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.
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Channel geometry of mountain streams Day, Terence James 1969
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Title | Channel geometry of mountain streams |
Creator |
Day, Terence James |
Publisher | University of British Columbia |
Date Issued | 1969 |
Description | Channel networks in the glaciated mountain basins of Coastal and southern interior British Columbia (Ashnola River Basin) offer opportunities for morphometric studies relating the parameters of the flow area (A) - discharge (Q) relationship to readily available channel and basin parameters. Steady flow conditions in rough channels are approximated by equations of the form A = a[formula omitted]Q[formula omitted] . The parameters, a[formula omitted] and b[formula omitted], vary individually with each channel and are related to channel dimensions; a[formula omitted] = .94 W[formula omitted]·⁴⁷ and b[formula omitted] = .3 W[formula omitted]·¹⁷. These results are independent of climate and under normal conditions give excellent predictions of the Q-A relations for rough channels in both regions. The systematic variation of channel dimensions within a basin are related to drainage area:W[formula omitted] = 3.7 DA·[formula omitted] for coastal basins and W[formula omitted] = 1.3 DA[formula omitted] for Ashnola basins. The influence of climate is reflected in the constants, with areas of higher precipitation having larger constants. Drainage area can replace W[formula omitted]: a[formula omitted] = 1.74 DA[formula omitted] and b[formula omitted] = .37 DA[formula omitted]. These relations are applicable only within a climatically homogeneous region. In rough channels the Q-A relations are considered independent of slope, a result of energy dissipation through frequent hydraulic jumps. The hydromorphological equations developed here are valid only for rough channels where tumbling flow predominates. |
Subject |
Rivers |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2011-05-27 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
IsShownAt | 10.14288/1.0102220 |
URI | http://hdl.handle.net/2429/34941 |
Degree |
Master of Arts - MA |
Program |
Geography |
Affiliation |
Arts, Faculty of Geography, Department of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
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