UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Channel geometry of mountain streams Day, Terence James 1969

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1970_A8 D38.pdf [ 5.18MB ]
Metadata
JSON: 831-1.0102220.json
JSON-LD: 831-1.0102220-ld.json
RDF/XML (Pretty): 831-1.0102220-rdf.xml
RDF/JSON: 831-1.0102220-rdf.json
Turtle: 831-1.0102220-turtle.txt
N-Triples: 831-1.0102220-rdf-ntriples.txt
Original Record: 831-1.0102220-source.json
Full Text
831-1.0102220-fulltext.txt
Citation
831-1.0102220.ris

Full Text

THE CHANNEL GEOMETRY OF MOUNTAIN STREAMS by TERRY J . DAY B . A . , University of B r i t i s h Columbia, 1967  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS In the Department of Geography  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA November,  1969  -  In  presenting  this  an a d v a n c e d  degree  the  shall  I  Library  f u r t h e r agree  for  scholarly  by  his  of  this  written  at make  tha  it  for  freely  permission  purposes  thesis  in p a r t i a l  the U n i v e r s i t y  may  representatives.  is  financial  V a n c o u v e r 8,  of  British  Canada  of  Columbia,  British  by  for  gain  Columbia  shall  the  that  not  requirements I  agree  r e f e r e n c e and copying  t h e Head o f  understood  of  The U n i v e r s i t y  of  for extensive  be g r a n t e d  It  fulfilment  available  permission.  Department  Date  thesis  of  or  that  study.  this  thesis  my D e p a r t m e n t  copying  for  or  publication  be a l l o w e d w i t h o u t  my  i  Abstract Channel networks i n the glaciated mountain basins of Coastal and southern i n t e r i o r B r i t i s h Columbia (Ashnola River Basin)  offer  opportunities for morphometric studies r e l a t i n g the parameters of the flow area (A) - discharge (Q) relationship to r e a d i l y available channel and basin parameters. Steady flow conditions i n rough channels are approximated by bA equations of the form A = a^Q .  The parameters,  a^ and b^, vary >  i n d i v i d u a l l y with each channel and are related to channel dimensions; .47 a  A  =  W  D*  .17 anc  * *A  =  W  D*  *  These results are independent of  climate and under normal conditions give excellent predictions of the Q-A relations for rough channels i n both regions. The systematic v a r i a t i o n of channel dimensions within a basin 53 are related to drainage area:  = 3.7 DA  for coastal basins and  . 52 = 1.3 DA* for Ashnola basins. The influence of climate i s reflected i n the constants, with areas of higher p r e c i p i t a t i o n having . 29 larger constants.  Drainage area can replace W^: a^ = 1.74 DA"  and  08 b^ = .37 DA'  .  These relations are applicable only within a climat-  i c a l l y homogeneous region. In rough channels the Q-A relations are considered independent of slope, a result of energy d i s s i p a t i o n through frequent hydraulic, jumps. The hydromorphological equations developed here are v a l i d only for rough channels where tumbling flow predominates.  ii  TABLE OF CONTENTS  Chapter I  II"  Page INTRODUCTION  1  Hydromorphologic Studies  1  Objectives  2  Channels of Mountain Basins .  2  DIMENSIONAL ANALYSIS  . .  6  Dimensional Analysis and S i m i l a r i t y  6  Dimensional Analysis  6  Assumptions  6  Similitude Considerations during Formative Conditions  7  Parameters of the Steady Flow Equations III  FIELD METHODS Selection of Test Reaches  IV  8 10 ......  10  Survey Measurements  11  Discharge Measurements  11  Method  II  Equipment  15  FIELD RESULTS  16  Flow Data  16  Channel Data  .21  iii Chapter V  Page BASIN CHARACTERISTICS  24  Relations Between Channel Dimensions and Basin Characteristics  24  Flow Equation Parameters and A v a i l a b l e Data . . . . . VI  HYDROMORPHOLOGICAL EQUATIONS  30  Coastal Relations .  VII  29  30  Channel Dimensions  30  Basin Dimensions  31  General Equations  31  Discussion  34  Interpretation  34  Accuracy  38  CONCLUSIONS  . .  49  PHOTOGRAPHS  51  BIBLIOGRAPHY  58  ±v  LIST OF TABLES TABLE  Page  1  Flow Data  17  2  Flow Data ( K e l l e r h a l a 1970)  18  3  Channel Data  22  4  Channel Data ( K e l l e r h a l s 1970)  5  M u l t i p l e Regression A n a l y s i s  6  Width-Drainage Area Relations for Coastal Basins  . . .  28  7  Width-Drainage Area Relations for Ashnola Streams . . .  28  8  Covariance A n a l y s i s of Flow Equations  38  9  Observed and Predicted Values for a. A Observed and Predicted Values for b.  39  10  ....  23  . . . . . . . .  26  4Q  V  LIST OF FIGURES FIGURE  Page  1  Longitudinal Stream P r o f i l e s  .  2  C a l i b r a t i o n Graph .  3  Time-Concentration Graph  4  Slesse Creek Lower  19  5  Ewart Creek Upper  20  6  Channel Width - Drainage Area Relations  7  Relations between Steady Flow Parameters and Channel  13 . . .  . . . . .  .  Widths for Coastal Basins 8  14  27  32  Relations between Steady Flow Parameters and Drainage Area for Coastal Basins . . .  9  4  33  Relations between Steady Flow Parameters and Channel Width  35  10  Comparison of Channel Types  37  11  Observed and Predicted Q-A Relations  12  Observed and Predicted Q-A Relations  43  13  Observed and Predicted Q-A Relations  44  14  Observed and Predicted Q-A Relations  45  15  Observed and Predicted Q-A Relations  .  46  16  Observed and Predicted Q-A Relations  . . . . . . . . .  47  \  . .  42  vi  LIST OF PHOTOGRAPHS PHOTOGRAPH  Page  1  Salt D i l u t i o n Equipment  51  2  Brockton Creek Section 1-2  3  F i r e Pool P l a c i d Creek Section 3-4  4  Upper Section of Furry Creek  52  5  Electrode S i t e Lower Section of Ewart Upper . . . .  53  6  I n j e c t i o n S i t e Ashnola Upper  53  7  Slesse Upper  54  8  Slesse Middle  54  9  Slesse Lower  54  10  Furry Creek  55  11  P h y l l i s Lower  55  12  Log Jams on Juniper Creek  56  13  Lower Section of Juniper Creek  56  14  Middle Section of Ewart Lower  57  15  Ashnola Lower Showing Road C o n s t r i c t i o n  57  . . . . . . . . .  51 52  vii  Acknowledgments  The study was  c a r r i e d out i n 1 9 6 8 , with f i n a n c i a l  assistance from the Disaster R e l i e f Fund through the Department of C i v i l Engineering, The University of B r i t i s h Columbia.  P a r t i c u l a r thanks i s due Mr. Rolf K e l l e r h a l s ,  formerly of the Department of Geography, The University of B r i t i s h Columbia, now with the Alberta Research Council, who Ph.D  o r i g i n a l l y designed the project i n support of his research. For their assistance i n the f i e l d , the author would  l i k e to thank Mr. Doug Marsh and Mr. Rod Dale-Johnson, who  served on a permanent basis, and also for occasional  assistance, Miss June Ryder. The author also wishes to thank h i s supervisors, Dr. G.R.  Gates, Department of Geography and Dr. M.C.  Department of C i v i l  Engineering.  Quick,  Notations and Abbreviations  Cross s e c t i o n a l flow area (m ) Intercepts from the f o l l o w i n g regressions log A = f ( l o g Q) log v  m  = f ( l o g Q)  log (Ag  2/3  / 4 / 3 ) = f (log Q g Y  1/3  / 5/3) y  Exponents of the above regression Concentration of s a l t i n j e c t i o n 2 Contributing drainage area (km ) Unspecified f u n c t i o n _2 A c c e l e r a t i o n due to g r a v i t y (ms <P  S  - P)g/P  s  Length (m) 3 -1 Discharge (m s  )  Formative Discharge Slope ( s i n 9) Mean t r a v e l time  (seconds)  Time coordinate (min. or sec.) V e l o c i t y (ms •*") Mean v e l o c i t y  )  Notation W  Width (m) W  D  W c W a  0  Channel width between high water marks Channel width of coastal streams Channel width of Ashnola streams Slope angle 2 -1  Y  Kinematic v i s c o s i t y (m s  P  )  S p e c i f i c mass (g cc P  s  P  S p e c i f i c mass of channel sediments S p e c i f i c mass of water  Abbreviation cc d  ;  Cubic centimeter Derivative  df  Degrees of freedom  km  Kilometer  Lo  Longitude  Lat  Latitude  log  Logarithm to base 10  m min. NaCl RSQ  s Std. Err  Meter Minutes Sodium chloride Fraction of t o t a l sample variance explained by a regression Seconds Standard error of estimate  1  CHAPTER I INTRODUCTION A.  Hydromorphologic Studies The underlying p r i n c i p l e of hydromorphologic studies i s the  interdependence between the b a s i c h y d r a u l i c , hydrologic and morphometric c h a r a c t e r i s t i c s of a stream and i t s n a t u r a l channel.  Other  workers have found that r e l a t i o n s between these c h a r a c t e r i s t i c s , u s u a l l y i n the form of s t a t i s t i c a l equations, permit the evaluation of any q u a n t i t a t i v e change i n the channel phase of the runoff process i n terms of channel and basin dimensions. A morphometric approach to hydrology i s of p a r t i c u l a r importance to i n v e s t i g a t i o n s of ungauged basins because the necessary parameters (e.g., drainage area, channel slope, etc.) can be obtained from the,only a v a i l a b l e sources of information, namely, topographic maps and high a l t i t u d e a i r photographs. Previous s t u d i e s , however, have confined themselves to using parameters such as stream orders ( S t a l l and Fok 1968), dischargefrequency r e l a t i o n s h i p s (Kondrat'ev 1959), discharge-flow depth r e l a tions at various frequencies (Thomas 1964 and Gann 1968) and depth of mean annual f l o o d - bankful depth r e l a t i o n s ( K i l p a t r i c k and Barnes 1964) . Information of t h i s type i s generally not a v a i l a b l e f o r ungauged mountain basins, a more d i r e c t approach i s required.  =>  Such an approach i s to e s t a b l i s h the s t a t i s t i c a l r e l a t i o n s between the r e a d i l y a v a i l a b l e channel parameters and the parameters of  2 a general steady flow equation.  Since channel geometry can be con-  sidered as c h a r a c t e r i s t i c of the Individual watershed, any systematic v a r i a t i o n of the channel dimensions can be explained i n terms of the characteristics  of the related basin.  and channel characteristics  If the connection between basin  can be established then i t i s possible  relate the parameters of the flow equations to basin properties  to  that  can be obtained r e a d i l y from maps and a i r photographs. B.  Objectives The objectives of this study are: (1)  to establish the h y d r a u l i c a l l y s i g n i f i c a n t  parameters  of mountain channel networks; (2)  to establish the s t a t i s t i c a l  relations between these  parameters and channel dimensions; (3)  to establish the relations between basin and channel characteristics  to permit the substitution of basin  properties i n (2); and (4)  to investigate regional climatic affects on these relations.  C.  Channels of Mountain Basins Basins of the P a c i f i c Ranges surrounding the lower mainland of  B r i t i s h Columbia offer ample opportunities for investigating the nature of these s t a t i s t i c a l  relations.  Few runoff and p r e c i p i t a t i o n 2  records are available for basins with areas smaller than 50 km. ; however, using lowland s i t e s as an index, p r e c i p i t a t i o n i n these basins varies from 224 to 445 cm.  Channel dimensions t y p i c a l l y used i n hydromorphological studies are slope and channel w i d t h , although the l a t t e r i s considered i n d i r e c t l y by means of discharges and drainage areas.  Russian authors (Kon-  d r a t ' e v 1959) also considered roughness, however estimates of t h i s parameter are v i r t u a l l y unobtainable from the a v a i l a b l e data sources-. and have proven to be an i m p r a c t i c a l f i e l d  measurement.  The channel networks of these mountain basins have developed i n v a l l e y s whose l o n g i t u d i n a l slope i s a r e l i c g l a c i a l feature.  Figure 1  i l l u s t r a t e s how channel slopes increase i n the lower sections of the drainage b a s i n .  In basins developed by stream a c t i o n alone the channel  slopes are r e l a t e d to discharge and drainage areas ( M i l l e r 1958 and Wolman 1955), however f o r basins developed by g l a c i a l a c t i o n channel slopes can be considered independent of both discharge and drainage area. Channel widths are generally w e l l defined i n these basins and Can be r e l a t e d to e i t h e r drainage area ( M i l l e r 1958) or a formative discharge.  The f o l l o w i n g f u n c t i o n a l r e l a t i o n i s suggested wD =  where  f ( DA , S , . . . )  (1.1)  i s the channel w i d t h , DA the c o n t r i b u t i n g drainage area, QD the  formative discharge and S channel slope.  Several independent v a r i a b l e s  may be missing from t h i s equation ( e . g . , climate and sediment supply) however i t i s hoped that the dominant independent v a r i a b l e s are i n c l u d e d . The effect of vegetation and log jams, an important factor i n streams with widths l e s s than 15 m . , i s a l s o ignored.  LONGITUDINAL  STREAM  PROFILES  Equation 1.1  also ignores the e f f e c t of roughness, f o r reasons  mentioned previously i t w i l l not be considered an e s s e n t i a l v a r i a b l e . The roughness elements (see photographs) are either of g l a c i a l or scree o r i g i n and f i e l d observation indicates that they can be moved during high flows.  F i e l d observation also indicates that f o r streams of a,  given s i z e ones with steeper slopes are rougher.  6  CHAPTER I I DIMENSIONAL ANALYSIS A.  Dimensional A n a l y s i s and S i m i l a r i t y Dimensional analysis can be employed to develop the c r i t e r i a  governing dynamic s i m i l a r i t y between flow s i t u a t i o n s which are geometrically s i m i l a r but d i f f e r e n t i n s i z e . Existence of dynamic s i m i l a r i t y between r e l a t e d systems i s dependent upon s i m i l a r i t y between the major formative processes and between r a t i o s of the geometric properties of the system.  The second  can not be f u l f i l l e d i n t h i s case as slope v a r i e s among the t e s t reaches, however i t i s s t i l l possible to use t h i s method to e s t a b l i s h the r e l a t i o n s between the dominant system B.  parameters.  Dimensional A n a l y s i s 1.  Assumptions D e f i n i t i o n of the formative processes i n steep channels i s  considered w i t h i n the framework of the following  assumptions:  (1)  Channel slope i s independent of discharge.  (2)  Any change i n cross s e c t i o n a l dimensions occurs only during high flows and can be considered as functions of a formative discharge.  (3)  Transport rates are low and do not affect channel performance during non-formative c o n d i t i o n s .  This assumption  7  loses i t ' s v a l i d i t y under high flow conditions when r e s i s tance and v e l o c i t y may be s i g n i f i c a n t l y influenced by the sediment load.  B.  Similitude Considerations During Formative Conditions Not a l l processes can be considered because of the r e s t r i c t i o n  that the system must be defined i n terms of r e a d i l y available data. The dominant variables influencing the channel forming process i n steep channels are thought to be: (1)  Q^, formative discharge, the dominant Independent variable  (2)  S,  channel slope  (3)  g,  acceleration due to gravity  (4)  g , gravity submergence force acting on the sediment s  ,  j  particles'*" (5)  y»  viscosity  These v a r i a b l e s , together with one resultant channel measurement are s u f f i c i e n t to define the process. the resultant measure.  Channel width, Wp,  was chosen as  The p i theorem can be used to reduce the number  of variables by the number of fundamental dimensional units and maintain the functional relationship between the variables.  The  still seven  variables mentioned have only two dimensional units, those of length and time; therefore four dimensionless parameters or p i terms can be formed which adequately define the channel forming process.  g  g  =  (P -P)g s  p  s  The most  satisfactory  grouping f o r t h i s study i s f( Q s D  1/3  > s , g , wDg1/3) = 0  Y5/8  g  (2.1)  y2/3 S  I f Y» g and g g can be assumed constant then Q D , S and  or any other  r e s u l t a n t channel measurement are s u f f i c i e n t to define the system. C.  Parameters of The Steady Flow Equation Steady flow conditions i n n a t u r a l channels can be defined by  the c o n t i n u i t y equation Q - Av m where A i s the flow area and v  the mean v e l o c i t y .  (2.2) Leopold and Maddock  (1954) show how A and v m vary with discharge as simple power functions at a given r i v e r c r o s s - s e c t i o n .  The functions of i n t e r e s t can be  approximated by the f o l l o w i n g flow equations  v  A « aAQbA  (2.3)  - a Qbv m v  (2.4) '  Flow area i s used instead of the usual separate s o l u t i o n s for width and depth because the i r r e g u l a r nature of the channel cross-section makes determination of these v a r i a b l e s d i f f i c u l t , i f not impossible. The exponents and constants of these equations can be considered as r e s u l t s of the i n t e r a c t i o n between the hydrologic and morphologic; characteristics tion 2.1.  of the channel and may replace the width term i n Equa-  Before t h i s can be done the equations must be expressed i n  9 non-dimensional forms, one of the many possible forms of Equation 2.3 i s  . 2/3 , , n 1/3,A Ag = a A ' (Qg ) Y4/3  (2.5)  Y5/3  1/3 substituting a^' and b^ for W^g i n Equation 2.1 Y2/3  f( Q D g 1 / 3 ,  S  (2.6)  ) =0  Y5/3  solving for the constants  (2.7)  = f ( Q D , S)  Equations 2.6 and 2.7 i l l u s t r a t e the connection between the channel forming process and the free parameters of the flow equations.  As  varies with the size of the drainage basin the constants a^ and b^ w i l l also vary.  Coates (1969) has shown how the exponent b^ increase with  the s i z e of the drainage basin.  10  CHAPTER I I I FIELD METHODS A.  S e l e c t i o n of Test Reaches This study was c a r r i e d out i n conjunction with a d o c t o r a l r e -  search project on runoff concentration i n steep channel networks designed by R. K e l l e r h a l s .  K e l l e r h a l s i s attempting to determine the  physics of wave propagation i n these channels and w i l l use the r e s u l t s of t h i s study to determine the r e l a t i o n s between the free  parameters  of h i s routing equations and the relevant basin dimensions. K e l l e r h a l s ' data i s e s s e n t i a l f o r t h i s study and the t e s t reaches selected by the author were intended to extend the width and slope range of t h i s data. K e l l e r h a l s ' data encompasses 12 test reaches on four creeks i n the v i c i n i t y of Vancouver, B r i t i s h Columbia (Brockton, Blaney, P l a c i d and P h y l l i s Creeks).  Widths of these streams ranged from .89 to  :  12.28 m. and to include l a r g e r streams further t e s t reaches were establ i s h e d , three on Slesse Creek near C h i l l i w a c k , B r i t i s h Columbia and one on Furry Creek near B r i t a n n i a Beach, B r i t i s h Columbia. An a d d i t i o n a l reach was established on P h y l l i s Creek to extend the slope range. The c l i m a t i c dependence of the v a r i a b l e s i n Equation 2.1 was , i n v e s t i g a t e d by e s t a b l i s h i n g t e s t reaches i n the Ashnola Basin i n south-central B r i t i s h Columbia. of 20 cm. per year.  R a i n f a l l i n t h i s area i s i n the order  Six reaches were s e l e c t e d , one on Juniper Creek,  two on Ewart Creek and three on the Ashnola R i v e r .  11 B.  Survey Measurements The two channel dimensions to be measured i n the f i e l d , width  and slope were determined  simultaneously by chaining and hand-levelling  along the reach at either 50 or 100 foot i n t e r v a l s , depending on the length of the reach. Channel width was measured from high water marks on either side of the channel, a feature generally well marked by vegetation. The photographs i l l u s t r a t e this feature. C.  Discharge Measurements 1.  Method Stream discharges were calculated by the " r e l a t i v e s a l t d i l u t i o n "  method.  The advantage of this method i s that the high degree of tur-  bulence i n mountain streams makes the results more accurate than most other methods.  Several c r i t i q u e s of this method exist i n the l i t e r a t u r e ,  the most recent being by Church and Kellerhals (1969).  Readers wanting  a.more complete explanation are referred to this a r t i c l e .  A brief  description follows. A solution of common s a l t (NaCl) i s injected into a stream as close as possible to the center of flow. j e c t i o n must be known.  The volume S^, of the in-;:  At some downstream point, beyond the mixing  length, an electrode i s placed i n the stream to measure the conductivity of the passing wave.  The conductivity of the solution wave w i l l r i s e  from zero (taken as the background conductivity) to a peak value then f a l l back to zero.  When the entire wave has passed  S  t„ - Qj c ( t ) d t Z  v  j  ::  (3.1)  12 where t^ and  are the i n i t i a l and f i n a l times of passage and c(t)  i s the observed concentration at any time t .  Conductivity readings  are converted into concentration by means of a c a l i b r a t i o n graph shown i n Figure 2.  The graph i s constructed by measuring concentration for i  known increments of s a l t s o l u t i o n . shown i n Figure 3.  A time-concentration graph i s  Discharge i s then given by Q =  g  {  1  v  (3.2)  c(t)dt  Assuming fast i n i t i a l dispersion the flow area can be calculated from the mean t r a v e l time (T) and flow length (L) A = Q_T L  (3.3)  and from continuity v m - Q_  (3.4)  A There are several possible sources of error associated with this method, the main ones being: (1)  incomplete mixing of the s o l u t i o n ; not a serious problem during high flows or over long reaches.  (2)  changes i n the background conditions due to  temperature  changes, movement of the electrode or upstream  disturbances.  CALIBRATION GRAPH  METER READING  2.  Equipment Photograph 1 shows the equipment necessary for s a l t d i l u t i o n  measurements.  The essential equipment i s : p l a s t i c tanks of 16, 50  and 100 l i t r e volumes, needle gauges for the two smaller tanks, mixing p a i l s , pipets, f l a s k s ,  electrode and a conductivity meter (in  this case a Barnstead PM-70CB).  16  CHAPTER IV FIELD RESULTS A.  Flow Data Flow equations for the t e s t reaches were established from l i n e a r  regressions of the logarithms of A and Q of Equation 2.3 and v m and Q of Equation 2.4.  The constants of these equations were determined i n  the f o l l o w i n g manner log A - log a A + b A l o g Q  (4.1)  log v m - log a v + b v l o g Q  (4.2)  and  Tables 1 and 2 l i s t these constants for the t e s t reaches along with the standard error of estimate.  A l l equations e x p l a i n at l e a s t 99%  of the data v a r i a n c e , the unexplained variance may be due e i t h e r to measurement errors or minor changes i n the channel c r o s s - s e c t i o n . Figures 4 and 5 show data points and regression l i n e s for two of the reaches. Both sets of constants need not be c a l c u l a t e d (or predicted) because from a combination of Equations 2 . 2 , 2.3 and 2.4 b. Q = aAQ  A  b . avQ  (4.3)  V  b. + b  Q - a .. a Q A  v  A  v  (4.4)  17  TABLE 1 FLOW DATA  Test Reach  Range of Q  P h y l l i s Low  .36  -  Furry  .91  -  3.41  No. of Flow Area Constants std Runs a b err  V e l o c i t y Constants std a b err  4  3.207  .3557  7.0%  .3117  .6444  7.0%  13.9  6  5.788  .5009  13.2%  .1727  .4993  13.2% i  Slesse Low  4.7  22.58  5  2.926  .5769  2.3%  .3417  .4238  2.3%  Slesse Mid  3.23 - 13.94  5  4.179  .5213  6.0%  .2453  .4789  6.0%  Slesse Up  3.04  -  13.07  4  2.922  .5993  4.8%  .3411  .4014  5.0%  Juniper  .23  -  2.70  4  3.377  .4075  4.6%  .2988  .5932  4.3%  Ewart Low  .45  -  8.08  4  3.253  .4365  7.9%  .3075  .5632  7.9%  Ewart Up  .50  -  15.76  5  4.091  .4184  13.7%  .2444  .5817  13.7%  Ashnola Low  1.58  -  31.52  4  3.967  .4208  1.0%  .2522  .5792  1T0%  Ashnola Mid  1.50 - 33.85  4  4.638  .4647  4.2%  .2155  .5353  4.1%  -  4  3.092  .5860  3.7%  .3232  .4141  3.7%  Ashnola Up  .79  19.03  18  TABLE 2 FLOW DATA ( K e l l e r h a l s 1970)  Test Reach  Range of Q  No. of Flow Area Constants std Runs a b err  V e l o c i t y Constants std a b err  Brockton 1-2 .00016 -  .158  10  .8104 .338  13.6%  1.240  .663  13.9%  Brockton 2-3 .00073 -  .110  7  .7183 .283  4.2%  1.394  .716  4.3%  Placid  1-2 .035  -  .096  4  1.879  .340  3.3%  .5311 .659  3.5%.  Placid  2-3 .015  -  .181  5  1.930  .360  6.3%  .5166 .692  6.4%  Placid  3-4 .014  -  .404  6  3.943  .466  5.4%  .2543 .536  5.4%  Blaney  1-3 .12  - 1.15  10  3.375  .478  8 %  .2972 .522  7.6%  Blaney  3-5 .092  - 1.17  18  3.483  .527  11 %  .2852 .467  11.9%  Blaney  5-4 .125  -  9  3.110  .439  9.2%  .322  .561  9.3%  Phyllis  1-2 .312  - 3.48  9  3.262  .541  7.0%  .3067 .469  7.0%  Phyllis  2-3 .228  - 3.61  11  3.219  .458  2.7%  .3123 .542  2.9%  Phyllis  3-4 .239  - 3.69  9  3.021  .479  4.1%  .3322 .511  4.2%  Phyllis  4-6 .240  - 3.72  8  3.199  .402  8.1%  .3130 .596  8.2%  1.1  SLESSE CREEK LOWER — Flow Area  •5  — Velocity  5  IO  Q  10  EWART CREEK UPPER — Flow Area  —  Velocity  21 and  therefore a. .a = 1 A v b. +b = 1 A v  (4.5)  Since storage per unit length i s the parameter of most hydrologic significance,  the relations between the constants i n Equation 4.1 and  the channel dimensions of width and slope w i l l be investigated. B.  Channel Data Channel slopes were measured along the water p r o f i l e since i t  was impossible to reach the thalweg i n the larger streams.  Slope was  calculated as drop over length or s i n 0. As previously mentioned channel widths were measured between high water marks.  Operator error was i n e v i t a b l e , however i t i s not  thought to amount to more than 10%. Drainage areas were planimetered from 1:50,000 scale maps except i n cases where the basins bordered on the United States - Canada boundary, here smaller scale United States maps had to be used.  22  TABLE 3 CHANNEL DATA  Creek  Location  Reach Length Drop (going up stream)' (m) (m)  Slope No. of Survey Stations  Width Coeff Drainof age V a r i a - Area (m) tions (km)  228.6 29.5  .129  16  20.25  .304  39.03  Furry  Lo 120° 12' Lat 40° 36'  Phyllis  Lo 123° 12* Lat 49° 36'  Low  128.3 30.8  .219  10  14.04  .167  11.81  Slesse  Lo 121° 39' Lat 40° 02'  Low  1402.1 46.97  .0335  47  26.73  .285  125.95  Lo 121° .38* Lat 49° 01'  Mid  541.9 23.47  .0433  18  22.84  .239  110.41  Lo 121° 38' Lat 49° 01'  Upper  583.7 20.04  .0343  21  19.54  .222  105.13  609.6 81.5  .134  41  6.03  .407  21.75  1124.7 45.93  .0408  36  14.19  .302  95.75  Lo 120° 02' Upper Lat 49° 06'  579.1 20.15  .0348  19  16.36  .267  90.75  Lo 120° 10' Low Lat 49° 10'  746.8 26.2  .0351  25  22.06  .225  409.5  1002.8 26.0  .0259  33  28.17  .218  408.5  .0104  17  21.14  .170  221.5  Juniper  Lo 120° 01» Lat 49° 06'  Ewart  Lo 120° 02* Low Lat 49° 08'  Ashnola  Lo 120° 10' Mid Lat 49° 10' Lo 120° 11' Upper Lat 49° 10' i-  490.4  5.09  23  TABLE 4 CHANNEL DATA ( K e l l e r h a l s 1970)  Creek  Brockton  Placid  Blaney  Phyllis  Location (Midreach) Mt. Seymour Park, Elev.4,000' Lo:122o 56' L a t : 4 9 ° 23'  Reach Length Drop (going down stream) (m) (m) Br 1-2 Br 2-3  119.  Nr.Britannia Beach, B.C. Ph 1-2 Elev.1,400' Lo:123° 11' Ph 2-3 L a t : 4 9 ° 34' Ph 3-4 Ph 4-6  Coeff of Variations  Drainage Area (km2)  8.8  .074  36  .89  .499  0.0665  80.5 28.1  .349  27  .99  .611  0.088  79.7  .083  64  2.75  .387  .614  21.6  .0355  41  3.16  .373  1.17  62.4  .0339  122  7.02  .400  2.60  685.  31.9  .0466  46  12.76  .435  7.43  335.  17.5  .039  23  11.06  .414  7.70  930.  85.3  .0947  62  12.92  .292  7.94  777.  23.7  .0305  52  11.48  .314  8.69  716.  34.9  .0487  48  12.57  .216  10.41  617.  39.5  .064  42  12.64  .190  10.99  305.  30.2  .099  21  12.28  .226  11.34  UBC Research Forest, P l 1-2 960. Elev.1,400' Lo:122° 34V P l 2-3 610. L a t : 4 9 ° 18.5 t P l 3-4 1844. UBC Research Forest, B l 1-3 Elev. 950' L o : 1 2 2 ° 3 4 . 5 * B l 1-5 Lat:49o 17' B l 5-4  Slope No. of Width Survey Stations (m)  24  CHAPTER V BASIN CHARACTERISTICS A.  Relations Between Channel Dimensions and Basin C h a r a c t e r i s t i c s S i m i l i t u d e considerations i n Chapter I I , Section A , suggest and S are s u f f i c i e n t to determine channel w i d t h .  drainage area, DA, can replace  Contributing  since discharges for constant  frequencies are p r o p o r t i o n a l to basin area ( M i l l e r 1958, Gann 1969). Relations to be established are then WD = f ( DA, S )  (5.1)  However, while Equation 2.1 i s independent of c l i m a t e , t h i s equation i s not.  For a given formative discharge and channel w i d t h , l a r g e r d r a i n -  age areas are required i n regions of lower p r e c i p i t a t i o n .  The constants  of Equation 5.1 w i l l r e f l e c t t h i s c l i m a t i c e f f e c t . The best f i t t i n g equations were supplied by m u l t i p l e regression analysis on the log transformed data W = 3.5 D A * 5 3 S~" 0 2 c  (5.2)  W = 1.3 D A ' 4 8 S~" 0 5 a  (5.3)  W represents channel widths i n the Coastal basins and W i n the c a Ashnola basins.  The equations e x p l a i n 98.5% and 97.1% of the v a r i a t i o n  i n WQ r e s p e c t i v e l y .  Data for Slesse Creek was not included because i t s  25 regional p r e c i p i t a t i o n regime (approximately 170 cm. per year) f a l l s between regional conditions of the two main areas. Low slope exponents indicate that this variable has l i t t l e a f f e c t on the equation.  Table 5 indicates that slope i s non-significant at  the 5% l e v e l (see Chapter VI, C . l for explanation).  Simple linear  regressions are then adequate  W - 3.7 DA" c  53  (5.4)  W = 1.3 DA* a  52  (5.5)  Both equations are s i g n i f i c a n t at the 1% l e v e l (RSQ's of .985 and .969) with standard errors of 13.8 and 12.7%. Figure 6 shows the data points and regression l i n e s , the scatter about the l i n e s r e f l e c t i n g the influence of lakes, log jams, e r o d i b i l i ty of sediments, canyons, etc.  Comparisons between observed and  predicted channel widths are shown i n Tables 6 and 7. Predicted widths, p a r t i c u l a r l y for the coastal equation, are generally quite accurate' f o r channels such as P h y l l i s Creek where the channel forming process is,not noticeably disturbed by bedrock and log jams.  The most serious errors  occur on Furry and Blaney Creeks, the former i s confined by the valley, walls and the l a t t e r has sections of i l l - d e f i n e d channels.  Ashnola  ?  Lower i s not considered i n Equation 5.3 and 5.5 (or Table 7) as a section i s constricted by a road.  i  Figure 6 also i l l u s t r a t e s the climatic dependence of the widthdrainage area r e l a t i o n s .  Coastal basins having a larger annual p r e c i p i -  tation experience larger possible formative discharges as compared to  26  TABLE 5 MULTIPLE REGRESSION ANALYSIS  Coastal B.C. RSQ F PROB STD ERR Y df  .9854 0.0000 14% 11  dependent v a r i a b l e W  Var.  Coeff.  Const S DA  3.457 - .0232 .525  Standard Error 15% 13% 5%  F-Ratio  F Prob.  .1875 702.8815  .6749 0.0000  I n t e r i o r B.C. RSQ F PROB STD ERR Y df  .9712 .0393 15% 2  dependent v a r i a b l e W  Var.  Coeff.  Standard Error  Const S DA  1.327 '-. .0584 .4769  36% 39% 31%  F-Ratio  0.1699 16.3687  F Prob.  .7136 .0634  28  TABLE 6 WIDTH-DRAINAGE AREA RELATION FOR COASTAL STREAMS  Stream  Drainage Area  Channel Width  Predicted Width  Brockton  1-2 2-3  .07 .09  .89 .99  .871 1.018  Placid  1-2 2- 3 3- 4  .61 1.17 2.60  2.75 3.16 7.02  2.833 3.982 6.060  Blaney  1-3 3-5 .5-4  7.43 7.70 7.94  12.76 11.06 12.92  10.536 10.736 10.911  1-2 2- 3 3- 4 4- 6 Low  8.69 10.41 10.99 11.34 11.81  11.48 12.57 12.64 12.28 14.04  11.442 12.584 12.949 13.165 13.449  39.03  20.25  25.246  Phyllis  Furry  TABLE 7 WIDTH-DRAINAGE AREA RELATION FOR ASHNOLA STREAMS Stream ' Juniper Ewart Upper Ewart Lower Ashnola Upper Ashnola Middle  Drainage Area  Channel Width  21.75 90.75 95.75 221.50 408.50  6.02 16.36 14.19 21.14 28.17  Predicted Width 6.404 13.428 13.907 21.325 29.286  29 the d r i e r Ashnola basins,  the difference being reflected i n the constant.  The constant can be interpreted as the possible channel width for  2 streams with drainage areas of 1 km. , 3.7 m. for the coastal basins and 1.3 m. for the Ashnola basins. S i m i l a r i t y of the exponents i n Equations 5.4 and 5.5 imply a s i m i l a r i t y of the channel forming process i n these two regions.  Co-  variance analysis indicates a p r o b a b i l i t y of 85% that the slopes of the regression l i n e s are the same.  It i s thought that these exponents  r e f l e c t the r e l a t i v e e r o d i b i l i t y of the channel l i n i n g sediments which are s i m i l a r for these regions.  Miller's  (1958) work substantiates t h i s  to a degree. B.  Flow Equation Parameters and Available Data Relations between formative discharge, drainage area and channel  width permit substitution of DA and  i n Equation 2.1  f< D A g 2 / 3 , S , £ Y4/3 g„  f( W D g 1 / 3 , Y2/3  S , g  ,  ) p0  (5.6)  ) =0  (5.7)  8.  Flow equation parameters can now be related to available basin and channel c h a r a c t e r i s t i c s .  Equation 5.6, being sensitive to climate,  v a l i d only within a c l i m a t i c a l l y homogeneous region. should be transferable  Equation 5.7 :  is j  from region to region depending upon s i m i l a r i t y  between the channel l i n i n g  sediments.  30  CHAPTER VI HYDROMORPHOLOGICAL EQUATIONS A.  Coastal Relations S t a t i s t i c a l r e l a t i o n s between the v a r i a b l e s i n Equations 5.6  and 5.7 were established from m u l t i p l e regressions of the logarithms of DA, W^, S, a^ and b^.  Data includes the t e s t reaches on F u r r y ,  P h y l l i s , Blaney, Brockton and the f i r s t two reaches on P l a c i d Creek. P l a c i d 3-4 was excluded because of the presence of two f i r e pools (Photograph 3 ) . 1.  Channel Dimensions Regression equations showing the s t a t i s t i c a l r e l a t i o n s h i p be-  tween channel dimensions, WQ and S, and the flow equation parameters are b A = .24 W D - 1 4 7 S'-  (6.1)  099  a A - .74 W D * 5 3 4 S " - 0 7  (6.20  with RSQ's of .727 and .95, standard errors of 13.2% and 15.8%, both equations are s i g n i f i c a n t at the 1% l e v e l .  Step-regression  analysis  i n d i c a t e s that slope i s not s i g n i f i c a n t at the 5% l e v e l and therefore can be excluded from the equations.  The r e s u l t i n g equations  are  31 b A = .30 W D - 1 6 3  a  A  =  , 8 7  W  (6.3)  D*54  ( 6  The RQS's are .63 and .94, standard errors are 14.8% and 16.1%.  '  4 )  With  11 degrees of freedom both equations are s t i l l s i g n i f i c a n t at the 1% l e v e l (see Figure 7 ) .  Removing slope from Equation 6.1 (b ) reduces A  the RSQ by 10% i n d i c a t i n g that slope does effect the numerical values of the h ^ ' s , however not enough to j u s t i f y i t s i n c l u s i o n i n the equation.  Removal of slope was at the 5% l e v e l .  Standard errors of both  sets of equations are e s s e n t i a l l y the same. 2.  Basin Dimensions S i m i l a r regression a n a l y s i s of DA, S, a^ and b'A give the f o l l o w -  ing r e l a t i o n s b A = .37 D A ' 0 8  (6.5)  a A = 1.74 D A * 2 9  (6.6)  DA explains 59.7% and 96.1% of the v a r i a t i o n i n b. and a. r e s p e c t i v e l y A  (see Figure 8 ) .  Standard errors are 15.4% and 13.1%.  s i g n i f i c a n t at the 1% l e v e l .  A  Both equations are  Including slope i n the equations gives RSQ's  of .697 and .967 and standard errors of 14% and 12.5% r e s p e c t i v e l y . B.  General Equations Since the r e l a t i o n between channel dimensions and flow equation  parameters i s independent of c l i m a t e , general equations can be  32  RELATIONS BETWEEN STEADY FLOW PARAMETERS  AND CHANNEL WIDTH  FOR COASTAL BASINS io  Figure 7  T  34 constructed using the data for the c o a s t a l , Slesse and Ashnola b a s i n s . The equations are b A = .30 W D ' 1 6 8  a  A  =  *  9  4  W  D'  (6.7)  4 ?  (  RSQ's are .61 and .86, standard errors of 13.1% and 21.1%.  6  *  8  )  Both equa-  tions are again s i g n i f i c a n t at the 1% l e v e l (19 degrees of freedom).  ,  Juniper Creek was not included i n these equations because of the extreme effect of log jams (Photographs 12 and 13).  Figure 9 shows these r e l a -  tions. C.  Discussion 1.  Interpretation The marginal s i g n i f i c a n c e of slope i s not s u r p r i s i n g as energy  d i s s i p a t i o n i n rough channels occurs mainly through frequent h y d r a u l i c jumps rather than by boundary f r i c t i o n .  The effect of slope w i l l  decrease w i t h i n c r e a s i n g channel roughness (steeper slopes) as proport i o n a l l y more of the flow occurs i n pools. l i t t l e effect on the channel forming process  Slope also appears to have (Equations 5.4 and 5 . 5 ) ;  suggesting that the pool-weir sequence s t i l l e x i s t s during very high discharges, p a r t i c u l a r l y i n the steeper channels. Channel width alone explains 8% to 15% more of the variance of the a^'s  than the b^'s because the constant r e f l e c t s the storage  c h a r a c t e r i s t i c s of the stream (a. i s the flow area at a discharge of  one cubic meter per second) and therefore i s d i r e c t l y related to channel and pool s i z e .  The exponent, on the other hand, appears to be more  sensitive to other channel dimensions, slope for example, explaining 11% of the variance. S i m i l a r i t y between the equations r e l a t i n g b^ and W  Q  for both  data sets may merely r e f l e c t a data bias towards rougher channels or that the i n t e r a c t i o n between the hydrologic and morphologic properties Is similar for both channel types.  Certainly more data i s required  before anything conclusive may be said. The constant i s better defined for coastal streams than f o r the t o t a l sample with an RSQ of .94 as compared to .86.  This difference  results from the s e n s i t i v i t y of the a^'s to pool storage.  The three  test reaches having more uniform channel p r o f i l e s (Ashnola Upper, Slesse Lower and Upper) have lower a^ values (3.09, 2.93 and  2.29  respectively). Nothing quantitative can be said about the effect of pool size or number, however Figure 10 i l l u s t r a t e s the s e n s i t i v i t y of the parameter of the Q-A r e l a t i o n s to these features.  Figure 10 includes only  the relations for the larger streams of Ewart, Slesse, Ashnola and Furry.  Covariance analysis indicates the exponents are s t a t i s t i c a l l y  the same f o r the larger pool-weir channels of Ewart, Ashnola Middle and Lower, Slesse Middle and Furry. three "smooth" channels mentioned  Similar r e s u l t s are found for ,,the  i n the preceding paragraph.  Table 8  shows the relations have p r o b a b i l i t i e s of 62% and 87% respectively.. Both results are s i g n i f i c a n t at the 1% l e v e l .  Extending the analysis  Figure 10  COMPARISON OF CHANNEL TYPES  38  to include a l l the Q-A r e l a t i o n s (also Table 8) the exponents are found to be d i f f e r e n t .  This r e s u l t i s also true for the small creeks alone  (excluding those of Slesse, Ewart, Ashnola and F u r r y ) , the effect of log jams, v e g e t a t i o n , e t c . , may e x p l a i n the d i f f e r e n c e . Steep slopes alone are not the only c r i t e r i o n for rough channels as the slopes for Slesse Upper and Lower and Ewart Upper are v i r t u a l l y the same (.034, .034 and .035) although only the l a t t e r q u a l i f i e s as a rough channel.  The coarseness of the channel l i n i n g sediments  explains  the d i f f e r e n c e , as Photographs 5 , 7 and 9 i n d i c a t e , only Ewart Upper, has sediments large enough to form pools of s i g n i f i c a n t s i z e .  TABLE 8 COVARIANCE ANALYSIS OF FLOW EQUATIONS  Title  2.  Degrees of Freedom  F Probability Value  Sign Level  T o t a l Sample  22  109  14.39  .0  Small Creeks  13  86  20.87  .0  Large Pool-Weir Creeks  5  16  .72  .62  1%  Smooth Channels  2  7  .14  .87  1%  Accuracy Tables 9 and 10 l i s t the observed and predicted values for a^ and  {>A using equations with width as the only independent v a r i a b l e .  The 95%  confidence band was c a l c u l a t e d to t e s t the accuracy of the p r e d i c t i o n s , the test assumes that i f the predicted value does not l i e w i t h i n the band  39  TABLE 9 OBSERVED AND PREDICTED VALUES FOR a. A  Reach  95% Band  Observed  Eq.6.8  Predicted Eq.6.4 Eq.6.6  Brockton  1-2  .81  .663 -  .991  .89  .814  .784  Brockton  2-3  .718  .648 -  .796  .94  .863  .815  Placid  1-2  1.879  1.082 - 3.26  1.517  1.505  1.507  Placid  2-3  1.930  1.468 - 2.54  1.619  1.624  1.820  Blaney  1-3  3.375  3.196 - 3.57  3.129  3.473  3.122  Blaney  3-5  3.483  3.305 - 3.672  2.925  3.213  3.155  Blaney  5-4  3.110  2.897 - 3.34  3.148  3.497  3.183  Phyllis  1-2  3.262  3.092 - 3.44  2.977  3.279  3.269  Phyllis  2-3  3.219  3.146  3.262  3.107  3.445  3.446  Phyllis  3-4  3.021  2.927 - 3.118  3.116  3.455  3.501  Phyllis  4-6  3.199  2.987 - 3.44  3.07  3.40  3.58 .  Phyllis  Low  3.21  2.77  3.63  3.66  3.58  5.79  4.59  - 3.71 - 7.30  3.89  4.47  5.07  - 3.39 - 5.81  4.47  Furry  -  Slesse  Low  2.926  2.52  Slesse  Mid  4.18  3.01  Slesse  Up  2.92  1.98  - 4.31  3.83  Ewart  Low  3.25  2.60  4.07  3.29  Ewart  Up  4.09  3.44  -  3.52  Ashnola  Low  3.97  3.81  Ashnola  Mid  4.64  3.88  Ashnola  Up  3.06  2.78  - 4.98 - 4.13 - 5.42 - 3.44  4.95  4.38 4.55 3.97  AC-  TABLE 10 OBSERVED AND PREDICTED VALUES FOR b  Reach  Observed  95% Band  Predicted Eq.6.7 Eq.6.3 Eq.6.5  Brockton  1-2  .338  .308 - .370  .291  .294  .294  Brockton  2-3  .283  .270 - .297  .297  .299  .302  Placid  1-2  .340  .219  -• .529  . 352  .353  .355  Placid  2-3  .306  .243 - .387  .361  .361  .410  Blaney  1-3  .478  .433 - .593  .456  .453  .438  Blaney  3-5  .527  .486 - .571  .445  .443  .439  Blaney  5-4  .439  .390 - .494  .457  .454  .440  Phyllis  1-2  .541  .459 - .639  .448  .445  .444  Phyllis  2-3  .458  .435 - .482  .445  .452  .450  Phyllis  3-4  .479  .444 - .516  .455  .452  .452  Phyllis  4-6  .402  .343 - .472  .453  .450  .454  Phyllis  Low  .356  .273 - .464  .463  .460  .456  .501  .345 - .729  .483  .488  .503  Furry Slesse  Low  .577  .500 - .665  .516  Slesse  Mid  .521  .358 - .758  .503  Slesse  Up  .599  .389 - .922  .490  Ewart  Low  .437  .316 - .603  .464  Ewart  Up  .418  .299 - .539  .475  Ashnola  Low  .421  .403 - .440  .514  Ashnola  Mid  .465  .392 - .552  .552  Ashnola  Up  .586  .506 - .679  .496  41 i t must be considered as d i f f e r e n t .  As this test i s sensitive to the  number of degrees of freedom i t must be applied with caution to the Q-A relations with less than about 6 df.  K e l l e r h a l s ' data i s w e l l suited  for  this test (see Table 1 and 2).  The same test can be used to test  for  s i m i l a r i t y or differences between the equations. Figures 11 to 16 give v i s u a l comparisons of the observed and  predicted Q-A r e l a t i o n s .  The predicted relations are based on the  following equations derived from combining equations 6.7 and 6.8 and 6.3 and 6.4  47  'V 3  A = .94 W D -/* 7 Q  17  u  OTT  c,  •  A = .87 W D , : > 4 Q for  (6.9)  .16  3W u  (6.10)  the t o t a l and coastal samples respectively. Both equations predict quite accurately the flow conditions i n  rougher, pooled channels except where extreme conditions p r e v a i l : large  'I  ;  pools on Furry r e s u l t i n underestimates; overestimates of Ashnola Lower are a result of the road c o n s t r i c t i o n ; underestimates of P h y l l i s  1-2  due to several large log jams; overestimates of Brockton 2-3 are due to the w a t e r f a l l nature of the channel.  In some cases p r e d i c t i o n errors  are compensating ( e . g . , P l a c i d 2-3, Ewart Lower and Upper). The most serious errors occur on the smooth channels, with the a^'s  being consistently higher and the b^'s being consistently lower.  This l a t t e r feature suggests a different mode of adjustment to discharge between the two channel types, with the rougher (and generally smaller)  OBSERVED _AND PREDICTED Q-A RELATIONS —  observed  predicted (Eq. 6.9)  ~ -  predicted (Eq. 6.10)  OBSERVED —  observed  AND PREDICTED  Q-A  — p r e d i c t e d (Eq.6-9)  — •  RELATIONS predicted (Eq-6.10)  Q  OBSERVED AND PREDICTED Q - A —  observed  predicted  RELATIONS ( E q . 6.9)  48 channels adjusting more through v e l o c i t y than through flow area. The increase of b^ with increasing channel width has also been noted by Coates (1969).  49  CHAPTER VII  CONCLUSIONS The objectives of this study are, as previously stated: (1) to determine the h y d r a u l i c a l l y s i g n i f i c a n t parameters of the equations governing steady flow i n rough channels; (2) to establish the s t a t i s t i c a l relations between these parameters and channel dimensions; (3) to establish the relations between basin and channel dimensions to permit substitution of basin parameters i n (2);  and, (4) to investigate  regional climatic e f f e c t s on these r e l a t i o n s . The study has produced the following conclusions: (1)  ;  Steady flow conditions i n rough channels are defined by.  functions of the form A = f(Q). Linear regressions of the form b  A  A = a^Q  provide good approximations of these functions with c o r r e l a -  t i o n c o e f f i c i e n t s of .99. (2)  The parameters of these equations vary i n d i v i d u a l l y with  each channel and are found to be related to channel and basin dimensions. (3)  The s t a t i s t i c a l equations r e l a t i n g these parameters and  channel dimensions are:  a. = .94 W" A D  .47  .17  and b. = .3 W.' A D  .  Both  equations are s i g n i f i c a n t at the 1% l e v e l and explain 86% and 61% of the data variance. (4)  The systematic v a r i a t i o n of channel dimensions are related  .53 to basin parameters:  W  = 3.7 DA"  f o r coastal basins and  50 W  D  =1.3  DA"  . 52  f o r Ashnola b a s i n s .  These r e l a t i o n s a r e i n f l u e n c e d  c l i m a t e and channel sediments, the former b e i n g r e f l e c t e d i n the and the l a t t e r i n the h^'s. e q u a t i o n s of ( 3 ) : a^ = 1.74 i s again at (5)  Drainage a r e a can r e p l a c e W  Q  DA"  .29  and b ^ = .37 DA"  08  .  a^'s  i n the  Significance  1%. E q u a t i o n s of (4) a r e v a l i d o n l y f o r c o a s t a l b a s i n s s i n c e  Wp-DA r e l a t i o n i s dependent upon c l i m a t e and t h e r e was  are independent  the  insufficient  d a t a to develop s i m i l a r e q u a t i o n s f o r the A s h n o l a b a s i n s . dimensions  by  As  channel  o f c l i m a t e , e q u a t i o n s i n (3) a r e a p p l i c a b l e  to rough channels i n both r e g i o n s . (6)  I t was  o r i g i n a l l y thought  t h a t w i d t h and s l o p e would be  suffic-  i e n t to r e p r e s e n t the c h a n n e l ; however, on the b a s i s o f s t e p - r e g r e s s i o n a n a l y s i s o n l y w i d t h proved s i g n i f i c a n t . p o o l s the Q-A (7)  As f l o w o c c u r s m a i n l y  r e l a t i o n s can be c o n s i d e r e d independent  of s l o p e .  Under normal c o n d i t i o n s the e q u a t i o n s i n (3) and  (4) p r o v i d e  good approximations f o r rough channels w i t h widths r a n g i n g from 20 m.,  through  .89 t o ;  however, f o r more u n i f o r m channels where tumbling f l o w does not  predominate  d i s c r e p a n c i e s between observed and p r e d i c t e d Q-A  become more s e v e r e .  relations  Photograph 1 S a l t D i l u t i o n Equipment (Courtesy R. K e l l e r h a l s )  Photograph 2 Brockton Creek S e c t i o n (Courtesy R.  1-2  Kellerhals)  Photograph 3 F i r e P o o l P l a c i d Creek, S e c t i o n (Courtesy R. K e l l e r h a l s )  Photograph 4 Upper S e c t i o n of F u r r y  Creek  3-4  Photograph 5 E l e c t r o d e S i t e Lower S e c t i o n of Ewart Upper  Photograph 6 I n j e c t i o n S i t e A s h n o l a Upper  58  Bibliography Brush, L . M . , 1961. "Drainage Basins, Channels and Flow Characteristics of Selected Streams i n Central Pennsylvania," United States Geological Survey, Professional Paper No. 282-F. Church, M. and K e l l e r h a l s , R., 1969. "Stream Gauging i n Isolated Areas Using Portable Equipment," Technical B u l l e t i n No. , Inland Waters Branch, Canada Dept. of Energy, Mines and Resources, (in press). Coates, D . R . , 1969. "Hydraulic Geometry i n a Glaciated Region," Paper Annual Meeting, American Geophysical Union. Gann, E . E . , 1968. "Flood Height-Frequency Relations for the Plains Area i n M i s s o u r i , " United States Geological Survey, Professional Paper No. 600-D, pp. D52-D53. Hely, A . G . and Olmsted, F . H . , 1963. "Some Relations between Streamflow Characteristics and the Environment i n the Delaware River Region," United States Geological Survey, Professional Paper No. 417-B. K e l l e r h a l s , R., 1970. Runoff Concentration i n Steep Channel Networks. Ph.D Thesis, The University of B r i t i s h Columbia. K i l p a t r i c k , F . A . , and Barnes, J r . , H . H . , 1964. "Channel Geometry of Piedmont Streams as Related to Frequency of F l o o d s , " United States Geological Survey, Professional Paper No. 422-E. "i  Kondrat'ev, N . E . , et a l . , 1959. "River Flow and River Channel Format i o n , " translated from Russian by: I s r a e l Program for S c i e n t i f i c Translation, Jerusalem. Langbein, W.B., 1964. "Geometry of River Channels," Journal of the. Hydraulic D i v i s i o n , ASCE, V o l . 90, No. HY2, pp. 301-311. Larson, C . L . , 1965. "A Two-Phase Approach to the Prediction of Peak Rates and Frequencies of Runoff for Small Ungauged Watersheds," Technical Report No. 53, Dept. of C i v i l Engineers, Stanford. Leopold, L . B . and Maddock, J r . , T . , 1953. "The Hydraulic Geometry of Stream Channels and some Physiographic Implications," United States Geological Survey, Professional Paper No. 252. M i l l e r , J . P . , 1958. "High Mountain Streams: Effects of Geology on i Channel Characteristics and Bed M a t e r i a l , " New Mexico, State Bureau of Mines and Mineral Resources, Memoir No. 4^.  59 Popov, I.V., 1964. "Hydromorphological P r i n c i p l e s of the Theory of Channel P r o c e s s e s and t h e i r use i n H y d r o t e c h n i c a l P l a n n i n g , " S e l e c t e d Papers, American G e o p h y s i c a l Unions No. 2_. Simons, D.B. and A l b e r t s o n , M.L., 1960. "Uniform Water Conveyance Channels i n A l l u v i a l M a t e r i a l , " J o u r n a l of the H y d r a u l i c s D i v i s i o n , ASCE, V o l . 86, HY5, pp. 33-71. S t a l l , J.B. and Fok, Y u - S i , 1968. " H y d r a u l i c Geometry of I l l i n o i s , " Research Report No. 15, U n i v e r s i t y of I l l i n o i s Water Resources < Center. Thomas, D.M., 1964. "Height-Frequency R e l a t i o n s f o r New J e r s e y F l o o d s , " U n i t e d S t a t e s G e o l o g i c a l Survey, P r o f e s s i o n a l Paper No. 475-D, pp. D202-D203. Walker, H.M. and Lev, J . , 1953. R i n e h a r t and Winston. W i l l i a m s , E . J . , 1959. Sons.  S t a t i s t i c a l Inference.  Regression A n a l y s i s .  New  York: H o l t ,  London: John W i l e y  and  Wolman, M.G., 1955. "The N a t u r a l Channel of Brandywine Creek, P e n n s y l v a n i a , " U n i t e d S t a t e s G e o l o g i c a l Survey, P r o f e s s i o n a l Paper No. 271.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0102220/manifest

Comment

Related Items