 3 2 E - 1 4  03  0. 4 4 3 5 E - 1 4  - 0 . 7 0 9 2 E  02  0 . 2 2 5 1 E - 1 5  - 0 . 7 0 1 0 E  02  0 . 7 1 0 4 E  0 0  0_.2_7_i_tE_ 0 1  34E  1  0 . 7 2 2 4 E 0  0  JD.7_L04E_  JD_0  0 . 7 1 0 4 E  0 0  0  .  2734E  0 1 0  .  2 7 3 4 6  0 1  0 . 7 2 2 4 E  0  0  0 . 7 1 0 4 E  0 0  0  .  2734E  0 1 0 .  2 7 3 4 E  0 1  0 . 7 2 2 3 E 0  0  2 7 3 4 _ E _ _ Q J L .  Q__.  JL._I22_t_E._0.Q...  ro ro  T  C C _C C C C C C _C C C C  SN L R *  PROGRAM FOR F L O O D R O U T I N G THROUGH S E Q U E N C E S OF N O N L I N E A R R E S E R V O I R S AND K I N E M A T I C C H A N N E L S , W R I T T E N I N F O R T R A N / 3 6 0 . 1 CONTROL C A R D P E R C H A N N E L ( C O N S I S T I N G OF S E V E R A L R E A C H E S ) : NO OF R E A C H E S , K R , ( 1 2 ) fi T I T L E OF C H A N N E L , T I T R , ( 1 0 A 4 ) . 3 CONTROL NO  c  NO  C  CARDS  PER  REACH;  1 CONTAINS: NO OF R E S E R V O I R S , N , ( 1 2 ) ; fi F A C T O R A L P H A L O C A L INFLOW A L O N G R E A C H , Q I N C , ( F 6 . 0 ) . _ _ •.  2  CONTAINS: T I T L E FOR R E A C H , T I T , ( 1 0 A A ) .  f  __ C C C C _C C C C C C _C C C C C C _C C C C C C C C C C C C C C C  253  NO  , AL,  (F6.0);  Parameter "Sigma" of text .  is  u  A 1  .  Alpha  II .  in  !_..„  D  i  SNLR .  3 CONTAINS: L E N G T H OF R E A C H , L , ( F 6 . 0 ) ; S T E A D Y FLOW P A R A M E T E R S , AA AND B A , ( F 6 . 0 ) ; F O R M A T I V E D I S C H A R G E , QD, ( F 6 . 0 ) „_ R A T I N G CURVE PARAMETERS, A H 1 , BH1, H O I , AH2, BH2, H02, ( F 6 . 0 ) ; STARTING T I M E , T S , ( F 6 . 0 ) ; TIME I N T . OF H - D A T A , P E L T , ( F 6 . 0 ) ; 2 X ; NO OF I N I T I A L H - D A T A , I N , ( 1 2 ) ; NO OF I N T E R V A L S TO B E C O M P U T E D , K, ( F 6 . 0 ) . R  DATA  CARDS:  INITIAL  H-DATA  ,  (12F6.0)  EXPLANATIONS: A L P H A = L ( R E S E R V O I R ) / L ( T O T A L R E A C H ) ._ _ GAUGE R A T I N G C U R V E S ARE D E F I N E D A S : Q = A H * ( H - H O ) * * B H , I N D E X 1 R E F E R S TO T H E U P S T R E A M G A U G E , I N D E X 2 TO T H E DOWNSTREAM ONE. TS I S T H E S T A R T I N G T I M E I N M I N U T E S OF T H E I N P U T D A T A . DATA : T H E PROGRAM R E A D S » I N ' H - D A T A , AND A S S U M E S THAT A L L F U R T H E R ( K - I N ) DATA P O I N T S A R E _ E Q U A L _ T O . T H E L A S T INPUT VALUE OUTPUT:  . .  THE PROGRAM P R I N T S T H E CONTROL CARD DATA A N D I N I T I A L H-DATA; I T T H E N R O U T E S T H E FLOW THROUGH S U C C E S S I V E R E A C H F S , WITH T H E O U T P U T OF R E A C H ( 1 - 1 ) + Q I N C B E C O M I N G I N P U T OF REACH ( I ) . •• • THE OUTFLOW OF E A C H R E A C H I S P R I N T E D , AND, I F T H E R A T I N G C U R V E P A R A M E T E R S ARE G I V E N , T H E GAUGE R E A D I N G S .  DIMENSION Q(100), Y(2) ,F(2) ,TEMP(2),H(IOO),T(100),Q1(100), 1 T I C 100) , T I T ( I O ) , TITR ( 1 0 ) COMMON F Q , Q I M 1 , BA REAL L  C 40  254  L O O P FOR REACHES READ ( 5 , 4 0 ) KR, TITR FORMAT ( 1 2 , 10A4) DO 41 KK = I ,KR  C C 30 20  1  C C 2 C C 3 C C 4  5 C C 43  90 C C 45  C C 6  READ  CONSTANTS  READ  ( 5 ,30).  ..N.. ,  AL  ,_.Q.I.NC_  _._  FORMAT ( I 2 , 2 F 6 . 0 ) READ ( 5 , 2 0 ) TIT FORMAT ( 10A4) ; READ (5 , 1) L , AA , B A , QD 1 TS , DELT , IN , K FORMAT! 12F6.0, 2 X , 2 12 .) ... KL= K K= K+1 IF ( K K . G T . 1 ) GO T O 4 3  ,  ; (H02, A H 1 , B H 1 , H O I , A H 2 , B H ? ,) .  READ I N I T I A L HIGHT DATA READ ( 5 , 2 ) ( H ( I ) , 1= . . 1 , I N ) FORMAT(12F6.0) IF ( I N . E Q . K ) GO T O 4 ; COMPLETE INITIAL ARRAY DO 3 I = IN, K H( I) = H( IN)... ._ CONVERT H I G H T TO D I S C H A R G E , DO 5 I = 1 , K T( I) = TS + ( I - l ) * DELT Q ( I )•=( ( H ( I ) - H 0 1 ) / A H l ) * * (1. CONTINUE ..... GO T O 4 5 ADJUST F O R KK . G T . 1 AND K L A IN = K IF < K L A . E Q . K ) GO T O 4 5 DO 9 0 N I . = K L A , . K . Q(N1) = Q(KLA)  .._  :..  _. COMPUTE  TIMES  /BHD ..  .NE.  ._  _ i  K  INITIAL CONSTANTS AD = A A * QD **BA FTT= ( L * A D * BA) / (N*QD*60.0 ) F T = F T T . * j .1 . 0 . - „ A L .) FQ = ( 1 . - A L )i / ( F T * A L ) TC = ( F T T * AL ) / ( Q ( l ) ** ( 1.0QFAC = Q ( l ) / QD IDT = 2 . 0 * D E L T / TC IF ( IDT .LT. 1 ) IDT = 1 IF ( OFAC . G T . 0 . 1 5 ) . I O T = 2*IDT _  _ BA))  WRITE I N I T I A L CONDITIONS WRITE ( 6 , 6) TITR , KK FORMAT < * 1 N O N - L I NEAR R E S E R V O I R R O U T I N G ' 1 / 10A4, ' R O U T I N G OVER ' , 1 2 , ' . REACH WRITE (6,21) TIT _  /  •)  'INITIAL  CONDITIONS'  255 21 31  7  FORMAT(1H0,  10A4  )  W R I T E ( 6 , 31> N • AL , QINC F O R M A T C O N = NO OF R E S . = • , 15, • AL(PHA) = L(RES)/L 1 F10.5 / ' QINCREMENT « ' , F10.5 ) ITS = TS WRITE ( 6 , 7 ) K L , I N , A A , B A , D E L T , I D T , I T S *t » Q D , 1 AH1, B H 1 , H 0 1 , AH2, BH2, H02, AO, FQ, FT FORMAT P O K , IN • , 2 1 7 , / • A A , BA •, 2 F 1 2 . 5 , / 1 * DT O F QO I N M I N , N O . S T E P S P E R D T • F10.5, 18 / 2 ' S T A R T I N G TIME , L E N G T H ( M ) , QO ' , 3X,I4, 2F 1 2 . 3 / 3 'AH1, BH1,H01,« , 3F15.6 /  4 5  8 C C 65 46 C C  C C  82 85  83 89 12  10  13 9 C C  «AH2, BH2, H02, « , 3F15.6 / / 'AD, FQ, FT, • , 5X, 3E15.6 // ) IF ( KK . G T . 1 ) GO T O 6 5 WRITE(6,8) ( I , T(I) , H (I) , Q(I ), I = 1, FORMAT ( ' N O TIME LEVEL DISCHARGE ' 1 < IX, 12,IX, F 7 . 1 , 2 X , F 7 . 3 , 2 X , F 1 0 . 5 >)  = \  CONVERT Q TO CONTINUE DO 4 6 1= 1 , Qll) =(Q(I)  NONDI MENS I O N A L K +  QINC)/  IN) //  Q  QD  A D V A N C E S O L U T I O N BY 1 R E S E R V O I R DO 9 I =1,N Y(l) = T(l) + FT / ( Q(1)** (l.-BAJ) Y(2) = Q(l) Ql(l) = Y(2) T K l l = Y d ) AIN = IDT D = DELT /AIN OO 10 J = 2,K COMPUTE Q(I-l) DT = F T / ( ( ( Q ( J - l ) + Ql(J-l))/2.) ^*(1. BA)) TO = T K J - l ) + D E L T / 2 . - DT DO 82 M = 1 , K IF (T(M) . G T . T O ) GO TO 8 5 CONTINUE IF (M . E Q . l ) GO T 0 B 3 QIM1 = Q(M-i) +((Q(M) - Q (M-1)) / DELT) #(T0 GO T O 8 9 QIM1 = Q (1) •__ _ _ __ C A L L RK ( Y , F , T E M P , D , 2 ,IDT ) FORMAT ( 6 E 1 4 . 4 , 215 ) QKJ) = Y(2)  T1IJI  =  CONTINUE DO 1 3 II Q (II) = T (II) = CONTINUE PRINT DO 5 0  :  -T(M-l)  )  Yd)  !  = 1,K Q1(11) T K I I )  ."  '  OUT R E S U L T S A F T E R I = 1,K .  1  REACH  _  _  _  .  50 11 61  C 41 70  256  Q( I ) = Q( I ) * QD IF { BH2 . L F . 0.0 ) GO T O 5 0 H U ) = AH2 * ( Q ( I ) * * B H 2 )+ H02 CONTINUE WRITE ( 6 , 1 1 ) N FORMAT(•ODISCHARGE AFTER « , I 2 , » RESERVOIRS * //) IF (. B H 2 . L E . _ Q . . Q ) W R I T E . . ( . . 6 , 6 1 ...I (_J_ ,. T ( I ) , . F O R M A T ( » NO TIME LEVEL DISCHARGE « // 1 ( IX, I2,1X, F7.W2X, 7X, 2X, F10.5 )) IF ( BH2 . G T . 0 . 0 . W R I T E ( 6 , 8 ) ( I, T(I), H(I), KLA = K  Q( I ) , 1 = l,K)  Q ( I ) , I = I,K)  CONTINUE WRITE ( 6 , 70) F O R M A T ( 1H1 ) STOP  C  END  SUBROUTINE C  4 11  AUXRK  (Y,F)  DIMENSION Y ( 2 ) , F(2) COMMON F O , Q 1 M 1 , BA IF ( Y(2) .LE. 0.0 ) STOP 6 F(2)= FQ* ( Q I M 1 * ( Y ( 2 ) * * ( 1 . - BA)) RETURN A END  . -  Y(2)**(2.  -  BA  ))  NON-LINEAR R E S E R V O I R ROUT I M G I N I T I A L CONDITIONS 8 L A N F Y C R E E K , O C T . 1 3 , 1 9 6 8 , 1.-3-5-4 BL.  CK.  REACH  1-3,  N = NO OF R E S . QINCREMENT =  =  DAM  9 0.02000  IN  12H15, AL(PHA)  FQ,  0 , 1 1 0 6 9 3F  FT,  NO  TIME  LEVEL  01 SCHARGE  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36  14.0 15.0 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 31.0 32.C 33.0 34.0 35.C 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45. C 46.0 47 . 0 48.0 49.0  1.265 1. 265 1.185 1. 180 1. 180 1. 180 1.181 1.182 1.183 1. 184 1.185 1.186 1. 186 1.187 1.188 1. 188 1. 189 1.189 1. 190 1. 190 1. 191 1.192 1. 193 1.193 1. 194 1. 195 1. 195 1. 196 1.197 1.197 1.198 1. 199 1.285 I. 290 1.293 1.295  1.09607 1 . 0 9 607 0.95794 0.94965 0.94965 0 .94965 0.95130 0.95296 0.95462 0 . 95628 0.95794 0.95960 0.95960 0 . 9 6 127 0 . 9 6 29 3 0.96293 0.96460 0.96460 0.96627 0.96627 0.96794 0.9696 2 0.97129 0 . 9 7 129 0.97297 0.97464 0.97464 0.97632 0 . 9 7 800 ' 0.978000.97969 0 . 9 8 137 1. 13 223 1. 1 4 1 3 7 1.14687 1.15054  DISCHARGE  AFTER  9  RESERVOIRS  R O U T I N G OVER  OUT  02  1.  REACH  45  = L<RES)/L  K , IN 50 36 AA , BA 3,37500 0.47800 D T . O F QO IN MIN , N O . S T E P S PER DT S T A R T I N G T I M E , LENGTH (M5 , QD AH 1, B H U H O l , 1. 3 2 0 0 0 0 AH2» 8 H 2 , H02, 1. „ 2 3 0 0 0 0 AD  257  =  0.70000  1.00000 14 686.000 12.000 0.445000 -0.110000 0.354000 14.000000 0.255037E  01  0.168043E  CO  'SNLR i Printout for one of the computations of Figure 24  NO  V (  1 2 3  4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 . 39 40 41 42 43 44 45 46 47 48 49 50 51  TIME 19.2 20.2 21.2 22.2 23.2 24.2 .. 25.2 26.2 27.2 28.2 29.2 30.2 31.2 32.2 33.2 34.2 35.2 36.2 37.2 38.2 39.2 40.2 41.2 42.2 43.2 44.2 45.2 46.2 47.2 48.2 49.2 50.2 51.2 52.2 53.2 54.2 55.2 56.2 '57.? 58.2 59 . 2 60.? 61.2 6 2.2 63.2 64.2 65.2 66.2 67.2 68. 2 69.2  LEVEL 15.279 15.279 15.279 15.279 15.279 15.279 15.278 15.278 15.276 15. 2 74 15.270 15.266 15.261 15.256 15.251 15.245 15.240 15.236 15.232 15.229 15.227 15.225 15.224 15.223 15.223 15.222 15.222 15.222 .15.223 15.223 15.223 15.224 15.224 15.225 15.225 15.226 15.226 15.227 15.229 15.232 15.236 15.241 15.24 8 15.255 15.2 62 15.270 15.276 15.282 15.287 15.290 15.293  258 DISCHARGE 1.11607 1.11607 1.11605 1.11603 1.11596 1.11568 1.11488 1.11302 1.10951 1. 10382 1.09577 1.08554 1.07 365 1.06033 1.04785 1.03539 1.02 39 6 1.01392 1.00 543 0.99853 ' 0.99313 0.98908 0.98619 C.98 42 7 G.98311 0.^8255 0.93244 0.98266 C.98314 G.98379 0.98459 C.98548 0.98 64 5 0.98748 0.98858 0.9893? 0.99 144 C.99390 0.99737 1.C0415 1.01337 1.02574 1 .04094 1.05812 1.07612 1.09 37 3 1.10993 1.12 406 1 . 1353 2 1.14 521 1.15 245  f  ROUTING NON - L I N E A R R E S E R V O I R INITIAL CONDITIONS BLANEY C R E E K . O C T . 1.3, 1 9 6 8 , 1 - 3 - 5 - 4 BL .  s  ?  CK.  REACH 3 - 5 ,  N = NC OF QINCREMENT  PES. =  DAM  6 0.0800 0  IN  12H15, AL(PHA)  OUT -  K , IN 60 61 AA , BA 3.48300 0 . 52700 DT OF QO IN MIN , N O . S T E P S PER DT S T A R T I N G TIME , LENGTH (M) , QD AH 1 , B H 1 , H 0 1 , 1. 2 3 0 0 0 0 AH 2 , B H 2 , H02 _ 1. 4 5 9 9 9 9 AD,  FQ,  DISCHARGE  0.129027E  FT,  AFTER  6  NO  TIME  LEVEL  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2L 22 23 24 25 26 27 28 29 3C 31 32 33 34 35  22.0 23.0 24.0 25.0 26.0 27.C 28.0 29.0 30.0 31.0 32.0 33.0 34.0 35.0 36.0 37.0. 38.0 39.0 40.0 Al .0 42.0 43.0 44 . C 4 5.0 46.C 47.0 48. C 49.0 50.0 51.0 52.0 53.0 54.0 55.0 56.0  1 1.0 49 1 1.049 1 1.049 1 1.049 1 1.C49 1 1.049 1 1.049 1 1.049 1 1.049 1 1.049 11.049 11.049 1 1.048 1 1. 047 1 1.046 11.044 1 1.041 1 1.038 1 1.034 1 1.03C 1 1.025 1 1.021 I 1.016 11.012 1 1.008 1 1.00 4 1 1.00 I 10.998 10 . 9 9 6 10.994 1 0.99.3 1 0 . 992 10 . 9 9 1 10 . 9 9 1 10 . 9 9 0  RESERVOIRS 0 I SCHARGE 1. 1.9 60 7 1. 1 9 6 0 6 1 . iQ605 1 . 19 604 1. 19 603 L . 19 602 1. 19 601 1. 1959 3 1 . 1 9 59 2 1. 1 9 5 7 6 1 . 1953 9 1. 1 9 46 6 1. 19332 1.19110 1.18775 1.18 306 1.17693 1 . 1 6 942 1.16 071 1.1510 9 1.1409 I 1. 13055 1 . 12033 1.11071 1.10179 1.09379 1.08 63 3 1. 0 8 09 4 1.07609 1.07224 1.069 2 9 1.06713 1 .0656 5 1.06474 1.06429  259 ROUTING  02  OVER  2.  REACH  45  L.RES./L  =  0 . 7 0 0 00  1.00000 4 14 335 . 0 0 0 12.000 0 .354000 1.4.000000 0 . 331000 9.50 0000 0.270925E  01  0.158188F  00  260  ( V f  3  6  3 7 3B 39 40 41 42 4 3 44 45 46 47 48 49 5 0 51 52 53 54 55 56 5 7 5 8 59 60 61  57.G 5 8 .0 59.0 6 0 .0 6 1 .0 62.0 6 3 .0 64.0 65.0 66.0 67.0 68.0 69. C 70.0 71.0 72.0 7 3.0 74.0 75.0 76.0 77.0 7 8 .0 79. C HO . 0 B 1 .0 8 2.0  10.990 10.990 10.99 1 10.991 10.991 10.992 10.99 3  10.99 3  10.995 10.996 10.99 9 1 1.00 2 1 1.007 11.012 11.018 1 1.024 1 1 .031 1 1.0 3 7 11.043 11.049 11.05 3 1. 1. 0 5 7 11.0 60 1 1.061 1 1.0 6 3 11.063  • 1 .06 42 2 1.C6445' 1.06 4 9 1 1.06 5 5 7 1.0664 2 1.06749 1. 0 6 8 8 9 1 .0708 1 1.0735 3 1.07740 1.08 28 2 1.09009 1.G9 9 4 ? 1.110 7 9 1.12 394 1 .] 3H3 7 1.15345 1.1 ', * '* 3 1 . 18 2 5 8 1.19 5 21 1.20 58 2 1.2142 0 1 . 2 2 " 4 -\ 1.22481 1.22 7 74 1.22^62  '  NGN-LI NEAR RESERVOIR ROUTING I N I T I A L CONDITIONS BLANEY CREEK, OCT. 13,1968, 1-3-5-4 BL . CK. REACH 5-4, DAM IN 12H15, OUT N = NO  OF  RES.  QINCREMENT =  =  0.0  12  AL(PHA)  261  ROUTING  OVER  3. .PEACH  45  = L (RF S ./L =  C.70000  K , IN • 70 71 AA » 3. 1 1000 0.4 3 900 OT OF QO IN MIN t NO. STEPS PFR DT 1.00 00 0 STARTING T l ME , LENGTH ( '") , 00 14 9 30.')00 13.000 ( .3310009.500000 .1. .4 59999 AH 1 RH1,H0 L , 0.7 8 30 00 4.00 00 0 0 • 0 .63000 0 AH? BH2 , HG? AD,  FO,  FT,  0.95 89 17E 0 1  D T SCHARGE AFTER 12 RESERVOIRS NO 1 2 3 4 5 6 7 8 Q  10 11 12 13 14 15 16 17 18 19 20 21 2? 23 24 25 26 27 23 ?9 30 31 3? 33 34 35  TIME  LEVEL  2 7.8 28 . 3 29.3 30 . 8 31.8 32.8 3 3.6 34 .8 35 . P 36.8 37.8 38.8 39.8 4 0.8 4 1.8 42 . 8 43.3 44.8 45 .8 46 .8 47 . 8 48 . P 49.6 50.8 51.8 52.8 53.8 54 .8 53 . « 56.8 57.8 58.3 5 9.8 60. 8 6 1 .3  4.37 3 4.873 4.373 4. 8 7.3 4. 87 3 4.87 3 4.87 3 4. 8 7.3 4. 3 7 3 4. P. 7 3 4.373 4.873 4.873 4.87 3 4.373 4. P73 4.873 4.873 4.873 4.873 4.873 4.873 4. 37? 4.87? 4.371 4. 370 4.869 4. 86 8 4.866 4. 8 64 4. 86 2 4 . 35 9 4.856 4.85? 4. 849 :  01 SCHARGE 1 . 19 607 1.. 1.9 60 6 1 . 19 605 1. 1960 4 1 . 1 960 3 1 . 19 60? 1.19 691 1 . 19 600 1.19 600 1.195°9 1.19 593 1 . 1 9 59 7 1.. 19 00 6 1.1959 3 1 . 19 5'"! 3 1 . 19 59 1 1.19 5 3 3 1.19 5 3 3 1.19 5 7 5 1 . 1 956? 1.1 •') 5 39 1. 1950 1 1. 19 4 4 1. 1.19 3 5 0 1.19 217 1. 19 0 3 4 1. 1. R79 0 1. 18 476 1 . 1 •<• }3 9 1 . 1 7 62 6 1.17Q39 1.1648 5 1 .15 8 2 2 1.13 1 1 ? 1 .14 3 70  0.341546E 0  0 . 1. ? 5 4 3 0 0 0 0  262 (  1  36 37 38 39 40 4 2  43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 50 59 60 61 62 63 64 65 66 67 68 69 70 71  62.8 63. S 64.8 65.8 66. 8 67 . 8 68.8 69.8 70.8 71.8 72.8 73 . 8 74 . 8 75.8 76. P 77 .8 78 . 8 79.6 00 .8 81.8 82.8 8 3.8 84.8 8 5.8 86.8 87.8 88. 8 89. 8 90.8 91.8 92.8 v 3 . 8 94 . 8 95.8 96.8 97 . R  4. 845 4. 842 4.838 4.8 35 4.832 4.82 8 4.826 4. 82 3 4.821 4.819 4.81 7 4.816 4.815 4.814 4.813 4.813 4.813 4.813 4.813 4.814 4.815 4.816 4.817 4.819 4.822 4.825. 4.829 4.834 4.83 9 4. 644 4.85 0 4.855 4. 8 60 4. 866 4.8 70 4.8 74  1 . 1 3 610 1.12843 1 . 1.2 09 9 1.11374 1.10 686 1. 10 044 1.09 45 5 1.0892 5 1.08456 1.08G49 1.07704 1.07419 1.07190 1.07014 1.06 88 7 1.C6807 1.06 771 1.06 73 0 1.06837 1.06947 1.0 7 120 1.07^68 1.07706 1.08143 1.08 709 1 .09 39 7 1.10 216 1. 11 1 5 9 1.12 211 1.13346 1.14 527 1.15 715 1 . 16869 1. 17952 1. 18 9 3 5 1.19 797  

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