Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A comparative study of multiply-controlled valley asymmetry in S.E. Wyoming and S.W. Manitoba Kennedy, Barbara A. 1967

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

Item Metadata

Download

Media
831-UBC_1967_A8 K42.pdf [ 9.32MB ]
Metadata
JSON: 831-1.0093734.json
JSON-LD: 831-1.0093734-ld.json
RDF/XML (Pretty): 831-1.0093734-rdf.xml
RDF/JSON: 831-1.0093734-rdf.json
Turtle: 831-1.0093734-turtle.txt
N-Triples: 831-1.0093734-rdf-ntriples.txt
Original Record: 831-1.0093734-source.json
Full Text
831-1.0093734-fulltext.txt
Citation
831-1.0093734.ris

Full Text

A COMPARATIVE STUDY OF MULTIPLY-'CONTROLLED VALLEY ASYMMETRY IN S.E. WYOMING AND S.W. MANITOBA by  BARBARA A, KENNEDY B.A.j University of Cambridge, 1965  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 t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 196?  In  presenting  for  an a d v a n c e d  that  thesis  thesis  degree  the L i b r a r y  study.  shall  I f u r t h e r agree for  Department or  this  make that  permission  representatives.  of  this  thesis  28th.  for  permission.  Geography  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a April,  Columbia  196?  of  the  It  is  I  reference  for extensive  be g r a n t e d  requirements  B r i t i s h Columbia,  freely available for  or  w i t h o u t my w r i t t e n  Date  it  p u r p o s e s may  by h i s  f u l f i l m e n t of  the U n i v e r s i t y  scholarly  p u b l i c a t i o n of  Department  at  in p a r t i a l  agree  and  copying  of  this  by t h e Head o f my understood  f i n a n c i a l gain  shall  that not  be  copying allowed  ABSTRACT The nature of the i n t e r - r e l a t i o n s h i p of v a l l e y - s i d e slopes and the streams at t h e i r base i s regarded as being of fundamental in the study of landscape morphology.  significance  One aspect of t h i s r e l a t i o n s h i p ,  the problem of the development of valley-side asymmetry i n east-trending v a l l e y s under the joint influence of microclimatic and stream controls, i s investigated i n two areas of uniform, f l a t - l y i n g beds, using the approach and techniques of experimental design.  Valleys i n both study areas have  been formed during the l a s t 12,000 years, so that the Importance of f o s s i l slope forms i s minimal.  The v a r i a t i o n i n l i t h o l o g y between the two areas  i s held t o be of less consequence than the difference i n climatic regimes, as f a r as the type of asymmetry developed. The molster of the two areas, S.W.  Manitoba, shows the t y p i c a l ,  valley-wide asymmetry regarded as c h a r a c t e r i s t i c of non-periglaclal regions, with north-facing slopes s i g n i f i c a n t l y steepened by 3.1°>  on average:  the  e f f e c t s of basal steepening by meandering streams are additive with the microclimatic differences.  In the d r i e r area, S.E. Wyoming, the effects of  the two controls are non-additive, and asymmetry i s a purely l o c a l i s e d development created by the over-steepening of shaded, north-facing undercut slopes.  The moisture a v a i l a b i l i t y i n t h i s environment  i s probably  increased by the formation of snowdrifts i n the winter months.  Asymmetry  r e s u l t i n g from differences i n aspect i s s t a t i s t i c a l l y i n s i g n i f i c a n t both  ii i n east-trending v a l l e y s without defined stream channels and i n southtrending v a l l e y s with meandering streams.  The absolute maximum angle i s found to be an excellent indicator both of l o c a l changes i n slope form and of the nature of the p r o f i l e s as a whole.  The degree of organisation of a l l p r o f i l e s studied, i n r e l a t i o n to  the maximum angle, i s high, with the exception of the south-facing slopes in those east-trending v a l l e y s i n Wyoming which lack defined channels.  Tn  general, t h e maximum angle appears more d i r e c t l y related to the other geometric features of the p r o f i l e than t o the c h a r a c t e r i s t i c s of s o i l , vegetation or nearby stream channel.  A consideration of a l l available data on multiply-controlled asymmetry i n non-periglacial areas leads t o the conclusion that differences in steepness of slopes with northern and southern aspects are more l i k e l y to develop i n regions of comparatively low humidity and that the v a l l e y wide asymmetry found i n Manitoba i s the most common form.  The s t r i c t l y  l o c a l i s e d asymmetry developed i n the Wyoming valleys appears t o be a specialized phenomenon confined t o a narrow area of semi-arid climate. It i s suggested that the l o c a l conditions of moisture a v a i l a b i l i t y are the prime controls of multiply-controlled v a l l e y asymmetry, i n that they w i l l determine the r e l a t i v e importance of slope and channel processes and hence the nature of the valley-side development.  TABLE OF CONTENTS PAGE F ix  Abstract Acknowledgments INTRODUCTION  1  CHAPTER I. THE PROBLEM AND APPROACH  7  1:1 1:2 1:3 1:4  Types of Multiply-controlled Asymmetry The Valleys and the P r o f i l e s The Choice of a 'Characteristic' Slope Parameter S t a t i s t i c a l Techniques  1 10 17 25  CHAPTER I I . THE: SETTINGS  28  11:1 11:2 11:3 11:4 11:5  28 34 37 b& 50  Geology and Denudation Chronology Climate and Hydrology S o i l s and S o i l Movement Vegetation and Microclimate Summary  CHAPTER I I I . VARIATION IN SLOPE FORM AND RELATED FEATURES 111:1 111:2 111:3 111:4 111:5 111:6  Maximum Angles Mean Angles Other Variables Reflecting Slope Geometry Non-geometric Variables Relating t o Slope Form Channel Characteristics Summary  CHAPTER IV. PATTERNS OF VARIATION IVsi IVs2 CHAPTER V.  Inter-valley Variation Intra-valley Variation  DISCUSSION AND CONCLUSIONS V:l V:2 V:3  BIBLIOGRAPHY  Multiply-controlled Asymmetry Relationship of Slopes and Streams Conclusion ~  53 53 6l 65 70 74 77 80 80 85 93 93 99 100 101  Iv  PAGE APPENDIX A,  NOTES ON THE VARIABLES EMPLOYED IN THE ANALYSES A:I. The Variables of the Manitoba Analysis A;II The Variables of the Wyoming Analysis  APPENDIX B. APPENDIX C.  10k 105 106  THE PRECIPITATION, RUNOFF, AMD DISCHARGE DISTRIBUTIONS, RHODES MANITOBA: 1959-1964  108  THE ANALYSES OF VARIANCE  115  C;I CsII C:III  Maximum Angles Strabler Maximum Angles Mean Angles  116 118 118  LIST OF TABLES PAGE I II III IV V  Additive cross-stream and cross-valley e f f e c t s The variables employed i n the Manitoba Study  12 (facing)  The experimental design, Manitoba  13  The experimental design, east—trending v a l l e y s with stream courses, Wyoming The experimental design, south-trending  15 17  v a l l e y s , Wyoming VI VII VIII  9  The variables employed i n the Wyoming Study Sample s t a t i s t i c s ^ Plateau de Bassigny, Haute-Marne Comparative magnitudes o f storms o f various durations and return periods S W. Manitoba and S E, Wyoming  18 (facing)  21  0  S  IX X  XI  XII XIII XIV  XV  51 (facing)  Cross-stream and cross-valley e f f e c t s , maximum angles, Manitoba  53  Cross-stream and cross-valley e f f e c t s , maximum angles: major factors only, Wyoming ( i )  5^  CrosB-stream and cross-valley e f f e c t s , maximum angles: a t an opposite meander bend, Wyoming ( i )  55  Ranked mean absolute maximum angles, undercut p r o f i l e s , Wyoming ( l )  56  Ranked mean Strahler maximum angles, undercut p r o f i l e s , Wyoming ( i )  59  Cross-stream and cross-valley e f f e c t s , maximum angles: Wyoming ( i i i )  6l  Arrangement o f ' t ' t e s t s  62  vi  PAGE  Differences i n mean angles, Manitoba  62  Cross-stream and cross-valley e f f e c t s , mean angles: Wyoming ( i )  63  Characteristic slope angles, undercut p r o f i l e s , Wyoming ( i )  6k  XIX  Cross-stream and cross-valley differences, geometric variables, Manitoba  66  XX  Cross-stream and cross-valley differences, geometric variables, Wyoming ( i )  67  Cross-valley difference, geometric variables, Wyoming ( i i )  68  Cross-stream and cross-valley differences, geometric variables, Wyoming ( i i i )  69  Cross-stream and cross-valley differences, non-geometric variables, Manitoba  70  Cross-stream and cross-valley differences, non-geometric variables, Wyoming ( i )  72  Cross-valley differences, non-geometric variables, Wyoming ( i i )  73-  Cross-stream and cross-valley differences, non-geometric variables, Wyoming ( i i i )  73  Cross-valley differences i n channel geometry, Wyoming ( i )  75  Cross-valley differences i n channel geometry, Wyoming ( i i i )  76  V a l l e y - t o - v a l l e y variations i n asymmetry, maximum angles, Wyoming  81  Cross-stream and cross-valley variations in R  85 (facing)  Frequency of occurrence of independent variables i n stable multiple regression equations  91 (facing)  XVI XVII  XVIII  XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX  2  XXXI  XXXII  Examples of slope asymmetry i n areas of non-periglacial climate  a) b)  9k (facing) 95 (facing)  LIST OF FIGURES PAGE 1:1 2 3  Slope p r o f i l e s influenced solely by erosional environment  7  Undercut slopes influenced by and cross-valley controls  9  cross-stream  One r e p l i c a t i o n of the experimental design,  Ik  east-trending v a l l e y s , Wyoming 18  k  The Strahler maximum angle  5  Representative  6  Relationship of Strahler and absolute maximum angles Adjustment of slope features t o changing  7  height/length integrals  erosional environment, undercut p r o f i l e s 11:1 2  22 2k  25 28 (facing)  Section of Riding Mountain shale Section of d r i f t , east bank of meander L i t t l e Pembina  28 (facing) 30 (facing)  3  Section of Ogallala formation  31 (facing)  k  Major terraces of the Gangplank streams  32 (facing)  5  Terraces, upper Lonetree Creek  32 (facing)  6  Terraces, Goose Creek  7  C h a r a c t e r i s t i c drainage pattern,  32 3k (facing)  Cheyenne area 3k (facing) 8  Climatic regime, Boissevain, Manitoba  9  Climatic regime, Cheyenne, Wyoming  10  Discharge, Pembina River at Rhodes  35  (facing)  viii  PAGE 1.1  E s t i m a t e d mean amounts o f s l o w mass 38 ( f a c i n g )  movements, M a n i t o b a and E„ F r a n c e 12  S o i l p r o f i l e , Goose Creek v a l l e y  hi ( f a c i n g )  13  S o i l p r o f i l e , t r i b u t a r y t o Duck Creek  hi ( f a c i n g )  Ik  S o i l t e m p e r a t u r e and m o i s t u r e c y c l e s , Archer: 1963-65 S a t u r a t e d s o i l r e s i s t a n c e , Ogallala, north-facing profiles  15 16 17 18 111:1  2  3  4  k2 ( f a c i n g ) 45  (facing)  Saturated s o i l r e s i s t a n c e , O g a l l a l a , south-facing p r o f i l e s  45  (facing)  Depth o f s o i l d i s t u r b a n c e / s i n e of s l o p e , O g a l l a l a  46 ( f a c i n g )  of angle  E s t i m a t e d mean amounts o f s l o w mass movements, S.E. Wyoming  47  S e c t i o n o f Goose Creek v a l l e y  57  Mean asymmetry, r e l a t e d t o d i f f e r e n c e s i n v e g e t a t i o n cover and e v a p o r a t i o n r a t e s  82 ( f a c i n g )  C o r r e l a t i o n s e t , n o r t h - f a c i n g slopes i n east-trending v a l l e y s with channels, Wyoming  88 ( f a c i n g )  C o r r e l a t i o n set,, a l l s l i p - o f f Manitoba  89 ( f a c i n g )  (facing)  profiles,  C o r r e l a t i o n s e t , south-facing slopes i n east-trending v a l l e y s w i t h channels, Wyoming  -  90 ( f a c i n g )  MAPS  P o r t i o n o f t h e Upper Pembina d r a i n a g e , west o f K i l l a r n e y , M a n i t o b a  11  (facing)  P o r t i o n o f t h e Gangplank, S,W„ o f Cheyenne, Wyoming  13  (facing)  ACKNOWLEDGMENTS The fieldwork  i n Manitoba was c a r r i e d out, i n 1 65> with f i n a n c i a l Q  assistanee from the P h i l i p Lake, Mary Euphrasia Mosely and Worts' T r a v e l l i n g Scholars' Funds and from Newnham College, a l l of the University of Cambridge. P a r t i c u l a r thanks are due t o Dr. B. M. Evans, l a t e l y of United College and to the s t a f f of the Departments of Geography and Agriculture, University of Manitoba at Winnipeg and, also, t o the members of the Department of Geography, University of Alberta at Edmonton, f o r t h e i r h o s p i t a l i t y and assistance„  The Wyoming fieldwork,  c a r r i e d out i n 1 6 6 , was supported by Q  grants from The University of B r i t i s h Columbia and the Department of Geography of that u n i v e r s i t y .  Thanks are due to the Departments of  Geology and Agriculture of the University of Wyoming, Laramie and t o Dr. B. R„ Mears of the former department i n p a r t i c u l a r , who provided a l l possible assistance.  Dr. J . D, Alyea, Wyoming State  Climatologist,  Cheyenne, was most generous with his a i d . The author would p a r t i c u l a r l y l i k e t o thank Miss J . Hobbs, Miss K. Alston and Miss J . Hutt, a l l of whom served as f i e l d assistants and without whose help the study could never have been undertaken. The analysis of the r e s u l t s would s i m i l a r l y have been impossible without the assistance of Dr. G. W. Eaton, Department of Agriculture, U. B. C , who developed the analysis of variance  programme used; and that of Mr. M. A.  X  Church, of the U. B. C. Department of Geography, who gave hours of h i s time.to the construction and reconstruction of the multiple regression programme.  F i n a l l y , the author's deepest gratitude i s due to Dr. M. A. Melton of the Department of Geography, f o r h i s support as research s t a t i s t i c a l consultant and c r i t i c ; are the author's alone.  supervisor,  the errors which have eluded h i s knife  INTRODUCTION Whatever the form i t i s merely an expression of the sum t o t a l of the forces . . . . D*A. W. Thompson The geomorphologist i s abundantly provided, with opportunities f o r the description and measurement of the forms of the landscape:  the com-  p l e x i t y of the physical systems involved makes any study of the mechanical f'orces at work a much more d i f f i c u l t task.  As a r e s u l t , geomorphologists  have tended t o follow the approach which Thompson advocated f o r b i o l o g i s t s {1917:  reprinted I961)  and t o concentrate t h e i r e f f o r t s upon the  description and analysis of the lancUforms themselves, not because they considered the study of the forces at work t o be Irrelevant, but on the assumption that any 3an3form must represent the i n t e r a c t i o n of force and resistance.  One rather unfortunate r e s u l t of t h i s orientation of geomorphic research towards the study of forms was the confusion which arose concerning the nature of the mechanical forces operating e f f e c t i v e l y i n any situation.  This confusion was largely c l a r i f i e d by Strahler's now  paper, published i n  classic  .1952, i n which geomorphic processes were c l a s s i f i e d  according t o the nature of the stress applied and the mechanical response of the materials involved.  Strahler advocated an adoption of the approach  of the physical sciences i n ge©morphology, with the ultimate aim of deducing " „ . . general mathematical models t o serve as quantitative laws . . „"  (1952, p. 937)o  This aim Strahler envisaged as being reached  2  through a number of steps, each of which represents, i n i t s e l f , one type of approach t o the problems of geomorphology.  The f i r s t of these steps  Strahler suggested should employ the tools of physics and study the s t r e s s - s t r a i n systems created by geomorphic processes:  the second step  required p r i n c i p a l l y the techniques of s t a t i s t i c s and i t s tentative goal was t o be the quantitative analysis of landforms together with the study of "causative f a c t o r s . "  It i s the l a t t e r approach which i s employed i n  the present work. As Melton has pointed o u t  1  (1967), the t o o l s of either Newtonian  or quantum mechanics provide only one possible ' f i r s t ' approach t o geomorphic problems:  a second and one which i s perhaps better suited t o the  complexities of such questions, l i e s through the u t i l i z a t i o n of an expanded concept of experimental design.  Such an approach i s founded upon  a selection of s i t u a t i o n s , by the investigator, on the a r b i t r a r y  assumption  that the e f f e c t i v e forces exerted by the "causative factors" vary.  Such a  selection plays the same r o l e as the application of various 'treatments' to f i e l d plots i n c l a s s i c a l a g r i c u l t u r a l experimentation.  The underlying  rationale i s that geomorphic processes do not operate everywhere with u n i form i n t e n s i t y , with the r e s u l t that landorms •— or features of landforms differ.  —  I f we analyse the variations i n forms as a function of the v a r i -  ation i n a p a r t i c u l a r process or combination of processes, we are assuming that the d i f f e r i n g i n t e n s i t i e s of operation of these processes are caused b y the a l t e r i n g r e l a t i o n s h i p between agents producing stresses and the response of materials t o those stresses.  Of i t s nature, such an approach involves  the use of s t a t i s t i c s , which i n themselves are merely one form of  -krhese views were presented at a Colloqium i n The Department of Geography, U. B. C. on March 9th, 1967.  3 description:  a l l assumptions regarding "causative f a c t o r s " must be b u i l t  into the experimental design by the investigator. This thesis i s concerned t o apply the techniques of experimental design, as so defined, t o the analysis of the variations i n those landforms produced by a p a r t i c u l a r type of intersection between the planar and l i n e a r elements of the landscape.  The complex r e l a t i o n s h i p of v a l l e y - s i d e slopes and the streams to which they are t r i b u t a r y i s , i n functional terms, probably the major determinant t o an understanding of the manner i n which any landscape formed by the action of running water w i l l develop.  C u l l i n g (1965) has employed  the analogy of supply and demand i n t h i s regard —  streams  debris and runoff provided from the adjacent slopes —  'consume' the  and the landscape  at any point w i l l r e f l e c t the nature of the r e l a t i o n s h i p between production and  consumption.  The i n t e r a c t i o n of slope and. stream i s , then, c r u c i a l i n any area of f l u v i a l erosion, but the varying nature of t h i s r e l a t i o n s h i p i s , as yet, l i t t l e understood.  A b r i e f discussion of three problems which  arise i n t h i s context w i l l demonstrate the rather l i m i t e d extent of knowledge i n t h i s d i r e c t i o n : a)  I f slopes are b a s a l l y undercut by a stream, i t appears that they  w i l l be steepened ( c f . Strahler, 1950* PP. 8 1 2 - 3 ) :  however, i t i s not  certain exactly what e f f e c t t h i s steepening has upon the subsequent production of debris and runoff from the slope and, ultimately, upon not only the form of the slope, but also that of the stream i t s e l f . b)  In areas of maturely dissected topography i t has been observed  (Strahler, 1950, are  p. 689) that steeper stream gradients, on the average,  associated with steeper v a l l e y - s i d e slopes:  i t i s not known why  this  k r e l a t i o n s h i p e x i s t s , or whether i t represents  a universal state of a f f a i r s ,  independent of the stage of erosional development. c)  Hack  (1965) has  shown that the form of meanders i s d i r e c t l y  related t o the nature of the l i t h o l o g y i n which they develop:  t h i s implies  that b a n k f u l l discharge cannot he as important a control of meander size and shape as has been suggested (Leopold & Wolman,  1957)> but  that, pre-  sumably, both the physical properties of the v a l l e y sides and the nature of the debris supplied from them play a s i g n i f i c a n t part.  This raises the  question of how f a r the form of meander t r a i n s i n areas of uniform l i t h o logy i s r e a l l y determined by the b a n k f u l l discharge and how f a r i t may be affected by l o c a l differences i n the volume and nature of the debris supply from the v a l l e y - s i d e slopes.  These three problems, which involve the nature of the r e l a t i o n s h i p between slope and stream, are a l l to some extent relevant to t h i s thesis but they are, however, subsidiary to the main question, namely:  what i s  the e f f e c t of microclimatic differences between the two sides of a v a l l e y upon the nature of the slope forms and,  i n p a r t i c u l a r , how i s t h i s e f f e c t  altered by the presence of an a c t i v e l y meandering stream? Cross-valley e f f e c t s Microclimatic differences ( i . e . variations i n exposure t o sun or wind, or both) w i l l e f f e c t the nature of the s o i l and vegetation slopes and may,  cover on  as a r e s u l t , a l t e r both the i n t e n s i t y and nature of the  e f f e c t i v e forces exerted by the denudational agents.  I f these variations  in microclimate are s u f f i c i e n t l y great, differences may develop i n the amounts (and possibly the nature) of debris and runoff produced by slopes of d i f f e r e n t aspect, even i n the same area.  Such differences i n micro-  climate w i l l be referred to throughout t h i s thesis as 'cross-valley'  5 controls of slope form. Asymmetry i n slope forms produced by the operation of such crossv a l l e y influences have been studied by a number of workers (e.g. H. T. U. Smith, 19^-9 j Budel, 1953)  and the major point of agreement would seem t o  be that microclimatic differences may be s u f f i c i e n t l y great, i n certain cases, t o produce completely asymmetric v a l l e y s .  I t i s generally suggested  that such a state of a f f a i r s r e s u l t s from the growth of a lens of debris along the base of one v a l l e y side, t o the extent that the stream i s pushed towards the other which i s then b a s a l l y corroded and steepened.  The con-  census seems to be that, i n the Northern Hemisphere, north-facing slopes w i l l be less steep than south-facing ones i n areas of p e r i g l a c i a l climate, but steeper i n other regions.  Cross-stream e f f e c t s As stated above, there i s an observed difference i n slope steepness associated with the presence or absence of a b a s a l l y corrading stream:  Melton has termed t h i s e f f e c t that of the ' l o c a l erosional  environment'  (i960):  i n the present work, i t w i l l be referred t o as the  'cross-stream' c o n t r o l .  I t i s necessary t o make t h i s d i s t i n c t i o n , as  Melton was concerned with a s i t u a t i o n i n which the r e l a t i o n s h i p of the main stream t o the v a l l e y sides was governed by the position of a l l u v i a l fans b u i l t up at the mouths of t r i b u t a r i e s :  i n the present case we are  concerned with the differences produced simply by the changing position of a meandering  stream.  We are, therefore, concerned with the e f f e c t upon slope form of the simultaneous action of two sets of geomorphic  controls:  those of  microclimate and erosional environment, operating i n the cross-valley and cross-stream d i r e c t i o n s , respectively.  6 The areas i n which the nature of t h i s p a r t i c u l a r type of multiply -controlled asymmetry has been studied are southwestern Manitoba and southeastern Wyoming.  The former area has a climate c l a s s i f i e d as 'dry,  subhuraid, mesothermal' (Thornthwaite " I I " c l a s s i f i c a t i o n , 1955) with a humidity index of 4.72 and an a r i d i t y index of 11.59: is  the l a t t e r region  'semiarid, mesothermal' with a zero humidity index and an a r i d i t y index  of 32.75.  The r e l a t i v e humidity of the two areas i s , therefore, a major  point of d i f f e r e n c e :  i n addition, the l i t h o l o g i e s are also disparate, the  Manitoban area being underlain by a sandy t i l l , whereas the Wyoming region i s one of sandy conglomerate.  Both groups of v a l l e y s studied are, however,  of post-Pliocene and probably post-Pleistocene age: there i s therefore l i t t l e l i k e l i h o o d of the extensive preservation of ' r e l i c t ' slope features. The s i m p l i c i t y of the erosional h i s t o r i e s of the two study areas makes them i d e a l f o r the application of an experimental design i n which the e f f e c t s i s o l a t e d are those due t o the action of two present-day processes.  CHAPTER I . THE PROBLEM AND APPROACH 1:1  Types of Multiply-controlled  Asymmetry  The primary research into the problem of v a l l e y asymmetry r e s u l t i n g from the interaction of microclimatic carried out by Melton  (i960).  and stream controls were  Melton was not concerned with situations i n  which the stream was meandering, but one i n which i t s position was determined by the deposition  of a l l u v i a l fans by t r i b u t a r i e s where they  debouched into the main v a l l e y .  However, Melton's work i s , i n e s s e n t i a l s ,  comparable with that t o be discussed below i n that the major d i v i s i o n s of h i s c l a s s i f i c a t i o n of slope categories were into north- and south-facing p r o f i l e s , with streams either at or away from t h e i r bases. I f we consider a section of an east- or west-trending v a l l e y , Pro-file  A  Profile  Profile.  D  P refill  C  N  Figure 1:1  Slope p r o f i l e s influenced  E>  s o l e l y by erosional environment.  8 such as that shown i n Figure 1:1,  with a meandering stream alternately  under-cutting the north- and south-facing v a l l e y sides, i t i s clear that there are several possible fashions i n which differences between the forms A, B, C, D may a)  slope  develop.  The f i r s t case, which i s that i l l u s t r a t e d i n Figure 1:1,  i s that  in which, owing t o the e f f i c i e n c y of stream erosion r e l a t i v e t o the e f f e c t s of the cross-valley controls, p r o f i l e s A and B are s t a t i s t i c a l l y s i m i l a r , as are C and D.  There are, however, s i g n i f i c a n t differences between slopes  A and C, which are of the same order of magnitude as those between B and D:  the variations between p r o f i l e s A and D, and B and C are also s t a t i s -  t i c a l l y similar.  In other words the form of the v a l l e y - s i d e slopes, i n  t h i s instance, i s e f f e c t i v e l y determined by the cross-stream Differences i n microclimate  may  controls.  e x i s t , but they are i n s u f f i c i e n t to a l t e r  the influence of the stream to any perceptible degree. b)  The reverse p o s s i b i l i t y , discussed above, i s that studied by Budel  and other workers, and involves such a complete dominance by the crossv a l l e y controls that the stream i s kept at, or very close t o , one v a l l e y side.  Since such a s i t u a t i o n precludes the p o s s i b i l i t y that the stream i s  meandering f r e e l y , we s h a l l not be concerned with t h i s case i n the  present  study. c)  A t h i r d s i t u a t i o n would be that i n which both cross-valley and  cross-stream  controls exert a perceptible influence upon the slope form.  In such a case, one v a l l e y side w i l l be steeper, on average, than the other, yet the difference i n amounts of debris production from opposing p r o f i l e s i s i n s u f f i c i e n t to e f f e c t the stream as completely as i n case b ) , with the r e s u l t that meanders e x i s t , together with cutbanks which alternate from one side of the v a l l e y t o the  other.  9 S t a t i s t i c a l l y , the e f f e c t s of the two sets of controls i n such a s i t u a t i o n would be additive, or v i r t u a l l y so: that i s t o say, cutbank A would be steepened by the stream t o exactly the same degree as cutbank B, but because of i t s aspect, B would have been the steeper, before undercutting of either p r o f i l e occurred. cross-stream  Table I  Table I shows: the. relationship/of- the  and cross-valley differences i n such a s i t u a t i o n .  Additive Cross-valley and Cross-stream E f f e c t s Cross-stream e f f e c t alone: differences s t a t i s t i c a l l y similar Cross-valley e f f e c t alone: differences s t a t i s t i c a l l y similar  It i s apparent that Slope B w i l l , therefore, be D]_ + D2 degrees steeper than Slope C.  This i s the s i t u a t i o n which Melton found i n a group  of v a l l e y s on the eastern flank of the Laramie Mountains, Wyoming (i960), d)  The fourth case, i l l u s t r a t e d i n Figure I:2, i s that i n which both Profile  Profile  Figure 1:2  A  Profile  D  Profile.  C  B  Undercut slopes influenced by cross-stream v a l l e y controls.  and cross-  10 cross-stream and cross-valley controls are present, but the l a t t e r are the weaker.  In such a s i t u a t i o n there w i l l be no general steepening of one  v a l l e y side, such as that found i n case c ) :  on the other hand, the increase  i n angle of the undercut p r o f i l e i s not the same i n positions A and B.  The implications of such a state of a f f a i r s are i n t e r e s t i n g : the e f f e c t s of cross-stream and cross-valley controls could not be considered additive, since the magnitude of the former influence w i l l depend upon the aspect of the slope being undercut.  S t a t i s t i c a l l y , t h i s represents  a s i g n i f i c a n t i n t e r a c t i o n between the two f a c t o r s .  To employ a metaphor  from chemistry, the stream i n such a case, would behave as a c a t a l y s t , i n that i t s presence or absence determines the i n t e n s i t y of the variations i n microclimate:  unlike a chemical c a t a l y s t , i t i s to be doubted that the  stream i t s e l f would remain unchanged as a r e s u l t of such an i n t e r a c t i o n .  If case b) i s disregarded, we have three types of asymmetry which may  exist i n east- or west-trending v a l l e y s .  The steepening of  v a l l e y - s i d e slope forms may be e n t i r e l y l o c a l i s e d at the outer curve of the meander bends, independent of aspect; i t may  s l i g h t l y e f f e c t one v a l l e y  side and have the cross-stream influence imposed upon i t i n a s t r a i g h t forward manner; or i t may be l o c a l i s e d , not merely at the concave meander bends, but on one v a l l e y side alone. 1:2 a)  The Valleys and the P r o f i l e s The selection of the study areas F i e l d observations of v a l l e y - s i d e slopes were made i n two sets  of east-trending v a l l e y s :  the c r i t e r i a on which the areas of study were  selected were f i v e - f o l d : i) streams.  The presence, i n east- or west-trending v a l l e y s , of meandering  MAP  1  -  P o r t i o n o f t h e Upper Pembina d r a i n a g e , West o f K i l l a r n e y , M a n i t o b a  11  ii)  The absence of steeply dipping beds, f a u l t s or strongly marked  joint patterns. iii)  The absence of systematic l i t h o l o g i c variations within the por-  tions of the v a l l e y s t o be studied. iv) v)  The absence of microclimatic variations over the study area, The absence of stream gradients i n excess of s i x degrees.  The importance of c r i t e r i a i ) and i i ) i s obvious.  Slopes of  uniform l i t h o l o g y were chosen because of the d i f f i c u l t i e s which would be introduced i f rock types of • varying erosional s u s c e p t i b i l i t y were present in one p r o f i l e ( c f . Schumm, 1956).  For much the same reason, i t was  necessary t o choose small study areas, without pronounced topographic differences, i n the hopes of excluding systematic climatic v a r i a t i o n s , which might have obscured the smaller-scale, cross-valley differences. The f i n a l c r i t e r i o n arises d i r e c t l y from Melton's work (i960): he concluded that asymmetry due t o microclimatic variations i s not s t a t i s t i c a l l y perceptible i n v a l l e y s with steep bed gradients. Streams with gradients greater than about s i x degrees are apparently able to remove a l l debris produced by the adjacent slopes, even i f there are d i s p a r i t i e s i n the rates of debris production r e s u l t i n g from the aspect of the p r o f i l e s . b)  The Manitoban example The f i r s t study area, which served as a p i l o t project f o r the  second, comprised the headwaters of the Pembina River, above Rhodes, Manitoba, together with two right-bank t r i b u t a r i e s . be seen from Map 1,  These streams, as may  do not flow due eastwards, but sections of t h e i r  courses are aligned so that opposing v a l l e y sides face due north and south. From such sections, f i f t y meander bends were selected on the basis of the trend of the v a l l e y , the closeness with which the meanders approached the  Facing page - 1 2  TABLE I I The Variables Employed i n The Manitoban Study  Variable:  Description:  Mean angle  Geometric;  stable  P r o f i l e height  Geometric;  stable  P r o f i l e length  Geometric;  stable  Soil plasticity  Non-geometric;  only moderately stable  Soil siltiness  Non-geometric;  only moderately stable  Stream gradient  Geometric;  only moderately stable  Maximum angle  Geometric;  only moderately stable  Length maximum angle  Geometric;  only moderately stable  Average vegetation cover  Non-geometric;  Length lower concavity  Geometric;  only moderately stable  Height/length i n t e g r a l  Geometric;  only moderately stable  Vegetation cover, maximum angle section  Non-geometric;  unstable  S o i l moisture content  Non-geometric;  unstable  only moderately stable  12  v a l l e y sides and the a c c e s s i b i l i t y of the s i t e s . Although such a system of selection of observation points can scarcely be termed random, i n the s t r i c t meaning of the term, the sample of one hundred profiles, i s held t o be representative of the population of a l l such meander bends within the area of study.  It i s apparent, however,  that such a subjective choice of the sample w i l l have introduced biases into the data, the e f f e c t s of which w i l l be to produce erroneous p r o b a b i l i t y l e v e l s when tested s t a t i s t i c a l l y .  At each meander bend a p r o f i l e was measured across the v a l l e y with a tape and Abney hand-level:  t h i s p r o f i l e was  continued up each  v a l l e y side to that point where the down-valley slope equalled that d i r e c t l y towards the channel (Rand, 1 9 6 1 ) .  A l i s t of the variables  measured f o r each p r o f i l e are given i n Table I I and c l a s s i f i e d on the basis of whether they represent geometric  or non-geometric features of the  p r o f i l e and also according t o t h e i r estimated s t a b i l i t y . an element, the longer i s i t s assumed relaxation time (see  The more 'stable' 1:3).  A discussion of the d e r i v a t i o n of each variable and i t s probable r e l i a b i l i t y i s to be found i n Appendix A, Part I. Of the f i f t y meander bends, equal numbers were swinging northwards and southwards, so that the complete two-by-two f a c t o r i a l experiment was  arranged as shown i n Table I I I , with twenty-five r e p l i c a t i o n s of each  situation.  Each complete r e p l i c a t i o n of a l l four categories comprised two  v a l l e y c r o s s - p r o f i l e s , plus two measurements of the stream gradient at the apex of each meander bend.  MAP  2 -  Portion of the Gangplank S.W.  of Cheyenne, Wyoming  13 Table  The Experimental Design, Manitoba A S P E C T 1  2  South-facing  STREAM  A Towards  25 r e p l i c a t i o n s  25 r e p l i c a t i o n s  MOVING  B Away  25 r e p l i c a t i o n s  25 r e p l i c a t i o n s  Sample s i z e :  c)  North-facing  100  The Wyoming example This second and more extensive survey was c a r r i e d out i n twelve  v a l l e y s i n a portion of the Gangplank area t o the southeast of Cheyenne, Wyoming (see Map 2)„ The experimental design employed i n t h i s case was rather more complex than that used i n Manitoba,, F i r s t l y , i t was decided t o attempt t o determine the manner i n which slope form varied around each meander bend and, as a c o r o l l a r y , whether there existed any perceptible difference between the forms of those meanders which were swinging northwards and those cutting southwards.  In  order t o investigate these related problems, two p r o f i l e s were measured on either side of that which had i t s base at the apex of the meander bend and two complementary p r o f i l e s were also measured on the s l i p - o f f v a l l e y side. These subsidiary p r o f i l e s , whose arrangement i s shown i n Figure Is3> were measured from points f i f t y feet away from the base of the main crosssection:  t h i s distance was quite a r b i t r a r y , but i n general the curvature  of the bends was not so great as t o make t h i s spacing impractical.  It was noted above that the p r o f i l e s measured i n Manitoba represented complete cross-sections of the v a l l e y s ; t h i s was necessary, because meanders which a c t i v e l y impinged upon the v a l l e y sides were rare  Ik  Profiles  1  I*  \  2A  if!  Profiles  /  i  iii  II  ,«  i  ii  p r o f i l<ts  Figure 1:3  »•*  HI  1 1f  1 /  2.6  II  Pro-Pile s  a. in  in  \  1A  One r e p l i c a t i o n of the experimental design, easttrending v a l l e y s , Wyoming.  with the r e s u l t that most 'valley-side p r o f i l e s ' actually included of the f l o o d p l a i n .  This s i t u a t i o n was  s p e c i f i c a l l y avoided i n Wyoming and  only those meanders were sampled which undercut the v a l l e y side: floodplain was  a section  as  the  therefore excluded from the measurements of the "basally  corraded slopes, i t was  judged advisable to exclude i t also from those of  the s l i p - o f f p r o f i l e s .  The width and gradient of the floodplain was  there-  fore measured from the apex of each meander bend d i r e c t l y t o the foot of the opposite slope, but t h i s distance was profile.  The  not considered to form a part of that  subsidiary p r o f i l e s were therefore either measured at a d i s -  tance of f i f t y feet from the apex of each bend, following the curvature of the stream course, or at a similar distance from the c e n t r a l , s l i p - o f f p r o f i l e , measured along the lane of intersection of f l o o d p l a i n and  valley  side „  The  experimental design employed i n t h i s category of the Wyoming  15  v a l l e y s was therefore a s p l i t - p l o t modification of that used i n Manitoba, the lay-out of which i s shown i n Table TV. Table IV  Thirty-two meander bends were  The experimental design, east-trending valleys with stream courses, Wyoming A S P E C T  EROSIONAL ENVIRONMENT STREAM POSITION  A  B  1  North-facing  i - 5 0 ' upstream i i - d i r e e t l y at base i i i - 5 0 ' downstream  n ~ n n =  16  i - 5 0 ' up v a l l e y i i - d i r e c t l y away I i i - 5 0 ' down v a l l e y  n n s n =  16 16  Sample s i z e ;  16 16  16  2  South-facing n = n = n =  16 16  n n = n =  16 16  16  16  192  sampled, with equal numbers swinging northwards and southwards:  each  complete r e p l i c a t i o n of the experiment involved twelve measurements of slope form, but only two of channel c h a r a c t e r i s t i c s , one at the apex of each meander bend.  The t o t a l sample of p r o f i l e s i n t h i s class of the  analysis was 1 9 2 . The 32 meander bends at which observations were taken represent a complete sample of a l l those bends cutting due north or south and d i r e c t l y impinging upon the v a l l e y sides i n the sections of the s i x easttreanding valleys which were studied.. As any series of meanders was  as  l i k e l y to be i n i t i a t e d by a bend cutting north as by one swinging south and as those meanders d i r e c t l y against the v a l l e y side did not necessarily alternate i n d i r e c t i o n , i t i s safe to assume that the a l l o c a t i o n of any observation t o one of the four p r i n c i p a l categories of the design was random.''-  On the other hand, the two subsidiary observations i n each -'•Br. Go W. Eaton; personal communication.  16 -<&-  s p l i t - p l o t can scarcely be described  as randomly arranged:  fortunately t h i s  problem has been frequently encountered i n the design of a g r i c u l t u r a l  ex-  periments and i t has been determined that t h i s systematic arrangement of subdivisions has l i t t l e e f f e c t upon the experimental error.^ In addition to the main section of the analysis, two ulations were also sampled: four east-trending  'control' pop-  the f i r s t comprised f i f t y - e i g h t p r o f i l e s from  valleys without clearly-defined water courses, the second,  f i f t y - t w o p r o f i l e s from three south-trending valleys with c l e a r l y defined, ephemeral channels.  The f i r s t sample enabled an estimate to be made of the  effectiveness of cross-valley controls, in t h i s area, i n the absence of an active stream channel; the second served a dual purpose, as i t was to confirm that differences in aspect did not perceptibly influence slope forms i n south-trending valleys and,  intended the  i n that case, to allow a deter-  mination of the behaviour of streams i n the absence of known cross-valley controls. In the four valleys which lacked d e f i n i t e stream channels, slope p r o f i l e s were taken i n pairs along the v a l l e y , at intervals approximately equal to one p r o f i l e length:  t h i s spacing was  considered s u f f i c i e n t to en-  sure that the p r o f i l e s were independent ( c f . Strahler, 1 9 5 0 ) . was  obviously  This design  s e l e c t i v e , rather than random, with the r e s u l t that biases  to be expected in the data, although they are not l i k e l y to be  are  important.  The t o t a l sample comprised twenty-eight north»fac&ng and twenty-eight south-facing slopes, plus twenty-eight measurements of v a l l e y  gradient.  South-trending v a l l e y s , w i t h or without defined water-courses, are extremely r a r e i n the study area, as a r e s u l t of the manner In which the drainage net has developed (see II:1b): however, three such v a l l e y i D r . A. Kozak, personal communication.  17 sections were sampled although the valleys and the channels were much smaller than those trending eastwards. to  As a r e s u l t , i t proved impossible  obtain three independent p r o f i l e s at each meander bend and so i t was  not necessary t o employ the s p l i t - p l o t form of f a c t o r i a l design, but the basic experiment contained only four categories, as i n Manitoba (see Table V ) . Each r e p l i c a t i o n of t h i s design comprised four measurements of slope p r o f i l e s and two of channel c h a r a c t e r i s t i c s .  Table V *~  The Experimental Design, South-trending Valleys, Wyoming.  EROSIONAL ENVIRONMENT  A S P E C T West-facing  STREAM POSITION  East-facing  Towards  13 r e p l i c a t i o n s  13 r e p l i c a t i o n s -  Away  13 r e p l i c a t i o n s  13 r e p l i c a t i o n s  Sample s i z e :  52  A l i s t of the features of slopes and channels which were included i n the study i s given i n Table VI; the variables are c l a s s i f i e d i n the same manner as those i n Table I I . Comments on the derivation and measurement-accuracy of each variable w i l l be found i n Appendix A, Part I I . 1:3  The Choice of a 'Characteristic' Slope Parameter It has become f a i r l y standard practice amongst geomorphologists  interested i n slope forms, t o take the ' c h a r a c t e r i s t i c ' angle of any p r o f i l e t o be the maximum angle, as defined by Strahler i n h i s 1950 paper. Strahler was working i n areas of maturely dissected topography, i n which floodplains were l i t t l e developed and, s i m i l a r l y where both r i v e r - c l i f f s and free-face segments were lacking.  The maximum angle segment, as  Strahler defined i t , was therefore the angle of the straight 'constant'  Facing page - 18  Table VI The Variables Employed i n The Wyoming Study a)  A l l Valleys Variable:  b)  Description:  Mean angle  Geometric; stable  P r o f i l e height  Geometric; stable  P r o f i l e length  Geometric; stable  Channel or v a l l e y gradient  Geometric; only moderately stable  Maximum angle  Geometric; only moderately stable  Length maximum angle  Geometric; only moderately stable  Height/length i n t e g r a l  Geometric; only moderately stable  Average vegetation cover  Non-geometric; only moderately stable  Vegetation cover, maximum angle  Non-geometric; unstable  S o i l temperature  Non-geometric; unstable  S o i l resistance  Non-geometric; unstable  Further Variables, Employed only in Those Valleys With Ephemeral Streams. Channel cross-sectional area  Geometric; only moderately stable  Channel width  Geometric; only moderately stable  Hydraulic radius  Geometric; only moderately stable  Dgij. stream bed material  Non-geometric; only moderately stable  D50 stream bed material  Non-geometric; only moderately stable  D10 stream bed material  Non-geometric; only moderately stable  18 slope which i n most cases l e d d i r e c t l y into a stream channel (see Figure Itk,  a).  Figure Isk  Other workers who have investigated faceted slopes such  The Strahler maximum angle.  as those shown i n Figure 1:4,  b and c ) , have tended to equate the angle  of the 'constant' slope with the angle  which Strahler measured.  Whether  or not t h i s practice i s s t r i c t l y j u s t i f i a b l e i n terms of Strahler's i n i t i a l d e f i n i t i o n , i t has been widely used and a l l workers would seem to have been unanimous i n excluding the free face or r i v e r - c l i f f segments from the class of maximum angles„ When embarking upon a quantitative study, i t i s generally advisable to accept the d e f i n i t i o n s of previous workers i n the same f i e l d , for the simple reason that t h i s avoids confusion and enables the d i r e c t comparison of r e s u l t s .  However, i n the present instance i t has been judged  advisable to disregard precedent and to re-define the maximum angle segment of any p r o f i l e as, quite simply, that portion o f the slope of f i v e feet or Bore i n length, which has the steepest angle;  the minimum length i s  a r b i t r a r y and derives from Strahler's o r i g i n a l f i e l d procedures,  (1950).  19 In order t o explain t h i s breach of precedent, i t i s necessary t o examine some of the properties of the Strahler maximum angle and those of other, possibly ' c h a r a c t e r i s t i c ' parameters, i n the l i g h t of the aims of t h i s p a r t i c u l a r study, a)  The Strahler maximum angle This angle, as defined above, represents  a f a i r l y long slope  segment, i n most areas of mature topography and Strahler found that "o  . . within an area of e s s e n t i a l l y uniform l i t h o l o g y , s o i l s , vegetation,  climate and stage of development, maximum angles tend to be normally d i s t r i b u t e d with low dispersion about a mean value The  ..."  (1950; p.  685).  chief conclusion from t h i s must be that t h i s maximum angle i s a r e l a -  t i v e l y invariant feature of any area, although Strahler (1950) and Melton (i960) have shown that, i n c e r t a i n cases, s i g n i f i c a n t l o c a l variations may be s t a t i s t i c a l l y detectable.  The r e l a t i v e length of t h i s segment, i n  r e l a t i o n t o that of the p r o f i l e as a whole i s , however, a more c r u c i a l factor, f o r i t means that the Strahler maximum angle w i l l respond f a i r l y slowly t o changes, p a r t i c u l a r l y very l o c a l i s e d ones brought about by a l t e r a t i o n s i n the erosional environment.  This comparative slowness i n  response t o changes of stream p o s i t i o n i s l i k e l y t o be marked i n any case where the Strahler maximum angle segment i s situated at some distance from the base of the slope or stream.  If we can consider that a v a l l e y as a whole w i l l re-adjust to some equilibrium condition, a f t e r a disturbance,  i n a relaxation time t ,  then because the Strahler maximum angle has been shown to be  representative  of equilibrium conditions, i t seems f a i r to assume that i t s relaxation time w i l l be on the order l / 2 t , t o t .  If the disturbance  i n equilibrium i s not  valley-wide, but e f f e c t s only some p r o f i l e s , f o r example, as a r e s u l t of  20  b a s a l corrasion of c e r t a i n p r o f i l e s , then the relaxation time of each slope may not be so long, but i t i s s t i l l l i k e l y t o be i n the order of l/2t. In the case that basal sapping, or the termination of basal sapping,  i s the cause of a temporary disruption of previous equilibrium  conditions, the relaxation time of any slope segment w i l l be a function of four f a c t o r s ;  the i n t e n s i t y of the disturbance; the resistance of the  materials involved] the length of the slope segment and the distance between the base of the segment and the stream.  It i s clear that the  f i r s t two factors w i l l apply equally t o a l l sections of the slope, prov i d i n g i t i s of uniform l i t h o l o g y , but that the l a t t e r two w i l l r e s u l t i n longer segments, or those not d i r e c t l y adjacent t o a channel, r e q u i r i n g a longer time of relaxation than those which are shorter or closer t o the stream. As the Strahler maximum angle cannot include the r i v e r - c l i f f section of a slope, by d e f i n i t i o n , and i s also generally representative of a r e l a t i v e l y large portion of the p r o f i l e as a whole, i t i s clear that i t s relaxation time w i l l be comparatively  lengthy, compared with the time  necessary f o r the stream course t o change p o s i t i o n . b)  The mean angle This angle has been variously defined;  as the f a l l from divide  to channel ( c f . Hadley, 1961)* as the r a t i o of p r o f i l e height t o the h o r i zontal equivalent of p r o f i l e length; or, as i n the present study, as the r a t i o of p r o f i l e height t o the ground length of the slope.  Whichever  d e f i n i t i o n i s used, i t i s u n r e a l i s t i c t o employ t h i s parameter t o characterise.. slope form i f free faces are at a l l w e l l developed.  21 In other eases, unless there i s a single, straight slope extending from divide t o channel, the mean angles however defined, w i l l be lower than the Strahler maximum and i t has been observed t h e i r d i s t r i b u t i o n has a lower dispersion than that of the maximum angles (see Table V I I ) . The mean c o e f f i c i e n t of v a r i a t i o n (s/X angles l i s t e d (Kennedy,  x  100) f o r the samples of maximum  1965) i s 51.04$, as against 37.9$ f o r those of the  mean angles.  The comparatively low dispersion of the d i s t r i b u t i o n of mean angles, plus the fact that t h i s parameter represents the whole length of the slope p r o f i l e , indicates that i t i s l i k e l y t o be an even poorer index of the extent of l o c a l or short-term disturbances of p r o f i l e form.  How-  ever, since movements of the stream w i l l e f f e c t the length of the slope and thus, t o a l i m i t e d degree, the value of the mean angle, i t would be unwise t o suggest that the relaxation time of t h i s parameter i s l i k e l y t o be longer than that of the maximum angle, but i t w i l l c e r t a i n l y be of the same general order of magnitude.  Table V I I  Sample S t a t i s t i c s , Plateau de Bassigny, Haute-Marne  Class of slopes  Variable  Mean  Standard Deviation  N  Uniform l i t h o l o g y , stream t o .  Max. angle Mean angle  22.1° 8.6°  9.1° 2.6°  45 45  Uniform l i t h o l o g y , stream f r o  Max. angle Mean angle  22.6° 7.8°  11.1° 3.2°  45 45  Varied l i t h o l o g y , stream t o .  Max. angle  16.0°  9.4°  45  Mean angle  7.3°  2.8°  45  Max. angle  12.0°  6.6°  45  Mean angle  6.2°  2.6°  45  Varied l i t h o l o g y , stream f r o  22  c)  The height/length Integral The concept of the height/length i n t e g r a l , which i s introduced  for the f i r s t time i n t h i s t h e s i s , i s closely related to that of the mean angle, but derives from Strahler's hypsometric i n t e g r a l  Little  Pem  bina.Manitoba.  NortH- facing, stream "towards  Figure 1:5  (1957).  b)  So«+k - fo,c (nej , str&o,rr\ away  Representative height/length  integrals.  The height/length i n t e g r a l represents the mean height of the curve of the slope p r o f i l e i n the same way that the hypsometric i n t e g r a l characterises the mean height of a three-dimensional 1:5).  In theory, t h i s value may  surface (see Figure  range widely, hut as the size of the  i n t e g r a l depends d i r e c t l y upon the r e l a t i v e distance between the steepest portion of the p r o f i l e and the base of the slope, values obtained from any one erosional environment w i l l tend to be r e l a t i v e l y constant.  In  general, the integrals of undercut slopes are greater than those of s l i p o f f p r o f i l e s ( c f . a and b, Figure  1:5).  23 The derivation of the height/length i n t e g r a l makes i t verysensitive t o any s h i f t of the p o s i t i o n of the stream r e l a t i v e t o the slope, so that i t s relaxation time may he said t o be instantaneous with the movement of the channel.  This aspect of the index was p a r t i c u l a r l y valuable  i n the case of the Manitoba p r o f i l e s , where the length of f l o o d p l a i n included i n each measurement varied considerably.  In the case of the main  category of the Wyoming slopes, only the undercut p r o f i l e s could be said t o have height/length integrals which changed r a p i d l y : those of the s l i p o f f slopes must be considered as possessing a much longer relaxation time, since any a l t e r a t i o n would require that the p o s i t i o n of the v a l l e y side intersection with the f l o o d p l a i n were changed.  d)  The absolute maximum angle If the absolute maximum angle i s defined as the gradient of the  steepest section of the p r o f i l e of more than f i v e feet i n length (this a r b i t r a r y length would vary, according t o the scale of the topography), then i t i s obvious that i t may represent any portion of the slope — face, constant slope, or r i v e r - c l i f f .  free  This angle w i l l , therefore, be a  poor indicator of the c h a r a c t e r i s t i c slope forms of any area and an equally poor b a s i s f o r comparisons between areas. However, where r i v e r - c l i f f s are present, but free faces absent, the absolute maximum angle w i l l be representative of only one of two s i t u ations, those i l l u s t r a t e d in Figure Is6„  In case a, the absolute maximum  angle 0 w i l l depart considerably from the Strahler maximum /& , but i n case b, where the slope i s protected from stream sapping, the two angles w i l l coincide.  This d e f i n i t i o n of the maximum angle possesses both advantages and disadvantages,  a l l of which arise from the f a c t that i t w i l l represent  2k  d i f f e r e n t situations and w i l l have a d i f f e r e n t relaxation time when drawn from d i f f e r e n t categories of slopes.  Figure It6  I f the p r o f i l e i s one with no channel  Relationship of Strahler and absolute maximum angles.  a c t i v e l y corrading at i t s base, 0  w i l l coincide with /3 and w i l l ,  therefore, have a similar relaxation time.  On the other hand, i n those  cases i n which 0 represents the r i v e r - c l i f f , i t s relaxation time w i l l be of a much shorter order, although i t i s u n l i k e l y t o be instantaneous with the s h i f t i n g of the channel, unless the p r o f i l e s are cut i n unconsolidated materials.  The use of the absolute maximum angle therefore allows an  estimate t o be made of the maximum i n t e n s i t y of l o c a l disturbances, which i s precisely the aim of t h i s study, and also of the variations i n departure from equilibrium around the meander bends„ Since we are, i n t h i s study, primarily interested i n l o c a l i s e d and probably short-lived variations i n slope form i t i s most appropriate to employ the absolute maximum angle as the chief diagnostic feature of the p r o f i l e s , rather than the mean angle which i s too general, or the hypsometric i n t e g r a l , which i s rather too constant i n the major category of the Wyoming analysis.  As emphasised above, the absolute maximum angle  25 w i l l , however, coincide with the Strahler maximum f o r a l l s l i p - o f f profiles.  F i n a l l y , i t has been stressed that the relaxation time of the four variables discussed i s not i d e n t i c a l . we may  It i s therefore suggested that  arrange them i n a sequence, f o r any slope, according to the order  of r a p i d i t y i n which they w i l l become re-adjusted to accommodate changes i n the l o c a l erosional environment.  Figure 1:7  i l l u s t r a t e s the progression  of changes i n the four v a r i a b l e s , f o r an undercut slope.  This sequence  Change Mean Angle Stream  Change  Moves  H/L Integral  Change *Absolute Max.  Angle^  Change Strahler "Max. Angle  Time Figure 1:7  Adjustment of slope features to changing erosional environment, undercut p r o f i l e s .  has been investigated f o r the p r i n c i p a l category of the Wyoming analysis and the r e s u l t s are set out i n Sections 1 and 2 of Chapter I I I . 1:4  S t a t i s t i c a l Techniques Three groups of s t a t i s t i c a l techniques were employed i n the  analysis of the f i e l d data, a)  Paired differences A l l p r o f i l e s included i n the study were measured i n p a i r s , so  that the various parameters could be analysed by means of paired Student's •t* t e s t s :  the exact design i s discussed below (111:2). The advantages  of t h i s p a r t i c u l a r s t a t i s t i c a l technique  i n asymmetry studies have been  26  discussed at some length by Melton ( i 9 6 0 ; p„ 1 3 9 )  and i t i s s u f f i c i e n t to  repeat here that the taking of paired differences ensures the removal of a l l non-random variations introduced by measurement errors, and by betweenv a l l e y or along-valley differences i n slope form,  b)  Analyses of variance The more important variables i n the study, notably the angles  of slope, were subjected to a more r e f i n e d analysis, using two-way analyses of variance.  The mean values f o r each category were then, i n c e r t a i n  cases tested separately by Duncan's new Torrie, i 9 6 0 ; pp.107-109).  multiple range t e s t (Steel and  This t e s t i s of p a r t i c u l a r value when the  interaction terms i n the analysis of variance are s i g n i f i c a n t , since i n such a s i t u a t i o n i t i s incorrect to proceed to test the s i g n i f i c a n c e of the main e f f e c t s against the error mean square. B r i e f l y , Duncan's t e s t involves the ranking of mean values  and  the t e s t i n g the differences between a l l possible combinations of pairs against a l e a s t s i g n i f i c a n t difference, calculated as Tv .05 x Sg, where Tv i s the standardised (not confidence  studentised range f o r the 95$ protection l e v e l  l e v e l ) and S5 i s obtained from the formula:  Although t h i s t e s t has not, to the author's knowledge, been previously employed by geomorphologists, i t has been found to be extremely valuable i n the d e t a i l e d analysis of variations between the sub-units i n the Wyoming study. c)  Correlation and  regression  Having selected the absolute maximum angle as the diagnostic  2?  variable f o r a l l p r o f i l e s , i t was of interest t o discover the degree and manner i n which the other factors were related t o the steepest portion of the p r o f i l e and, i n addition, the fashion i n which these relationships altered, from one category of slopes t o another. The techniques of multiple, step-wise regression and correlation were therefore employed t o determine the nature of these i n t e r - r e l a t i o n ships, and the r e s u l t s of these analyses and t h e i r implications are discussed f u l l y i n Chapter I ? .  Facing page - 28  Figure 1 1 : 2  Section of d r i f t , east bank of meander, L i t t l e Pembina, Manitoba.  CHAPTER I I . II;1 a)  THE SETTINGS  Geology and Denudation Chronology Manitoba A succinct summary of conditions i n t h i s area i s provided by  Halstead (1959* P« 7):  "Continental g l a c i e r s , upon entering t h i s area,  rode over a surface of sedimentary rocks l a r g e l y composed of shales and during r e t r e a t covered t h i s bedrock with g l a c i a l deposits."  In the par-  t i c u l a r portion of the region i n which we are interested (see Map l ) , the sedimentary rocks involved are the Riding Mountain shales of Cretaceous age (see Figure I I : l ) , but as Elsonjs map of the s u r f i c i a l geology (included i n Halstead, 1959) suggests, and f i e l d observations  confirm,  the three streams studied have not succeeded i n c u t t i n g down through the g l a c i a l deposits t o the bedrock.  All  slopes measured i n t h i s sample are, therefore, formed i n  t i l l , which Elson describes as "ground moraine: . . . ranging from sandy to  clayey sandy, containing a few irregular bodies and lenses of s i l t and  sand; l o c a l l y overlain by a layer of clayey s i l t 1 foot t o 3 feet t h i c k . " (See Figure 11:2).  The w e l l records mapped by Halstead, (1959; map 1066A),  show that, i n the area of study, the t i l l i n general has a minimum depth of between 2k and 50 feet and i n one well a c t u a l l y within the Upper Pembina v a l l e y , bedrock i s not encountered u n t i l 60 feet, below the surface.  Given the depth and completeness of the ground moraine cover, i t  29 appears u n l i k e l y that the bedrock exerts any major influence upon v a l l e y shape or form:  s t r u c t u r a l control would scarcely be pronounced anyway,  since the regional dip, towards the southeast, i s as low as 5 to 10 feet per mile (Halsteadj p. 7)-  It might, however, be argued that the nature  of the buried Riding Mountain topography could w e l l influence the nature of the present streams, p a r t i c u l a r l y as regards t h e i r d i r e c t i o n and degree of i n c i s i o n .  I f r e l i a n c e i s placed on Halstead's map  of the r e l a t i o n of  p r e - g l a c i a l and present topography (1959* F i g . 2 ) , t h i s l a s t d i f f i c u l t y may be discounted, f o r i t appears that the p r e - g l a c i a l ancestor of the Upper Pembina flowed, not due east, but almost d i r e c t l y north and joined the former course of the Assiniboine i n the v i c i n i t y of the present town of S h i l o , east of Brandon.  It i s therefore d i f f i c u l t t o believe that the present p o s i t i o n of the streams i n t h i s area might have been influenced by pre-Pleistocene events.  In f a c t , since the l a s t ice sheet which covered the region d i d  not begin to t h i n and retreat u n t i l about 1 2 , 0 0 0 years B.P. 19591  P. 1 1 i t  (Halstead,  would seem reasonably c e r t a i n that t h i s landscape i s one  of the p o s t - g l a c i a l formation alone.  As the larger features of g l a c i a l  and f l u v i o - g l a c i a l deposition are largely absent, the r o l e of the late Pleistocene ice sheets i n t h i s region may be considered as purely o b l i t eratives  the formation of the e x i s t i n g landscape owes l i t t l e to t h e i r  passage, but represents the action of f l u v i a l erosion over a  comparatively  short period of geologic time.  For these reasons, the area would seem to be extremely suitable f o r a study of slope development, as any  'hangover' elements w i l l  represent a short, p o s t - g l a c i a l timespan, and there can be no question of the preservation of Pliocene forms.  Facing page - 3 0  Figure 11:3  Section of Ogallala formation, exposed byrailway cutting, Belvoir Ranch, Wyoming. (Photo courtesy, M. A. Melton.)  30  b)  Wyoming The area of study (see Map  2) consists of a portion of the  Plio-Pleistocene surface, known as the Gangplank where t h i s surface i s developed on the Ogallala formation of Pliocene age.  The mode of o r i g i n  of both the Gangplank and the Ogallala are topics outside the scope of the present paper:  discussions of the problems may be found i n Moore  (19591 passim) and Thornbury ( 1 9 6 5 , p. 2 8 8 ) .  The slope of the surface and  the dip of the underlying beds are similar i n d i r e c t i o n and very gentle (approximately  80 feet per mile) towards the east, according to Moore  (p. 9 9 ) . The Ogallala formation (see Figure 11:3)  consists primarily of  coarse-grained arkosic sandstones, s i l t s t o n e s and conglomerates and reaches a maximum thickness of 300 feet i n the study area.  One unusual feature of  t h i s formation i s the presence within i t of t h i n and discontinuous bands of limestone (Moorej pp. 46-53)> but there were no exposures of t h i s bed in the areas from which measurements were obtained. The Quaternary h i s t o r y of the area has been dominated by the discontinuous erosion of the T e r t i a r y deposits.  There i s clear evidence  of down-wearing of the Sherman surface, which cuts across the granites to the west, of about 5 f e e t , and i t would seem l i k e l y that the Gangplank surface has been s i m i l a r l y degraded. been played by f l u v i a l erosion:  However, a more obvious role has  Moore (p. 86) estimates that the maximum  depth of Quaternary i n c i s i o n i s greater than 300 f e e t .  Climatic o s c i l l a -  t i o n s , p a r t i c u l a r l y since the end of the Pleistocene, are generallyaccepted to have caused t h i s i n c i s i o n to take place i n a discontinuous fashion, r e s u l t i n g i n the formation of a number of terrace l e v e l s . Leopold and M i l l e r (1954) have studied s i m i l a r terrace sequences i n other  FIGURE 11:4  -  The Major Terraces of the Gangplank Streams. (After Leopold and M i l l e r , 1954, Figure 5)  31 parts of the Gangplank and have i d e n t i f i e d three u n i t s :  these are the  Kaycee (20 - 50 feet above the present streams), the Moorcroft (8 f e e t ) and the Lightning ( 4 - 7  feet):  12  these forms and the presumed extent  of the associated deposits are shown i n Figure  11:4.  Leopold and M i l l e r have attempted to trace the terrace systems headward into the g l a c i a l features of the Wind River area and, as a r e s u l t , have t e n t a t i v e l y given a date t o the Kaycee terrace which i s l a t e r than that of the l a s t moraine:  they consider (1954^ p. 46) that the  climatic indications given by the Kaycee deposits and by a buried palaeosol i n p a r t i c u l a r , suggest that t h i s terrace formed i n or shortly after the Altithermal ( 8 , 0 0 0 - 4 , 5 0 0 years B.P.).  They further suggest that  the Moorcroft represents a period of deposition which ended about 760  B.P.  and that the l a t e s t period of down-cutting, which formed the Lightning terrace, was  i n i t i a t e d as recently as 80  If we may  B.P.  correlate Leopold and M i l l e r ' s three terrace l e v e l s  with those found at 25 - 40 f e e t , 10 - 16 feet and 4 - 8 present  feet above the  streams i n the valleys studied,, then i t would appear that these  v a l l e y s represent, at the outside, a record of the Pleistocene alone (o. 1 m i l l i o n years) and that, i n a l l p r o b a b i l i t y the inner v a l l e y s (with which we  s h a l l be primarily concerned, for reasons discussed below) have  been formed within the l a s t 8 , 0 0 0 years at most.  The time-scale  i s , therefore, r e l a t i v e l y comparable to that suggested f o r the  involved formation  of the Manitoba valleys and i t i s s i m i l a r l y u n l i k e l y that any r e l i c s of Pliocene forms are  preserved.  Of the three terrace l e v e l s found i n the v a l l e y s studied, only the lowest i s generally present:  the two higher surfaces are found at  variable heights and with d i f f e r i n g degrees of preservation.  Figure  11:5  Figure 11:5  KEY:  Figure 11:6  Terraces, upper Lonetree Creek (looking west).  G I II III  -  Gangplank surface 'Kaycee' (?) terrace 'Moorcroft' (?) terrace 'Lightning' (?) terrace  Terraces, Goose Creek (looking northeast).  32 shows the upper section of Lonetree Creek, with the -Gangplank surface the remnants of the three terrace l e v e l s : the highest terrace (Kaycee?) preserved  Figure 11:6  and  shows a portion of  along the south side of Goose  Creek at a height of 30 - 35 feet and the youngest surface below i t . Figures 11:5 of the v a l l e y sides.  and 6 also c l e a r l y show the degree of d i s s e c t i o n It seems that before the highest terrace  was  entrenched, the drainage consisted of numerous s u b - p a r a l l e l , east-flowing streams and that the i n c i s i o n of the major drainage l i n e s caused t h e i r t r i b u t a r i e s to swing north/south near t h e i r mouths. pattern i s therefore pinnate (see Figure 11:7) trending  The present drainage  and v a l l e y sections  either due north or south are extremely r a r e .  Even those g u l l i e s  which develop d i r e c t l y on the main v a l l e y side are more l i k e l y to possess  N  Figure 11:7  Characteristic drainage pattern, Cheyenne area. ( S i m p l i f i e d from a section of Spotwood Creek, Emkay Quadrangle.)  33 t r i b u t a r i e s on t h e i r western, than on t h e i r eastern banks, f o r reasons which are obvious i f the cross-section i n Figure 11:7  i s studied.  A l l in  a l l , therefore, t h i s area i s characterised by large numbers of small streams which flow almost p a r a l l e l with the major drainage l i n e s and cause an extensive d i s s e c t i o n of the v a l l e y sides. Perhaps the major r e s u l t of the p a r t i c u l a r manner i n which t h i s d i s s e c t i o n occurs, i s the almost complete separation of the drainage of the upper v a l l e y sides from that of the terraces: of  i n many cases (see form  6,800 foot contour north of main stream i n Figure 11:7)  the former i s  channelled along the t r i b u t a r i e s , rather than into the main stream directly.  Thus, i f we are concerned, as we are, with the manner of  development of the v a l l e y sides i n r e l a t i o n t o the behaviour of the major streams, i n many cases we can ignore that portion of the v a l l e y side which l i e s above the highest terrace:  i t i s f o r t h i s reason that i t was  sug-  gested that the period of slope development i s e s s e n t i a l l y of the order of  8,000 years, or l e s s .  Of course i n some instances —  the south-facing bank i n the foreground of Figure 11:5  f o r example, that of —  a l l terraces  have been removed by stream action and i t i s possible, though not very probable, that the slope form may  date i n part from before the A l t i t h e r m a l .  On f i n a l point should be made here: remnants preserved  the number of terrace  and the s i g n i f i c a n t position which they occupy i n com-  parison with the bedrock as regards the formation  of v a l l e y walls, raises  the question of whether we are t r u l y considering an area of homogenous lithology.  From the b r i e f description of the nature of the Ogallala given  above and from Figure II:3> i t should be apparent that t h i s i s a  formation  of variable composition and, further, that i t i s a product of geologically late deposition i n a semi-arid environment.  The re-worked material i n the  Facing page - 34  FIGURE 11:8  -  Climatic regime, Bpissevain, Manitoba  FIGURE 11:9  -  Climatic regime, Cheyenne, Wyoming  (Thornthwaite water balances from Rain I I I Programme, M. A. Melton)  34  terrace deposits i s of l o c a l derivation and neither i t s mode of deposition, nor i t s composition vary substantially from that of the parent formationo  As t h i s i s the case, the task of disentangling Ogallala i n  s i t u from that which has been re-worked would prove formidable, i n the present author's view and i s c e r t a i n l y beyond the scope of t h i s study. 11:2  Climate and Hydrology  a) Manitoba According t o the revised Thornthwaite c l a s s i f i c a t i o n ( 1 9 5 5 ) the climate of t h i s area i s described as 'dry, subhumid, mesothermal, with l i t t l e surplus at any time of year,' or C^B]_d. Geomorphically, the mean annual d i s t r i b u t i o n of heat- and m o i s t u r e - a v a i l a b i l i t y are of greater importance than are the annual values _per se:  these d i s t r i b u t i o n s , f o r Boissevain, are shown i n Figure 11:8.  This s t a t i o n , which has 25 years of records, l i e s only 5 miles west of the most westerly study segment and i t s climate may be taken as representative of that of the surrounding area. The mean annual temperature at Boissevain i s only 3 7 ° F„, with 194 days of f r o s t , on average, per year and 5 months when mean temperatures are below freezing.  The average annual- total, of p r e c i p i t a t i o n i s 19.3  inches and the p r e c i p i t a t i o n regime shows a very marked springtime peak with a secondary maximum i n August created by convectional storms.  Winter  p r e c i p i t a t i o n i s low - 3 ° 7 Inches f o r the 5 below-freezing months - but the combination of snow melt, spring rains and r i s i n g temperatures i s s u f f i c i e n t t o produce a small surplus of moisture, allowing substantial runoff t o occur i n A p r i l and May ( f o r an assumed water-holding capacity of the s o i l of 12 cms.).  The a r i d i t y index f o r t h i s station i s low -  11.59 - but the humidity index even lower - 4.72.  Facing page - 35  FIGURE 11:10  -  Discharge, Pembina River at Rhodes, Manitoba.  35 However, despite the apparent a r i d i t y of the area, streamflow i s maintained f o r most of the above-freezing months:  Figure 11:10  shows  the discharge curves f o r the Pembina at Rhodes, f o r the whole period of available records (1959-64),  graph, which may be taken as character-  i s i n g discharge conditions i n the study area, shows the monthly discharges expressed as percentages of the annual t o t a l s .  The mean annual discharge  f o r the period of record was 3*819 c.f „s. (though t h i s i s scarcely a r e l i a b l e f i g u r e ) j the peak discharge generally occurs i n A p r i l and i s , on average, almost h a l f the annual t o t a l ; the channel i s always frozen i n the period Hovember-»February „  Runoff i s low:  the Thornthwaite water balance programme  predicts a surplus of 2.64 cm. or 1.04 inches i n A p r i l , with runoff i n A p r i l and May:  t h i s i s conservative, since i t does not allow f o r short-  term runoff associated with summer storms, but even so i t agrees closely with the mean, observed value of 1.72 10$ of the mean annual r a i n f a l l .  inches, which represents less than  I f the cumulative percentage frequencies  of p r e c i p i t a t i o n ( P ), runoff ( R ) and discharge ( Q ) are plotted f o r each year (see Appendix B) and the degree of departure of the curves from one another i s tested by the Kolmogoroff-Smirov procedure, i t i s found that the R and Q d i s t r i b u t i o n s are i d e n t i c a l , but that both depart s i g n i f i c a n t l y from the P curve.  I t i s c l e a r , therefore, that i t i s not the p r e c i p i t a t i o n  regime i t s e l f which i s the primary control of stream flow, but rather the d i s t r i b u t i o n of temperature, i n that both the cold winters and the hot summers of the area prove e f f e c t i v e i n reducing runoff and, therefore, the amount of discharge.  As the three streams whose valleys comprised the study area usually continue t o flow u n t i l at least l a t e August, i t seems reasonable t o  36  class them as intermittent, rather than ephemeral or permanent,  b)  Wyoming The climate of t h i s region i s c l a s s i f i e d by the revised  Thornthwaite system (1955) as 'semi-arid, mesothermal, with no water surplus at any time of year,' or DB-j_d.  The p r i n c i p a l difference between t h i s  area and that i n Manitoba i s therefore the amount of moisture a v a i l a b l e . Climatic records f o r the standard U. S. Weather Bureau period of 30 years are available f o r Cheyenne (Municipal A i r p o r t S t a t i o n ) :  the tem-  perature and p r e c i p i t a t i o n regimes are summarised i n Figure 1 1 : 9 .  As  Cheyenne i s situated within 12 miles of the most easterly study segment and at a comparable elevation ( 6 , 1 0 0 f e e t ) , i t seems reasonable that i t s climate w i l l be similar t o that of the v a l l e y s i n which measurements were made:  there i s no station with complete climatic records situated closer  to the study  area.  If Figures 11:8 and 9 are compared, i t i s clear that the climate of Cheyenne i s a c t u a l l y less extreme than that of Boissevain, as f a r as temperature c h a r a c t e r i s t i c s , but that the nature of the p r e c i p i t a t i o n and water balance regimes j u s t i f y the inclusion of the Wyoming station in the semi-arid category.  Cheyenne has only four months with mean a i r  temperatures below f r e e z i n g and an average of 170 days of f r o s t each year: the annual temperature, i n consequence, i s perceptibly higher than that of Boissevain, averaging 4 5 . 7 ° «  The mean annual p r e c i p i t a t i o n , on the  other hand, i s only 1 5 . 0 inches, the regime showing a single peak, i n May, which coincides with the spring r i s e i n a i r temperatures.  The low t o t a l  p r e c i p i t a t i o n and the high summer a i r temperatures combine t o create a c h a r a c t e r i s t i c a l l y semi-arid water balance at t h i s s t a t i o n , with a zero humidity  index and an a r i d i t y index of 3 2 . 7 5 :  there i s no surplus  37 predicted, even i n the spring and the summer d e f i c i t i s considerablygreater than at Boissevain.  As a consequence, i t i s scarcely surprising that the streams of the area exhibit the t y p i c a l l y  'flashy' discharge pattern of semi-arid  regions, with summer flow r e s u l t i n g exclusively from thunderstorms. are,  understandably, no gauging stations i n the study area.  There  It i s clear  that these streams should be classed as ephemeral rather than intermittent.  11:3  S o i l s and S o i l Movement  a) Manitoba The reconnaissance s o i l survey carried out by the Manitoba Department of Agriculture classes the s o i l s of the Killarney-Boissevain area as  „ . dark brown steppe and black earth t r a n s i t i o n s o i l s ,  developed on t i l l .  . .": the p a r t i c u l a r s o i l type represented i s that  member of the Waskada Clay Loams which develops on smooth undulating topography. The depth of s o i l development i s variable — to several f e e t .  from a few inches  Prom laboratory tests of the mechanical properties of  the s o i l s (Burmister, 1951) both p l a s t i c i t y and s i l t content were found t o be uniformly high; from 0 t o 40.  the two indices are roughly logarithmic and may range  The mean value of the P l a s t i c i t y Index was found t o be 2 1 . 2  and that of the S i l t Index, 31.3s  t h i s would place the s o i l s i n the  general category of ' S i l t y CLAYS, with a highly objectionable degree of p l a s t i c i t y , very l i a b l e t o displacement and compression.'  The height of  c a p i l l a r y r i s e i n such s o i l s would, t h e o r e t i c a l l y , be i n the region of 15 - 25 f e e t .  S o i l moisture content was found t o be uniformly high -- t h i s  was not unexpected, since the samples were collected during a period of frequent thunderstorms —  the average content being l6„9$> by weight.  N E. France  83  22.5°  19.^.°  S.W. Mo.n i -Vtobcx  lo  49.  0%  14.3°  ©.7  FIGURE 11:11  -  Estimated mean amounts of slow mass movements, Manitoba and E. France.  S(Vitf  of euylc  of jrounj slope  38  From the 'nature of the s o i l s and the c h a r a c t e r i s t i c s of the clim-"f :  ate regime, i t i s to be expected that s o i l creep and other slow mass movements, notably t r a n s l a t i o n s l i d e s , w i l l be important mechanisms of downslope debris movement.  It i s obviously desirable, therefore, to obtain some index  of the amount of s o i l movement, f o r t h i s , together with small s l i p s ,  accounts  f o r much of the transportation of material t o the stream channels and the progressive reduction of slopes below t h e i r angle of s t a b i l i t y .  Unfortun-  ately, i n a short period of study i t i s impossible to obtain values f o r observed rates of movement and any such measurements would be suspect.  extremely  However, on many slopes there are indications of downslope s o i l  movement, i n the form of pile-ups behind obstacles and small tension cracks or t u r f breaks and i t i s maintained that, by measuring the v e r t i c a l extent of these features, a reasonable estimate of r e l a t i v e amounts of movement can be made.  Such measurements w i l l obviously include material moved by  rain-beat and treading by stock, but as these processes aid i n the downhill progress of debris i n the landscape, there would seem to be no cause to object to the inclusion of t h e i r effects i n t h i s study. (Kennedy, 1965)  A previous study  having demonstrated the usefulness of t h i s approach,  measurements of the v e r t i c a l extent of small features r e s u l t i n g from mass movements were therefore made, both i n Manitoba and Wyoming. When the information so obtained i n Manitoba i s plotted against the sine of the angle of ground slope, which represents the magnitude of the downslope component of gravity ( c f . Schumm, 1 9 6 7 ) , clear, positive relationships are observed (see Figure I I : l l ) .  The data has been divided  into two groups, representing a l l observations from north- and south-facing slopes and although the samples are not very large, that from the northf a c i n g p r o f i l e s i s s u f f i c i e n t to produce a highly s i g n i f i c a n t c o r r e l a t i o n , with a c o e f f i c i e n t of determination ( r ) of 57%. 2  39 It i s i n t e r e s t i n g that there appears t o be some difference i n the i n t e n s i t y of movement on the two classes of v a l l e y sides?  f o r the  south-facing slopes the threshold angle of movement (represented by the X intercept) i s i n the region of 1 1 , 5 ° and the increase i n amount of movement with increasing slope i s moderate.  On the north-facing slopes, however,  although the threshold angle i s higher ( 1 5 ° ) , so i s the increase i n movement with steepening slope.  The estimated depth of disturbance on both  classes of slopes would be similar —  2.5 inches —  at an angle of 2 2 ° ,  but f o r a 3 7 ° slope the value predicted f o r a north-facing slope would be 8 . 0 inches, as against 6 . 0 inches f o r one f a c i n g south.  Absolutely, these values are probably u n r e l i a b l e :  i t is  i n t e r e s t i n g , however, that the threshold of movement i s higher on the north-facing slopes, i n d i c a t i n g that perhaps the greater degree of vegetat i o n cover on these p r o f i l e s may t o some extent i n h i b i t mass movements: the north-facing slopes have, on average, "]% more vegetation, s t a t i s t i c a l l y a highly s i g n i f i c a n t increase over the amount for the south-facing profiles. As f a r as the rates of increase i n depth of disturbance with increasing ground slope, i t should be noted that the regression l i n e f i t t e d to the data from the north-facing slopes i n Manitoba has an exponent which i s i d e n t i c a l t o that obtained from the observations made i n the Plateau de Bassigny, 30 inches.  an area of sandy limestones which has an. annual r a i n f a l l of The s i m i l a r i t y of these two relationships and the departure of  the l i n e representing the drier., south-facing slopes, leads t o the tentative conclusion that, whereas the threshold of mass movement may be determined by the degree of vegetation cover, the amount of movement above t h i s threshold w i l l be dependent on the general moistness of the environment.  -  40  S i n c e no m i c r o c l i m a t i c o b s e r v a t i o n s were made i n M a n i t o b a , t h e s u g g e s t i o n t h a t t h e d i f f e r e n t r a t e s o f s o i l movement on n o r t h - and s o u t h f a c i n g s l o p e s a r i s e from v a r i a t i o n s i n t h e m o i s t n e s s o f t h e two e n v i r o n ments i s d i f f i c u l t t o p r o v e , b u t t h e r e are t h r e e f a i r l y c l e a r i n d i c a t i o n s that t h i s i s i)  sos-  The v e g e t a t i o n cover o f t h e n o r t h - f a c i n g s l o p e s i s s i g n i f i c a n t l y greater.  ii)  The m o i s t u r e c o n t e n t of t h e s o i l samples from t h e n o r t h - f a c i n g p r o f i l e s was found t o be s i g n i f i c a n t l y g r e a t e r t h a n t h a t  of  t h o s e from t h e s o u t h - f a c i n g s l o p e s , b y 5 $ . iii)  The s o i l samples from t h e n o r t h - f a c i n g p r o f i l e s , when t e s t e d i n t h e l a b o r a t o r y , were found t o be s i g n i f i c a n t l y more p l a s t i c t h a n t h o s e from t h e s o u t h - f a c i n g s l o p e s ; b o t h s e t s of were t e s t e d a t f i e l d  samples  capacity.  I t a p p e a r s , t h e n , t h a t a l t h o u g h c o n d i t i o n s on t h e s o u t h e r n v a l l e y s i d e s i n t h i s a r e a w i l l t e n d t o m i t i g a t e a g a i n s t mass movements a t a n g l e s b e l o w about 1 5 ° , above t h i s t h e r e s i s t i n g f o r c e s e x e r t e d by t h e v e g e t a t i o n c o v e r w i l l be overcome by t h e c o m b i n a t i o n o f r e l a t i v e l y h i g h m o i s t u r e c o n t e n t and p l a s t i c i t y o f t h e s o i l , w i t h t h e r e s u l t t h a t movement w i l l be i n c r e a s i n g l y f a c i l i t a t e d as t h e angle o f s l o p e i n c r e a s e s .  The  d r i e r , more s p a r s e l y v e g e t a t e d environment of t h e n o r t h e r n s l o p e s w i t h l e s s p l a s t i c s o i l s , a l l o w s movement t o o c c u r a t l o w e r a n g l e s , b u t t h e amount i s r e s t r i c t e d by t h e l a c k o f m o i s t u r e .  I t i s , of course, p o s s i b l e t h a t the  a c t u a l volume o f m a t e r i a l moved from t h e s o u t h - f a c i n g s l o p e s may be for  greater,  i t w i l l be i n c r e a s e d b y m a t e r i a l f o r c i b l y washed downslope d u r i n g  s t o r m s , a t y p e o f movement which w i l l be more i n h i b i t e d by t h e c l o s e r v e g e t a t i o n n e t on t h e n o r t h - f a c i n g s l o p e s .  F a c i n g page - Ul  F i g u r e 11:12  S o i l p r o f i l e , Goose Creek v a l l e y . (Upper 2k i n c h e s o f A s c a l o n s e r i e s p r o f i l e exposed on the s o u t h e r n v a l l e y s i d e . )  F i g u r e 11:13  S o i l p r o f i l e , t r i b u t a r y t o Duck Creek. (Upper 36 i n c h e s o f p r o f i l e exposed i n head c u t . )  41  b)  Wyoming The s o i l s of t h i s area are the same or very similar to the  Ascalon'series which, according to Eindschadler (1964) consists of " . . . well-drained, moderately  dark-colored Chestnut s o i l s developing on piedmont  surfaces from s t r a t i f i e d , generally gravelly, calcareous alluvium underlain by a l l u v i a t e d granite gravel." When dry, the Ascalon i s c h a r a c t e r i s t i c a l l y greyish and s l i g h t l y compact and i t s chief features are shown i n Figures 11:12  and  13.  It i s not suggested that the s o i l s which were studied i n the course of t h i s investigation are representative of the undisturbed Ascalon, but they must include most of the members of the c h a r a c t e r i s t i c catena: f u l l development of the t y p i c a l Ascalon p r o f i l e i s presumably limited to the broader  interfluves.  The empirical;tests used to evaluate s o i l c h a r a c t e r i s t i c s i n Manitoba were replaced, i n Wyoming, by f i e l d measurements of s o i l temperature and e l e c t r i c a l resistance (a function of s o i l moisture) taken with a S o i l Test instrument.  1  The nature of the s o i l varies so r a p i d l y , as a  r e s u l t of the changing character of the Ogallala i t s e l f , that i t would be d i f f i c u l t to generalise the mechanical properties of the s o i l s on one slope, and impossible f o r those on 300.  It does seem u n l i k e l y , however,  that these s o i l s are as inherently prone to creep displacements as the Manitoban ones:  Bindschadler (1964; p. 2 ) describes the Ascalon series as  being only s l i g h t l y p l a s t i c , when wet and f i e l d observations indicated that the proportion of clay and s i l t sized material i s f a i r l y  The f i e l d observations of s o i l temperatures j j i  ^-Soil Moisture Meter, model M C - 3 0 0 A .  low.  were used l a r g e l y to  FIGURE II:lb  -  S o i l temperature and moisture cycles, Archer:  I963-I965.  42  determine cross-valley differences and were of l i t t l e value as f a r as the annual pattern of temperature  and moisture cycles were concerned.  nately, data on the temperature  Fortu-  and moisture regimes of an Ascalon s o i l i s  available from the Archer Dryland F i e l d Station, some 20 miles northeast of the area of studyo  1  One of the most important controls of the amount of s o i l movement i s the number of freeze-thaw and moisture-change cycles i n the upper layer of t h e r e g o l i t h ;  Figure I I s l 4 shows the generalised pattern of changes i n  the upper 12 inches of t h e s o i l p r o f i l e at the Archer s t a t i o n .  As t h i s  station i s away from the area of study and represents a bare fallow on a 1$ slope, no attempt should be made t o translate the absolute values of these observations t o t h e region southwest of Cheyenne, but i s probably v a l i d -to consider that the seasonal trends i n both cases have roughly the same d i r e c t i o n and order of magnitude. Figure IIsl4 shows c l e a r l y the very high l e v e l s reached by mean s o i l temperatures  i n June and July, even at 8 inches below the surface and  s i m i l a r l y high values were obtained i n the f i e l d :  the average  observed at 6 inches depth on north-facing slopes was 79<>9  0  t h e south-facing p r o f i l e s :  temperature 8 5 , 2 ° on  readings of over 90° were common i n the f i r s t  part of July, when the mean a i r temperature  registered 95°•  Such extreme  heating w i l l obviously e f f e c t the s o i l moisture c o n t e n t and the graph shows t h a t t h i s declines sharply, following the period of maximum temperatures. The cold winters, with p r e v a i l i n g l i g h t snow cover, enable the recharge of s o i l moisture t o begin b e f o r e the spring thaw and t h i s process, expectably, r e a c h e s i t s peak during the spring r a i n f a l l maximum„  The f a c t that the  ^Temperature data, U, S. Weather Bureau, 1964-5J moisture data, courtesy Mr, E, Dowding, Department of Agriculture, University of Wyoming, Laramie.  43 presence of snow cover enables recharge t o begin before the period of greatest r a i n f a l l i s important, f o r the p r e c i p i t a t i o n w i l l f a l l on s o i l with f a i r l y high moisture content and, consequently, lowered  infiltration  capacity and perhaps lesser strength.  Now the Archer station i s s i t e d on an exposed, f l a t area with the r e s u l t that blown snow i s u n l i k e l y t o accumulate t o any depth: there i s a perceptible months„  even so,  increase i n the s o i l moisture during the winter  In areas of i r r e g u l a r topography, such as the valleys studied,  the e f f e c t of d r i f t i n g i s l i k e l y t o be a highly s i g n i f i c a n t f a c t o r i n determining the degree of winter recharge.  1  During the months of December,  January and February over the period 1949-1954, winds blew from the northwest, west and southwest f o r 78.6$ of the time, with average speeds i n the region of 17 m.p.h. (U. S. Weather Bureau, 1956) which indicates that the winds from the west are dominant during the winter months.  Drifting is  therefore l i k e l y t o occur on the eastern side of any obstacle:  winds from  due west were most common (40$) but there i s l i t t l e difference i n the f r e quency of occurrence of those from north- and southwest respectively).  (18.9$ and 19.7$>  However, although d r i f t s may form on the eastern sides of  a l l obstac3.es, those with a southerly aspect are l i k e l y to melt more r a p i d l y than those sheltered i n north-facing locations.  The l i k e l i h o o d of  d r i f t s p e r s i s t i n g and allowing considerable recharge of s o i l moisture would, therefore, be greater on the western edge of north-facing meanders than in. the comparable s i t u a t i o n f o r south-facing bends.  The  importance  of t h i s consideration w i l l be more f u l l y discussed below.  Possibly as a r e s u l t of the t h i n snow cover, the change i n s o i l ^-The author i s indebted t o Mr. S„ B. Gutcalt, Department of Geography, U.B.C., f o r t h i s observation.  kk moisture observed at the Archer station over the two year period was small —  less than one inch i n the top 12 inches of s o i l —  ence was,  but a further i n f l u -  i n a l l p r o b a b i l i t y , the low moisture holding capacity of the s o i l  i t s e l f , indicated by the low p a s t i c i t y and low clay and s i l t content.  The  moisture holding capacity of any s o i l i s closely related to the saturated pore-water pressure and i s probably of more importance i n determining both the degree and nature of s o i l movement than i s the i n f i l t r a t i o n rate, per se, as saturated s o i l s , p a r t i c u l a r l y those of moderate t o high p l a s t i c i t y , w i l l move by creep f a r more r e a d i l y than w i l l well-drained ones. The importance of the manner i n which a saturated surface layer of s o i l w i l l behave i s therefore c l e a r .  One measure of the moisture con-  tent i s the saturated e l e c t r i c a l resistance —  the lower the value, the  greater the absolute amount of water held by the s o i l at i t s saturation point —  and f i e l d t e s t s were therefore carried out i n order to determine  how t h i s quality varied on slopes of d i f f e r i n g angle and aspect. The procedure followed was simple:  a s o i l probe was  inserted  p a r a l l e l to the ground surface on the u p h i l l side of a trench 6 inches deep, which was then f i l l e d i n . Water was added t o the surface and continuous readings of the e l e c t r i c a l resistance were made u n t i l these s e t t l e d t o a steady value:  more water was then added and i f , after a  time, there was no d e c l i n e . i n the resistance, t h i s value was taken to represent saturated conditions.  If the readings of resistance continued to  decline, the procedure was continued u n t i l a steady minimal value was obtained.  As these tests were carried out i n the height of the Wyoming  summer, a l l the s o i l s were extremely dry and required the addition of at least a gallon of water, over a small area, t o b r i n g them to saturation: i t i s improbable, therefore, that t h i s state i s ever reached under natural  Facing page - 4 5  X  3a  X X X  X X X  a*  X V X  X  X  x  ft  >  X  X  X  x  "  • "  X X  X X  X X  Sbo Sa-feraVe e/  2oo  FIGURE 11:15 -  N =  i  5,Ooo  1,000  6.1ecrhr Ica I r e s ijta.nce  >  ohms-  Saturated s o i l resistance, Ogallala, north-facing p r o f i l e s .  27  X s. 1,400 oKrv  *  s•  X  If X  t  X X X X  x  X  X  3  X  X  *  t  X  <  : X  Xx  it  X  1  '  X  X• X  1  Saturi+ad  FIGURE I I : l 6  -  fcltctr!  cal  res i  stance.,  oh>v\s  Saturated s o i l resistance, Ogallala, south-facing p r o f i l e s .  10,000  45 conditions during t h e summer months, but i t may be a t t a i n e d , b r i e f l y during t h e spring, p a r t i c u l a r l y on t h e s i t e s o f snow d r i f t s and t h i s i s probably t h e period when most s o i l movement by creep occurs. Figures 11:15 and l 6 show the d i s t r i b u t i o n of the values of saturated e l e c t r i c a l resistance of the upper s o i l on a s e l e c t i o n of northand south-facing slopes. The data from the south-facing p r o f i l e s cannot be said t o show any r e a l trend:  resistances at a l l angles tend t o c l u s t e r around 1 , 0 0 0  ohms, with a mean value of 1 , 4 0 0 ohms and a median value of 1 , 0 5 0 .  The  sample from the north-facing slopes, on the other hand, does appear t o possess a non-random component, with the highest values of saturated resistance and, therefore, the lowest actual water content clustered i n the region of 1 7 ° .  A one-way analysis of variance was therefore c a r r i e d out on  the 29 observations, which were divided into 5 classes:  the highest class  mean, 3*788 ohms, i s found i n the range 14.5 - 19<>4 j the lowest, 9&3 ohms, 0  in the class below 9 . 4 ° :  the difference between the two classes just f a i l s  to be s i g n i f i c a n t at the 95$ level . 1  There i s , therefore, no clear evidence  i  of a systematic v a r i a t i o n i n saturated s o i l resistance with angle of slope, but t h e r e i s some i n d i c a t i o n that the resistance increases with slope u n t i l the l a t t e r i s i n the region of 1 7 ° and t h e n declines.  I t i s suggested that  t h i s may have some connection with the observed pattern of s o i l movement on the north-facing slopes. Figure 11:17 shows the plot of 87 observations of small mass movement features made on north-facing slopes, against the sine of the angle o f ground slope. .438)  I t i s clear that, i n the region of 26° (sine =  a rather dramatic change i n the amount o f movement takes place.  change may, however, be explained i n physical terms, f o r the region  This  c Q  X  u y  V «*•  c  v.  X  x  -»  X  X X  %  X X  ;  V  X X X  0/ FIGURE 11:17  XX  -  !*A  X  X  0*2.  V  X  X XX X X X 3 :x xx K X XXX X X XX XX > X xx :xx#< ®K @ ^ X  0-3  or  4  anj/e. af~  Nl OS jr&u  n J  Depth of s o i l disturbance/sine of slope angle: Ogallala formation, Cheyenne area. Northfacing p r o f i l e s .  =  0-6  87  0-7  46 26 - 2 7 ° i s that of the angle of s l i d i n g f r i c t i o n (Melton,1964) which represents the lower angle of s t a b i l i t y f o r natural slopes (creep, of course can and does operate on slopes which have attained t h i s angle and i s a primary cause of t h e i r reduction below i t ) . If the observations are divided into two groups, one of those from slopes of less than 2 5 . 5 ° and another of those from slopes of more than 27°> with observations f a l l i n g between those values excluded, separate regression l i n e s may be f i t t e d .  two  These l i n e s are shown i n  Figure:l8, together with that f i t t e d to the observations from south-facing slopes„  Perhaps the most s t r i k i n g feature of Figure I I : l 8 i s the close p a r a l l e l l i s m of the trend f o r the south-facing slopes with that f o r the lower north-facing p r o f i l e s and the very pronounced departure exhibited by the t h i r d curve.  It would seem that the forces which would operate to move  the s o i l mantle on any slope l y i n g at more than 27° are, f o r some reason, only e f f e c t i v e on the north-facing p r o f i l e s :  either because the forces  themselves are increased, or the resistance to them lessened.  There would  seem to be no prima f a c i e reason why the i n s t a b i l i t y of north-facing slopes should be the greater:  one explanation might be that the sample of steep,  south-facing slopes was much smaller, but t h i s i s not the cases  there i s  no s i g n i f i c a n t difference between the absolute maximum angles of the  two  categories„ However, i f we review some of the evidence which has already been presented, concerning the differences i n slope characteristics  which seem  to be dependent upon aspect, i t i s possible to formulate a tentative hypothesis.  o  C3 W  N Sowth-f<xcCr.g  01  o I2.H  c U  c:  o)  •J=-3  53.2%  N o r f h - f cui*> rig  V  22.1*  (<2?-5°> North-fox inj  fD  r-  /  12.8%  1f  ( >27 0 ° )  «i S O  /  o  -ll c: «)  of  FIGURE lit18  a«o/e  of  ground s/ope  Estimated mean amounts of slow mass movements, S.E. Wyoming.  bl  i)  Snow d r i f t s are l i k e l y to "be deepest and to p e r s i s t longest i n sheltered s i t u a t i o n s with a northeasterly aspect:  s o i l moisture  i s , therefore, l i k e l y to be highest i n these locations, even before the a r r i v a l of the spring r a i n s , ii)  Evaporation from any north-facing slope w i l l be lower than from a comparable, south-facing one:  vegetation cover, as a conse-  quence, w i l l be more complete i n the former s i t u a t i o n .  In these  Wyoming v a l l e y s , north-facing slopes have, on average, 6% more vegetation than do the south-facing p r o f i l e s , a s i g n i f i c a n t difference. iii)  The e l e c t r i c a l resistance of saturated s o i l on north-facing p r o f i l e s does not appear to increase or decrease methodically with the angle of slope, but reaches a maximum at angles of about 17°.  S o i l s at greater angles are, therefore, capable of  holding greater amounts of moisture. Putting these three facts together, we may  postulate that,  whereas the s o i l on a steep south-facing slope w i l l merely be d r i e r , less well-vegetated and have approximately  the same, or possibly a lower satur-  ated resistance than that at a lower angle, the s i t u a t i o n on a north-facing p r o f i l e i s quite d i f f e r e n t .  Let us suppose that a cutbank i s formed by a  stream impinging against a north-facing p r o f i l e :  the curve of the bank  w i l l afford a suitable s i t e f o r the development of a snow d r i f t i n the following winter, however small, and the presence of t h i s d r i f t w i l l increase the moisture of the underlying s o i l :  however, i t w i l l also, i f  the bank i s s t i l l at a low angle, increase the l i k e l i h o o d of a f i r m veget a t i o n cover developing.  I f , however, the cutbank continues to grow and  to increase i n angle, the size of the winter d r i f t i s also l i k e l y to increase; but as the slope steepens, not only w i l l the degree of vegetation  48 cover f a l l but, at angles greater than 17°* "the amount of water i n the s o i l , when, saturated, w i l l increase.  This r i s e i n moisture content of  the s o i l represents an increase i n the void r a t i o under unconfined f a i l u r e (Terzaghi and Peck, 1948; p. 82).  shearing  Therefore, by the time the slope  attains the angle of s l i d i n g f r i c t i o n , not only w i l l the available moisture i n the environment be comparatively high, but the mechanical r e s i s t i n g capacity of both s o i l and vegetation w i l l be low. It i s suggested that i t i s t h i s sequence of events, or something very s i m i l a r , which not only accounts f o r the observed increase of s o i l movement on north-facing slopes but which i s a prime f a c t o r i n the development of the asymmetry t y p i c a l of these v a l l e y s (see III s i ) .  lis4 a)  Vegetation and Microclimate Manitoba The greater part of the three valleys studied i s covered by  rough, long-grass pasture, but thickets of small willows ( S a l i x ) are found on some of the north-facing slopes and also on the meander s c r o l l s .  Mean  vegetation cover i s i n the region of 70$ and the north-facing slopes are s i g n i f i c a n t l y better vegetated than the opposing p r o f i l e s , both with respect t o the maximum angle section and the. slope as a whole.  This i s  undoubtedly a major f a c t o r governing s o i l moisture and, as stated above, i t i s the north-facing p r o f i l e s which possess the moister s o i l s :  the pro-  portion of vegetation cover i s also presumed t o influence the lower, l i m i t i n g angle of s o i l movement. The agriculture of the area i s one of mixed farming, but there i s l i t t l e c u l t i v a t i o n of either the f l o o r s or the sides of these v a l l e y s . The importance of grazing stock i n aiding downslope movement of s o i l i s undoubtedly great.  k-9 b)  Wyoming This region i s also primarily grass-covered, although the  vegetation i s f a r less lush than i n Manitoba, and small c a c t i , notably p r i c k l y pear (Opuntia) are common on the northern slopes and the i n t e r f l u v e s . There are no trees i n any of the v a l l e y s studied, but the steeper slopes, apparently regardless of t h e i r aspect, are frequently covered by a dense scrub of mountain mahoghany (Cercocarpus  sp.) and poison oak (Rhus sp.).  l o c u l t i v a t i o n i s carried out i n t h i s area, but there i s extensive ranching of both cattle and sheep and, again, the treading of these  animals  must be accounted of some significance i n aiding s o i l movement.  The average proportion of vegetation cover i s roughly 50$ and the degree of difference between north- and south-facing slopes varies according to the category of v a l l e y s .  In those without a true stream channel the  north-facing slopes are the b e t t e r vegetated (by 3 $ ) , but the cross-valley differences are less pronounced than i n the v a l l e y s with well-defined, ephemeral stream channels  (difference:  7$).  The o v e r a l l vegetation cover  in the l a t t e r group of v a l l e y s i s however, less complete, owing to the substantial area of n e a r - v e r t i c a l and, therefore, bare r i v e r - c l i f f s . Both the degree of vegetation cover and the angle of slope are d i r e c t l y r e f l e c t e d i n the values of s o i l temperature, i n addition to the aspect of the p r o f i l e :  these temperatures represent at-a-point observations  taken v i r t u a l l y simultaneously on the maximum angle sections of both v a l l e y sides.  The temperatures recorded f o r the north-facing slopes i n both groups  of v a l l e y s were s i g n i f i c a n t l y lower than those from the south-facing profiles:  by -k«k°  i n those with channels and by -6.2°  i n those without.  actual values obtained i n the l a t t e r group of v a l l e y s were noticeably higher, presumably because the slopes are gentler and l i e more nearly  The  50  normal to the sun's rays, with the r e s u l t that the s l i g h t l y increased vegetation cover i s i n s u f f i c i e n t to prevent extreme heating. A strong suggestion that the s i g n i f i c a n t differences i n vegetation cover between north- and south-facing p r o f i l e s i s due to microclimatic e f f e c t s , comes from the observed differences i n i n t e n s i t y of evaporation, as measured by standard black B e l l a n i plate atmometers.  Readings were made  f o r a period of three hours i n each v a l l e y , during the middle of the  day.  The observations therefore represent the time, both of day and of year, when the sun's rays are most nearly v e r t i c a l .  Any difference i n rates of  evaporation can thus be taken as a minimum, f o r the more oblique the angle of incidence, the greater the r e l a t i v e amount of i s o l a t i o n received by the south-facing slopes.  The mean hourly-rate of evaporation observed on the  north-facing p r o f i l e s was 6.22 0.55  cc./hour greater;  nificant.  cc. and that f o r the opposing slopes  t h i s difference was  was  found to be s t a t i s t i c a l l y  However s l i g h t the differences i n humidity,  sig-  i n general terms,  i t seems clear that the south-facing slopes are the d r i e r , as i n Manitoba, although the evidence  i n the case of the Wyoming v a l l e y s i s rather more  direct.  II;5  Summary In Manitoba, studies of slope form were carried out i n three,  east-trending v a l l e y s with intermittent streams, flowing i n a r e l a t i v e l y homogenous cover of sandy t i l l , at an a l t i t u d e of approximately  1,600  feet.  The v a l l e y s have been formed within the l a s t 1 2 , 0 0 0 years and no traces of the Pliocene slope forms can have been preserved.  The climate of the area  i s generally cool, with severe winters and marked spring and summer prec i p i t a t i o n maxima.  The s o i l cover i s generally complete and i s highly  p l a s t i c i n nature; as a r e s u l t , amounts of s o i l movement are f a i r l y  Facing page - 51  Table VIII  COMPARATIVE MAGNITUDES OF STORMS OF VARIOUS DURATIONS AND RETURN PERIODS, S.W. MANITOBA & S.E. WYOMING  STORM  BOISSEVAIN AREA  CHEYENNE AREA  30 minute storm:1 10 50 100  year year year year  0.6 1.25 1.7 1.85  inch inch inch inch  0.5 inch 1.1 inch 1.5 inch 1.75 inch  60 minute . storm :1 10 50 100  year year year year  0.75 inch 1.6 inch 2 . 1 inch 2 . 3 inch  0.6 1.45 1.75 2.2  inch inch inch inch  1.5 inch 3.15 inch 4 . 2 inch 4 . 7 inch  1.45 2.9 3.9 4.0  inch inch inch inch  24 hour storm:1 10 50 100  year year year year  (Data from U. S. Weather Bureau: R a i n f a l l Frequency Atlas of the United States. Technical Paper No. 40, Washington, 1961.)  51 considerable, p a r t i c u l a r l y on the steeper of the north-facing p r o f i l e s , which are moister and have a more complete cover of vegetation. In Wyoming, three classes of v a l l e y s were investigated: those with east-flowing, ephemeral streams; those trending east, but lacking well-defined channels; and those with south-flowing, ephemeral streams. A l l streams are well incised i n the Ggallala formation, which i s of rather complex l i t h o l o g y , but i s generally represented by a sandy conglomerate. Terraces are preserved along most of the major v a l l e y s and the nature of the development of the drainage network has been such that the majority of the upper v a l l e y sides are not d i r e c t l y t r i b u t a r y t o the main streams.  A  maximum date of 8 , 0 0 0 years can be given f o r the development of the present v a l l e y forms.  The temperature regime i n the Cheyenne area i s e s s e n t i a l l y similar t o that around Boissevain, despite the f a c t that the former region l i e s at a height of 6 , 0 0 0 feet, but the p r e c i p i t a t i o n regime, with a single, spring maximum, coupled with higher mean annual temperatures, rather than a sub-humid climate.  r e s u l t s i n semi-arid,  Surprisingly, as Table VIII shows, the  lower amounts of p r e c i p i t a t i o n received i n the Cheyenne area are also associated with s l i g h t l y lower i n t e n s i t i e s of storms, although i t i s possible that, f o r durations of under 30 minutes, t h i s may be reversed. The s o i l s of the Wyoming study area are only s l i g h t l y p l a s t i c and the e l e c t r i c a l resistance of dry s o i l i s very high indeed:  when saturated,  t h e i r resistance i s lowered and there appears t o be a possible r e l a t i o n between the r e l a t i v e resistance of saturated s o i l s at d i f f e r e n t angles on the north-facing slopes and the observed increase i n amount of s o i l movement on those p r o f i l e s above the angle of s l i d i n g f r i c t i o n .  The increase  52 i n s o i l moisture i n these situations i s probably related t o the d i s t r i b u t i o n of winter snow d r i f t s .  Lower slopes show small and similar amounts of  creep movement, independent of t h e i r aspect.  Vegetation cover i s generally poor and i s less complete on south-facing p r o f i l e s , presumably because of more intense evaporation.  CHAPTER I I I .  VARIATION IN SLOPE FORM AND RELATED FEATURES  This chapter describes the r e s u l t s of the various  discriminatory  analyses employed t o determine the pattern of v a r i a t i o n of the morphometric variables. 111:1 a)  Maximum Angles Manitoba Table IX the mean valueB and the e f f e c t s of the two controls f o r  the entire sample: Table IX ~  each c e l l represents the mean of 25 observations.  Cross-stream and cross-valley e f f e c t s , maximum angles; Manitoba.  1  2  North-facing  South-facing  Mean  Effects  A  Stream  towards  24.1°  19.0°  21.55°  •I- 3.95°  B  Stream  away  14.2°  13.5°  13.85°  - 3.95°  Means  19.15°  16.25°  + 1.55°  - 1.55°  Effects  An analysis of variance  X = 17o6° N = 100  (see Appendix C s l ) shows that the i n t e r -  action of column and row e f f e c t s i s i n s i g n i f i c a n t ; i . e . , the cross-stream and cross-valley variations i n maximum angle are additive.  Both sets of  controls have a s i g n i f i c a n t e f f e c t upon the means, though the cross-stream influence, of  7.9°>  Is the more s i g n i f i c a n t and twice as great as that  54  produced by the cross-valley factor ( 3 » 1 ° ) . b)  Wyoming (i)  East-flowing,  ephemeral streams  The i n i t i a l analysis of variance (see Appendix C s l ) was carried out on exactly the same classes of slopes as i n Manitoba, and the mean values and e f f e c t s of the two p r i n c i p a l controls are shown i n Table X: each c e l l mean represents 48 observations.  Table X '  Cross-stream and cross-valley e f f e c t s , maximum angles; major factors only, Wyoming ( i ) . 1  2  North-facing  South-facing  Mean  Effects  A  Stream  towards  46.01°  41.78°  43.9°  +13.85°  B  Stream  away  17.01°  15.40°  16.2°  -13.85°  Means  31.51°  28.59°  Effects  + 1.46°  -  1.46°  X = 30.05°  N = 192  Ih t h i s case, although the e f f e c t s due t o the p o s i t i o n of the stream are highly s i g n i f i c a n t (p > 99%), those due t o aspect are judged t o be i n s i g n i f i c a n t at the 95$ l e v e l .  The power of the t e s t (/S ) t o detect  the mean cross-valley difference of 2 . 9 2 ° was therefore  calculated, using  the Pearson and Harley curves (1951) and found t o be only 0 . 4 0 :  this  indicates that such a difference would be detected only 40$ of the time. difference of 6 . 5 5 ° * on the other hand, would have an 80$ p r o b a b i l i t y of detection.  It i s impossible t o say, from the available evidence at t h i s stage, whether there i s a true cross-valley asymmetry i n these v a l l e y s . However, i t i s clear that the mean difference r e s u l t i n g from v a r i a t i o n i n  A  55 aspect i s considerably smaller than that produced by the cross-stream controls. The analysis shown i n Table X included a l l p r o f i l e s measured i n t h i s class of east-trending v a l l e y s , but i t was thought t o be of interest t o examine the v a r i a t i o n produced d i r e c t l y at and opposite the apex of a meander bend:  the maximum angles of p r o f i l e s l A i i , 2 B i i , 2 A i i  and I B i i were therefore tested separately, as shown i n Table XI. Each c e l l represents the mean of 16  Table XI  observations.  Cross-stream and cross-valley e f f e c t s , maximum angles: at and opposite meander bend, Wyoming ( i ) . Means  2  1  Effects  Ai i  59.53°  40.69°  50.11°  + 16.67°  B i i  17.44°  16.09°  16.77°  -16.67°  Means  38.49°  28.39°  + 5.05°  -5.05°  X =  Effects  33.44°  N = 64  The analysis of variance (see Appendix C : l ) shows that, i n t h i s case, the i n t e r a c t i o n of cross-stream cant (p -  95  y  97°5$).  and cross-valley e f f e c t s Is s i g n i f i -  This i s highly unusual and of great importance,  for i t implies that straightforward, additive r e l a t i o n s h i p of microclimatic and stream influences disappears  at the meander bends.  In p a r t i c u l a r , the  t o t a l v a r i a t i o n produced i n position l A i i i s f a r greater than would be expected.  This i s clear evidence of a ' c a t a l y t i c  1  r e l a t i o n s h i p between  slope and stream.  To investigate more f u l l y the nature of t h i s i n t e r a c t i o n , a complete analysis of variance was carried out which allowed the evaluation  56  of the e f f e c t s produced by positions around the meander bends, i n addition to those of the two, p r i n c i p a l controls (see Appendix C s l ) .  This analysis  demonstrated an o v e r a l l significance of the i n t e r a c t i o n of aspect, stream p o s i t i o n and l o c a t i o n around meanders and so the 12 mean values were tested for s i g n i f i c a n t , pair-wise differences using Duncan's test (see I : 4 b ) „  The s i g n i f i c a n t value of the i n t e r a c t i o n term i s produced primarily by the extreme oversteepening of the maximum angles of those north-facing slopes at the apex of a meander bend;  the mean value f o r the  l A i i p r o f i l e s , 59«53°i d i f f e r s s i g n i f i c a n t l y from a l l other means at the 95$ protection l e v e l .  In other words, the average absolute maximum angle  i n s i t u a t i o n l A i i i s not only s i g n i f i c a n t l y steeper than at any position along the concave bank of the south-facing meanders, but also than that of the adjacent, north-facing p r o f i l e s . the 6 means from the undercut slopes.  Table X I I shows the ranked order of I t i s noticeable that the north-  f a c i n g p r o f i l e s are not uniformly steeper, another source of interaction, Table XII ~  Ranked mean absolute maximum angles, undercut p r o f i l e s , Wyoming.  lAii  2Ai  lAlil  2Aiii  2Ali  59<.53°  43.75°  41.38°  40.91°  40.69°  lAi 37-13°  and i n f a c t the lowest of the 6 mean values, f u l l y 22° less steep than that of the c e n t r a l , north-facing p r o f i l e s , i s from the category of slopes only 50 feet upstream. C l e a r l y there i s a difference i n the sequence of maximum angles developed around meanders with d i f f e r e n t aspects.  The north-facing slopes  appear t o be very sharply steepened at that point where the apex of the meander actually impinges upon the v a l l e y sides, but the maximum angle so  formed does not r e t a i n i t s steepness over any distance, nor, i t may  be  presumed, f o r any length of time, but declines markedly i n the up-valley direction.  No such tendency i s observable i n the case of the south-facing  undercut slopes:  the p r o f i l e s i n a l l three situations around the meander  bends maintain similar maximum angles.  The immediate inference i s that the  form of the cutbank and therefore the curve of the meander, must very according to the aspect of the bend.  Figure III s i shows the portion of the Goose Creek v a l l e y from which a sample was  collected:  i t i s clear that, i n t h i s case, the ampli-  tude of those meanders which swing northwards Is considerably wider than  Figure I I I s l  Section of Goose Creek v a l l e y . (Simplified from U. S. Geological Survey 1:24,000 map, Emkay Quadrangle.)  those which cut against the southern v a l l e y sides and similar forms are found i n the f i v e other east-trending v a l l e y s .  It i s suggest that an  explanation of t h i s difference i n meander form and of the steepness of the adjacent slopes, i s to be found i n the persistence of snow d r i f t s on slopes with a northeasterly aspect. The i n i t i a l undercutting of a north-facing slope w i l l create a steepened section which w i l l be r e l a t i v e l y protected from d i r e c t insolation and which w i l l , therefore, be better able to r e t a i n a moist s o i l cover.  58  The accumulation of d r i f t e d snow along the meander scar w i l l s t i l l further r a i s e the s o i l moisture content, with the probable r e s u l t that bank-cutting during the period of spring stream-flow w i l l be f a c i l i t a t e d .  However,  although very steep cutbanks can be maintained at the apex of bends, the steepened slopes with t h e i r lowered vegetation cover and moist s o i l s must be extremely l i a b l e t o small s l i p s and t o creep (no evidence of major s l i d e s was observed).  It i s suggested that even as the central p r o f i l e at  a north-facing meander i s a t t a i n i n g i t s maximum angle, the slope immediately upstream (which represents the former position of the apex of the bend, or the point of greatest erosion) w i l l be r a p i d l y degraded by small mass movements.  The very i n t e n s i t y of the disturbance i n the equilibrium slope  form ensures that the over-steepened maximum angle sections are short-lived, at least i n space and probably also i n time.  This hypothesis, which would account f o r the i n t e r a c t i o n of cross-stream and cross-valley e f f e c t s , i s supported not only by the evidence of the sequence of maximum angles themselves and the amplitudes of the meander bends, but t o some extent by the nature of the stream channels (see below) and of evaporation rates.  In addition, such a theory would provide  a s a t i s f a c t o r y explanation f o r the increased depths of s o i l movement on north-facing slopes above 27° and the absence of t h i s increase from the south-facing p r o f i l e s . It has been pointed out that the relaxation time of the absolute maximum angle section i s r e l a t i v e l y short.  It i s of i n t e r e s t , therefore,  to consider the pattern of v a r i a t i o n i n the Strahler maximum angle around the meander bends, f o r t h i s value w i l l be more representative of the less ephemeral changes i n slope form.  These values were therefore computed f o r  the undercut p r o f i l e s and the mean variations tested by an analysis of  59 variance (see Appendix C I l ) .  This analysis also showed that there i s a  s i g n i f i c a n t i n t e r a c t i o n between aspect, stream p o s i t i o n and s i t u a t i o n around the meander bend?  as the Strahler angle i s geometrically d i s t i n c t from the  absolute maximum angle, the suggestion that the pattern of steepening observed i n the l a t t e r i s not r e s t r i c t e d to the r i v e r - c l i f f , but that i t s e f f e c t s are propagated u p ~ p r o f l i e , i s i n e v i t a b l e . Table XIII shows the ranked means of the 6 undercut p r o f i l e s , plus that of the steepest of the s l i p - o f f slopes.  Those means which are underlined by the same l i n e do not  d i f f e r s i g n i f i c a n t l y from each other at the 95$ protection l e v e l . Table XIII  a  )  Ranked mean Strahler maximum angles, undercut p r o f i l e s , Wyoming.  1A11  lAili  50.1°  37»3°  b)  2Aii 3^.9°  2Ai  2Aiii  lAi  33.8°  33.2°  30.9°  3311 17.4°  . c)  The source of the s i g n i f i c a n t i n t e r a c t i o n i s two-fold:  first,  the great difference between the mean Strahler angles of north-facing prof i l e s i i and i j and, second, the fact that the l a t t e r Is s t a t i s t i c a l l y indistinguishable from the steepest of the s l i p - o f f categories.  Clearly,  on these north-facing slopes, the r e s u l t of over-steepening associated with basal corrasion i s a very rapid r e s t o r a t i o n of the  ' c h a r a c t e r i s t i c ' angle  of the constant  On the  slope section of the v a l l e y side.  south-facing  p r o f i l e s , on the other hand, there i s no s i g n i f i c a n t difference i n the-mean values of the Strahler maximum angle attained at any point around the meander bend and i t i s clear that the large meander amplitude i s associated with uniform constant  slopes, whose angles are roughly intermediate between  the extremes found on the north-facing v a l l e y sides.  60  It would appear that meander amplitude,  i n these v a l l e y s at  l e a s t , cannot be considered as s o l e l y a function of discharge, just as the steepest sections of the slope p r o f i l e s are not simply r e l a t e d t o the addition of cross-stream  and cross-valley influences.  I t i s u n l i k e l y that  t h i s i s a chance association.  (ii)  East-trending, channel-less v a l l e y s The mean difference i n maximum angle (which i n t h i s case i s  i d e n t i c a l t o the Strahler maximum) i s only 1.95° between north-facing (15.05°) and south-facing (13.1.0°) slopes.  This difference f a i l s t o be  judged s i g n i f i c a n t at the 95$ l e v e l when tested by a paired Student's ' t ' test.  The power of the t e s t , f o r t h i s difference, i s however only 0.35*  from the Pearson and Hartley curves (1951) and the cross-valley v a r i a t i o n would have t o be i n the region of 3.6° before the p r o b a b i l i t y of i t s detection would r i s e t o 8C$„ It i s , therefore, possible that the north-facing slopes i n these v a l l e y s are, i n r e a l i t y , steeper than the south-facing p r o f i l e s , but the evidence concerning the significance of the observed mean difference i s inconclusive. It should be noted that the values of the maximum angles i n these v a l l e y s correspond  closely t o those f o r the s l i p - o f f p r o f i l e s i n those east-  trending v a l l e y s with stream channels;  the mean of the north-facing pro-  f i l e s being 1 7 . 0 1 ° , i n the l a t t e r group, as compared with a mean of 1 5 . 4 ° for the south-facing slopes.  Duncan's t e s t f a i l e d t o reveal any s i g n i f i -  cant difference between these two mean values, although the power of the test t o detect a v a r i a t i o n of 1 . 6 l ° i s 0 . 4 8 (Pearson and Hartley, 195l)« A difference of only 2.3° would have an 80$ p r o b a b i l i t y of being detected.  6l There i s , t h e n , a c l o s e s i m i l a r i t y b o t h i n t h e a b s o l u t e v a l u e s t h e maximum angle i n t h e c h a n n e l - l e s s v a l l e y s o f t h o s e w i t h stream c o u r s e s ,  t h e presence  (iii)  I t i s c l e a r t h a t s t r o n g l y marked,  i n p r o f i l e s t e e p n e s s can o n l y d e v e l o p ,  slopes cross-  i n t h i s area,  in  of an a c t i v e l y u n d e r c u t t i n g s t r e a m .  S o u t h - f l o w i n g , ephemeral An a n a l y s i s  that,  profiles  and i n t h e degree o f d i f f e r e n c e between  o f n o r t h e r n and s o u t h e r n a s p e c t . valley differences  and on t h e s l i p - o f f  of  of variance  ID. t h i s e a s e , t o o , t h e r e  T a b l e XI¥  streams  (see T a b l e X I ? and A p p e n d i x C : l )  shows  Is a s i g n i f i c a n t i n t e r a c t i o n between  cross-  C r o s s - s t r e a m and c r o s s - v a l l e y e f f e c t s , maximum a n g l e s : Wyoming ( i i i ) West-facing  Stream  towards  n : 1 3 25„2*°  Stream  away  n:13  l 6  East-facing  Means  Effects  o  29.3°  + 6.6°  3 i 6°  16.1°  -6.6°  n:13  „6°  n ? 1  3 3 o 2  5 o  Means  21.0°  2h.k°  Effects  -1.7°  + 1.7°  stream and c r o s s - v a l l e y  N = 52  X = 22.7°  e f f e c t s w h i c h a r i s e s from t h e f a c t t h a t ,  whereas  the s t e e p e r undercut s l o p e s a r e t h o s e which f a c e e a s t , i t i s t h e w e s t f a c i n g s l i p - o f f p r o f i l e s w h i c h have h i g h e r a n g l e s . produce s i g n i f i c a n t d i f f e r e n c e s environment, but d i f f e r e n t  T h i s r e v e r s a l does n o t  between s l o p e s o f s i m i l a r  aspect.  The o n l y s i g n i f i c a n t v a r i a t i o n s  mean maximum a n g l e a r e t h o s e produced b y t h e c r o s s - s t r e a m  111:2  erosional in  controls.  Mean A n g l e s  (NOTE: c h a p t e r employ two  Unless otherwise  s t a t e d , the remaining analyses  " p a i r e d ' and one ' s t a n d a r d " S t u d e n t ' s  't'  in this  tests,  62  arranged as shown i n Table XV,  East- and west-facing should be substituted  for north and south, f o r the south-trending v a l l e y s ,  A single, 'paired,'  test was employed f o r the data from the channel-less v a l l e y s . )  Table XV D^  Arrangement of ' t ' tests  =  (North-facing, stream t o - South-facing stream f r o ) / N  T>2 -  (South-facing, stream t o - North-facing stream f r o ) / N or: D  1  =  (1A - 2B)  D  2  «  (2A - IB) / N  / S  D l and D2 estimate mean cross-stream e f f e c t s (Dl - D2) / 2 estimates mean cross-valley e f f e c t a)  Manitoba The four mean values of the mean angle, f o r each environment, are  shown i n Table XVI: Table XVI  each represents 25 observations.  Differences i n mean angles, Manitoba  1A  : 12.4°  2B  :  2A  : 10,8°  2B  : 5o8°  (Dl - D2)  /2  4.9°  Dl -  + 7.5°  D2  + 5,0°  a  - + 1.25°  Both the cross-stream and the cross-valley differences are judged to be s i g n i f i c a n t and the r e l a t i v e size of the e f f e c t s produced by both controls are comparable t o those i n the maximum angles.  I t seems that the  joint influences of microclimate and l o c a l erosional environment extend systematically over the complete v a l l e y side, i n t h i s area, although t h e i r effects become less pronounced when the whole p r o f i l e , rather than i t s steepest section, i s considered.  63 b)  Wyoming (i)  East-flowing, ephemeral streams This data was tested by an analysis of variance (see Appendix C:  m)  i n order t o f a c i l i t a t e comparison with the absolute and Strahler maxi-  mum  angles.  The basic 2 x 2  d i v i s i o n of the analysis i s shown i n  Table XVII, i n which each c e l l represents the mean of 48 observations.  Table XVII ~*  Cross-stream and cross-valley e f f e c t s , mean angles, Wyoming ( i ) .  1  2  A  19.86°  18.26°  19.06°  +4.1°  B  11.81°  9.92°  10.86°  -4.1°  15.83°  14.09°  + 0.87  -0.87°  Means Effects  0  Means  Effects  X = 14.96°  N=  192  This analysis shows tjhat the i n t e r a c t i o n of the two p r i n c i p a l f a c t o r s , both with each other and with position around the meander bend, is insignificant.  The e f f e c t s of cross-stream and cross-valley controls  may therefore be tested d i r e c t l y and both are found t o be highly s i g n i f i cant.  It i s s u r p r i s i n g that the cross-valley e f f e c t s emerges so strongly,  since the north-facing slopes are, on average, only 1.74° south-facing p r o f i l e s .  steeper than the  This e f f e c t can, however, be traced t o i t s source  when the 12 i n d i v i d u a l means are examined by Duncan's t e s t :  the only case  i n which the north-facing p r o f i l e s prove t o be s i g n i f i c a n t l y steeper i s i n the category l A i i , or at the apex of the meander bends.  That the  average  mean angle i n t h i s p o s i t i o n i s so high (22.7°) i s undoubtedly due t o the very substantial proportion of the t o t a l slope occupied by the r i v e r - c l i f f j the value of the mean angle i s related geometrically to that of the maximum angle i n a way that the Strahler maximum angle i s not, f o r the l a s t  64 mentioned index i s , physically, quite d i s t i n c t from the cutbank i t s e l f . It i s clear that the importance of the d i r e c t conjunction of an active stream and a north-facing slope as a source of 'positive feedback extends beyond the r i v e r - c l i f f the  itself.  1  The analysis of the v a r i a t i o n of  mean angles indicates that such i s the strength of t h i s interaction  that the form of the slope as a whole i s affected.  Table XVIII l i s t s the values f o r the three sets of slope angles —  absolute maximum, Strahler maximum and mean -- f o r the undercut p r o f i l e s Table XVIII  Characteristic slope angles, undercut p r o f i l e s , Wyoming ( i ) , Worth-facing  Angle  Profile:  i  ii  iii  Absolute maximum  37.1°  59.5°  41.4°  Strahler maximum  30.9°  50.1°  37.3°  Mean  18.9°  22.7°  18.0°  South-facing Angle  Profile ;  i  ii  iii  Absolute maximum  43,8°  40.7°  40.9°  Strahler maximum  33.8°  34.9°  33.2°  Mean  19.4°  18.3°  17.1°  of northern and southern aspect.  Clearly the mean values themselves  reduce as both the distance of the slope segment from the stream and i t s length, increase and, i n addition, the differences around the meander bend also decline.  65 (ii)  East-trending,  channel-less valleys  . The average value of the mean angle of north-facing p r o f i l e s i s 8.8° and of south-facing  slopes, f.h : 0  the mean difference of 1.3° i s  judged t o be s t a t i s t i c a l l y s i g n i f i c a n t . Undoubtedly the main factor which enables a difference of t h i s size t o be detected i s the low variance of the mean values. As i n the case of the maximum angles, both the average values of the mean angles i n these valleys and the differences due t o aspect are closely comparable t o those observed on the s l i p - o f f p r o f i l e s of the easttrending valleys with stream channels. It i s possible, then, for s i g n i f i c a n t differences i n slope steepness t o be produced by cross-valley influences alone, i n t h i s area, but t h e i r magnitude i s f a r less than that of those, more l o c a l i s e d , v a r i a tions r e s u l t i n g from the interaction of cross-stream and cross-valley controls. (iii)  South-flowing, ephemeral streams The cross-stream difference i n mean angles averages 6.0°, which  i s judged t o be highly s i g n i f i c a n t . The cross-valley v a r i a t i o n of 1.2° i s , on the other hand, i n s i g n i f i c a n t . Moreover, the d i r e c t i o n of the crossv a l l e y asymmetry i n the mean angles i s the reverse of that observed for the maximum angles.  Such a r e v e r s a l , i n the two most basic indices of  slope form, i s the clearest possible indication that there i s no e f f e c t i v e cross-valley difference i n microclimate i n these v a l l e y s .  III?3 a)  Other Variables R e f l e c t i n g Slope Geometry  Manitoba There are f i v e variables remaining i n t h i s category: the  66  height/length i n t e g r a l ; the p r o f i l e height; the p r o f i l e length; the length ($) of the lower concavity; the length ($) of the maximum angle section.  Table XIX l i s t s the mean values of these v a r i a b l e s , together with  the cross-stream and cross-valley d i f f e r e n c e s . Each mean represents 2 5 observations.  Table XXX Cross-stream and cross-valley differences, " ~ " ~ * g e o m e t r i c v a r i a b l e s , Manitoba. Erosional Environment  Integral  Profile Height  1A  58.9$  41.0*  224'  19.3$  2B  36.4$  39.1*  499'  65 0 9$  2A  59.7$  42.7  215"  23.9$  IB  41.2$  36.6'  434'  59.9$  9.6$  Dl  22.5$**  2„0  „ 275 ' * *  -46.6$**  4.3$  D2  18.5$**  -6.0'*  „ 219'**  -36.0$**  2.2$  _  - 5.3$**  1.05$  (Dl - D2)/2  H/L  2.0$  Profile Length  s  !  4.0'**  56'**  $ length Lower Cone.  $ length Max. 12.5$ 8.2$ 11.8$  The height/length i n t e g r a l , which, i t may be r e c a l l e d , represents the mean height of the p r o f i l e  i s p a r t i c u l a r l y , sensitive t o the p o s i -  t i o n of the steepest section of the slope, r e l a t i v e t o the stream.  It i s ,  therefore, scarcely s u r p r i s i n g that t h i s parameter i s influenced solely by l o c a l erosional environment.  The next three variables show a s i g n i f i c a n t  degree of response t o both sets of c o n t r o l l i n g f o r c e s :  the stream, however,  i s c l e a r l y the major influence over the v a r i a t i o n In the length of the lower concavity (as would be expected) and also as regards the length of slope as a whole.  The fact that the north-facing slopes are s i g n i f i c a n t l y the  shorter and the more c l o s e l y associated with the meandering streams does suggest that there i s a tendency, i n these v a l l e y s , f o r the stream t o be  6? positioned more towards the south.  This s i t u a t i o n i s that which i s  generally suggested t o occur as a r e s u l t of disproportionate production of debris on the south-facing p r o f i l e s , a suggestion which does not altogether agree with the observations made of s o i l movement phenomena. However, i t i s possible that there may be a greater volume of material moving on the lower south-facing slopes and also, that washing of loose surface  particles  during the summer thunderstorms may supply debris d i r e c t l y t o the stream, without leaving obvious Indications on the p r o f i l e .  b)  Wyoming The variables considered i n t h i s section include the height/  length i n t e g r a l , the p r o f i l e height, the p r o f i l e length and the length (absolute) of the maximum angle section. (i)  East-flowing, ephemeral streams The relavent information concerning these four variables i s  summarised i n Table XX: Table XX " Erosional Environment  each mean value represents 4B observations.  Cross-stream and cross-valley differences geometric v a r i a b l e s , Wyoming (i)„ H/L  Integral  Profile Height  Profile Length  Length Max, Angle  1A  63.5$  38.3'  130.1'  15.9'  2B  53.9$  38.5  s  229.8'  38.3'  2A  60.3$  51,1'  177.7'  16.1'  IB  54.3$  40.8'  202.4'  32.6'  Dl  9.6$**  -0.2'  -99.8'**  -22.3'**  D2  6.0$*  10,3'*  -24.8'  -16.5'**  1.8$  -5.2'  -37.5'*  (Dl--D2)/2|  -2,9  68  As In the case of the Manitohan v a l l e y s , the most s i g n i f i c a n t portion of the v a r i a t i o n i n the height/length i n t e g r a l i s controlled solely by the r e l a t i v e position of the stream, and t h i s i s also the case regarding the length of the maximum angle section, which l a t t e r variable i s s i g n i f i cantly greater on the s l i p - o f f p r o f i l e s . The pattern of v a r i a t i o n i n p r o f i l e height and length i s not quite so straightforward;  south-facing slopes, when undercut, are s i g n i -  f i c a n t l y higher than the north-facing p r o f i l e s , but the difference i n height of the two classes of v a l l e y sides does not appear to be uniform. Cn the other hand, both the undercut, north-facing p r o f i l e s and the whole class of north-facing slopes emerge as s i g n i f i c a n t l y shorter than the opposing v a l l e y sides.  This i s further evidence of the more d r a s t i c under-  cutting of north-facing p r o f i l e s , as a r e s u l t of t h e i r more humid microenvironment „ (ii)  East-trending, channel-less valleys The cross-valley differences i n mean values of the four variables  under review, are l i s t e d i n Table XXIJ Table XXI ~™ ~ Variable  each mean represents 28  observations.  Cross-valley differences, geometric v a r i a b l e s , Wyoming ( i i ) . Mean value:North-facing South-facing  Difference  H / L integral  49.2$  50.0$  0.8$  P r o f i l e height  44.1'  36.1'  7.6'**  P r o f i l e length  321.6'  288.5  34.9*  32.4'  Length max.  angle  ]  33.1' 2.5'  6  9  The only case of a s i g n i f i c a n t degree of cross-valley v a r i a t i o n i s that of p r o f i l e height, the north-facing slopes, on average, being some ,7.5,' feet higher.  This s i t u a t i o n i s the reverse of that i n the corre-  sponding set of v a l l e y s with ephemeral streams, where there i s some tendency f o r the south-facing slopes to be the  (iii)  higher.  South-flowing, ephemeral streams The cross-stream  Table XXII;  and cross-valley differences are shown i n  each mean represents 13  Table XXII  observations.  Cross-stream and cross-valley differences, geometric variables, Wyoming ( i i i ) . H/L  Profile Length  Length Max. Angle  Integral  Profile Height  E-f., A  60.7$  31.3'  103.4'  11.9'  W-fB  55.2$  34.8'  160.9'  39.8'  A  59.2$  38.2«  114.4'  22.0*  E-f., B  58.5$  19.8'  107.1'  14.7'  3.5'  -57.5'  Erosional Environment  W-f.,  Dl  5.5$  D2  0.6$  18.5'**  2.4$  -7„5'**  (Dl - D2) / 2  7.3' -32.4'  -27.9'** 7.2' -17.6'**  At f i r s t glance the cross-valley component of v a r i a t i o n appears t o be so strong that one i s l e d to wonder whether the r e j e c t i o n of the hypothesis of microclimatic differences in-these v a l l e y s was wise.  altogether  However, i f the cross-section i n Figure I I ; 7 i s r e c a l l e d , i t was  pointed out that these v a l l e y s , although they possess meandering stream courses, are also generally more deeply i n c i s e d on t h e i r eastern sides as a r e s u l t of the manner i n which the drainage network as a whole has  TO  developed,,  I t i s , therefore, f o r purely ' h i s t o r i c ' reasons that the west-  facing p r o f i l e s are s i g n i f i c a n t l y the higher and have the longer maximum angle sections.  From the above discussion i t i s clear that these valleys are not i d e a l as a control sample, since t h e i r present form does not r e s u l t s o l e l y from the behaviour of the streams within them, but has been influenced by the deep i n c i s i o n of the major, east-flowing streams.  I t should be noted,  however, that although some of the geometric variables are influenced by the l a t t e r set of circumstances, those r e l a t i n g most d i r e c t l y t o the mechanics of debris formation and removal — angles and the height/length i n t e g r a l —  namely, the maximum and mean  are apparently affected only by  the meandering of the south-flowing streams.  As our i n t e r e s t , i n t h i s  study, i s focused p r i n c i p a l l y upon the three factors named, i t i s maintained that t h i s set of v a l l e y s i s of value as a control.sample, although t o a more l i m i t e d extent than was o r i g i n a l l y anticipated.  III.4 a)  Hon-geometric Variables Relating t o Slope Form  Manitoba Table X X I I I - —  Gross-stream and cross-valley differences, non-geometric variables, Manitoba Average veg. %  Erosional Environment  Max. Angle veg. $  Soil Moisture $  Plastic. Index  Silt Index  1A.  70.4%  67.9$  19.0$  23.7  29.9  2B  74.0/o  65.9$  11.8$  19.9  27.0  2A  61.9$  63.0$  16.6$  21.7  32.9  IB  80.1$  72.0$  20.0$  19.4  34.3  Dl  -3 .6$ -18.256**  D2  (Bl -  D2)  / 2  7.3$**  2.0% -9.0$  7.2%** -3.4$ 5»3$**  3.8 -2.3 3.05**  2.9 -1.4 2.15  71 The means and differences are tabulated i n Table XXIII:  each  mean represents 25 observations. With the exception of the s i l t index, a l l these variables demonstrate a strong, cross-valley component of control, which i s generally greater, i n absolute terms, than the cross-stream v a r i a t i o n .  As these  variables represent the c h a r a c t e r i s t i c s of the s o i l and vegetation cover, t h i s i s scarcely unexpected, f o r It Is through such f a c t o r s , i f anywhere, that differences i n temperature and moisture regimes produced by the aspect of the slopes w i l l be manifested.  The f a c t that the north-facing slopes  have s i g n i f i c a n t l y moister and more p l a s t i c s o i l s which support a more complete vegetation cover would seem to be clear evidence that the microclimatic regime on these slopes i s more humid than that on the south-facing profiles.  b)  Wyoming There are only four variables i n t h i s section of the analysis:  the percentage vegetation cover of the whole slope and of the maximum angle section; and the temperature and e l e c t r i c a l resistance of the s o i l at a depth of 6 inches on the maximum angle section. (i)  East-flowing, ephemeral, streams The mean values and differences are l i s t e d i n Table  each  XXX?:  mean represents 48 observations. The pattern of differences i n these v a l l e y s i s c l e a r l y very similar to that i n Manitoba, i n that the north-facing slopes are better vegetated and t h e i r s o i l s are cooler (even i n a very hot summer).  What  should be noted, however, i s the f a r greater importance of cross-stream variations both i n absolute and r e l a t i v e terms, p a r t i c u l a r l y as f a r as the  72 Table XXIV  Cross-stream and cross-valley d i f f e r e n c e s , non-geometric variables, Wyoming ( i ) . Average •Veg. $  Erosional Environment  Max. Angle Veg. $  Soil Temperature  Soil Resistance  1A  43.4$  16.2$  71.2°  926,420 ohm  2B  53.9$  46.9$  78.3°  906,920 ohm  2A  37.5$  19.6$  75.8°  937,290 ohm  IB  62.3$  59.0$  75.9°  917,500 ohm  Dl  -10.5$**  -30.6$**  -7.1°**  19,500 ohm  D2  -24.8$**  -39.4$**  1„5°*  19,790 ohm  (Dl - D2) / 2  7.2$**  vegetation cover i s concerned.  -4.3°**  4.4$*  -145  ohm  The very low percentage of cover on the  undercut slopes i s obviously related to the importance of the steep cutbanks in these v a l l e y s . The values f o r s o i l resistance are not a very good index of v a r i a b i l i t y , f o r e l e c t r i c resistance, being a function of both s o i l temperature and s o i l moisture, was uniformly at the upper l i m i t of measurement. (ii)  East-trending, channel-less v a l l e y s Table XXV l i s t s the cross-valley variations i n the mean values:  each mean represents 28 observations. The pattern of variations i s e s s e n t i a l l y the same as that shown i n Table XXIV.  However, the differences i n vegetation cover, p a r t i c u l a r l y  on the maximum angle section, are considerably less than those i n the v a l l e y s with ephemeral stream channels. over-steepened  This i s because of the absence of  slope sections i n the channel-less v a l l e y s and the generally  low angle of t h e i r slopes as a whole.  The indications are that there i s  a true, cross-valley difference i n microclimate i n these v a l l e y s , but that,  73  i n the absence of active streams, i t s e f f e c t upon the proportion of vegetation  cover i s f a i r l y l i m i t e d .  Table XXV "  Cross-valley differences, non-geometric v a r i a b l e s , Wyoming ( i i ) .  Mean value.Difference lorth-facing South-facing  Variable  58.2$  54.6$  3.6'$*  Max. angle veg. f  55oC$  5 1 . 3$  3-.7$*  S o i l temperature  86.4°  92.6°  -6.2°**  Average veg  0  $  9 0 8 , 0 0 0 ohms  S o i l resistance  (iii)  9 0 4 , 0 0 0 ohms  4,000 ohms  South-flowing, ephemeral streams Table XO'I l i s t s the mean values and differences;  each mean  represents 13 observations.  Table XXVI _____ Erosional Environment  Cross-stream and cross-valley differences, non-geometric variables, Wyoming ( i i i ) . Average * Veg. $  Max. Angle Veg. $  Soil Resistance  Soil Temperature  E-f., A  38.836  24.5$  79.0°  9 2 9 , 2 3 0 ohms  W-f.,  52.7$  48.6$  74.7°  928,460 ohms  29.1$  15.8$  68.2°  9 1 9 , 2 3 0 ohms  48.8$  45.0$  77.8°  9 6 3 , 0 7 0 ohms  B  W-f., A E  —  f.  ,  B  Dl  -13,9$**  -24.4$**  4.4°  D2  -19.7$**  -29.2$**  -.11.6°**  ^43,840 ohms  8.0°**  25,770 ohms  (III - D2) / 2  P oqi  & 0 >-rj0  7,700 ohms  It i s c l e a r t h a t the v a r i a t i o n i n v e g e t a t i o n cover i n these v a l l e y s i s c o n t r o l l e d s o l e l y by the p o s i t i o n of the streams  s  thus substan-  t i a t i n g the hypothesis that there i s s o appreciable d i f f e r e n c e i n  lb  microclimate between the v a l l e y sides.  The v a r i a t i o n s i n s o i l temperature  apparently contradict t h i s statement, since the east-facing p r o f i l e s were found to be s i g n i f i c a n t l y warmer.  The sample of measurements was  not,  however, t r u l y representative, since readings were made around mid-day when the western slopes had been exposed to d i r e c t sunlight f o r a f a r longer period than the opposite v a l l e y sides.  The differences i n vegetation cover, together with those i n the angles of slope, confirm that, i n r e a l i t y , aspect pgr se has no c o n t r o l over slope c h a r a c t e r i s t i c s i n these v a l l e y s .  Ill;5 a)  Channel C h a r a c t e r i s t i c s  Manitoba The only c h a r a c t e r i s t i c of stream geometry which was measured i n  t h i s area was the bed gradient at each meander bend.  The mean angle of  those streams cutting towards north-facing slopes was  found to be 0.42°  as compared with  0.30° f o r  those swinging northwards:  there i s no  signifi-  cant, s t a t i s t i c a l difference between the two samples.  There i s no  evidence,  therefore, on which speculations regarding the adaptation of the  channel  geometry to that of the adjacent slopes may be based. b)  Wyoming (i)  East-flowing, ephemeral streams Table XXVII l i s t s the mean values and the differences f o r the 7 each mean represents 16  variables:  observations.  In view of the evidence that there i s , i n these v a l l e y s , a very high degree of i n t e r r e l a t i o n s h i p between the behaviour  of the streams and  the form of the slopes, p a r t i c u l a r l y at the apex of a north-facing meander bend, i t was  considered e s s e n t i a l to examine the major aspects of the  75 channel geometry as i t varies from one side of the v a l l e y t o the other, i n the hopes that t h i s would provide information on the manner i n which stream and slope are inter-connected.  Table XXVII  Cross-valley differences i n channel geometry, Wyoming ( i  Variable Bed gradient  Stream t o , North-facing  Difference  1.0°  0.7°  -0.3°  12.3'  Channel width  13.5'  Channel area  28.0 aq..  Hydraulic radius  Stream t o , South-facing  1  0.86'  1.1*  36.0 sq„'  - 8 . 0 sq.'** -0.17'  1.03'  8U  6.79  mms.  7.03  mms.  -0.24  mms.  %0  2.62  mms.  2.36  mms.  0.26  mms.  O.67  mms.  O.65  mms.  0.02  mms.  D  The most obvious feature of Table XXVII i s the f a c t that the geometry of t h i s sample of channel cross-sections i s very l i t t l e by the aspect of the meander bends.  affected  In part, t h i s i s perhaps due to lack  of refinement i n the measuring techniques, but the e r r a t i c nature of the hydrologic regime i n t h i s area i s probably an a d d i t i o n a l f a c t o r .  It may  be said that those streams cutting southwards and associated with the highly over-steepened  set of north-facing p r o f i l e s appear s l i g h t l y less  steep and t o have s l i g h t l y wider beds than do the set of north-swinging meanders.  More important, there i s a very strong suggestion that the  former set of channels are s i g n i f i c a n t l y shallower i n cross-section.  Such  a s i t u a t i o n may be explained as a d i r e c t r e s u l t of the over-steepening of the adjacent p r o f i l e s , which w i l l cause a large volume of debris to f a l l d i r e c t l y into the stream channel at the apex of the bend.  76 We have, then, one i n d i c a t i o n , a l b e i t a reasonably firm one, of s i g n i f i c a n t feedback between the slopes and the streams i n t h i s area. I t i s questionable whether excessive debris production w i l l , i n r e a l i t y , affect only one aspect of the channel geometry, without causing compensatory adjustments i n other f a c t o r s .  The f a i l u r e of the present study t o b r i n g  such adjustments t o l i g h t i s undoubtedly a r e s u l t of the small sample s i z e , in view of the I r r e g u l a r i t y of channel form In t h i s area.  The confirmation  that feedback does occur, however, suggests that further investigation of t h i s problem would be worthwhile. (ii)  South-flowing, ephemeral streams Although these valleys are considerably smaller than the major,  east-trending ones studied, nonetheless they possess well-defined stream courses and the a b i l i t y of the streams t o influence the form of the adjacent slopes would seem t o have been proved.  An analysis of the 7  features of the channel geometry was therefore carried out and the mean values and differences are l i s t e d i n Table XXVIIls  each mean represents  13 observations. Table XXVIII  Variable  Cross-valley differences i n channel geometry, Wyoming ( i i i ) Stream t o , East-facing  Stream t o , West-facing  Bed gradient  1.2°  1.5°  Channel width  6.7"  6.3'  Channel area Hydraulic radius  D  50  DlO  14.6 so..' O.Y2  -0.3°  13.6 sq.'  1.0 sq.' 0.11 '  0,61'  3  Difference  7.85 rams,  9.97  mms,  -2.12  mms,  2.37  mms,  3.10  mms,  -0.73  mms,  O.56 mms,  0.73  mms,  -0.17  mms,  77 None of the differences produced by stream p o s i t i o n were judged to be s t a t i s t i c a l l y s i g n i f i c a n t at the 95% l e v e l .  As there are no s i g n i -  f i c a n t differences i n the forms of the undercut slopes i n the two situations, t h i s r e s u l t i s therefore  Ill;6  consistent.  Summary  In Manitoba, the maximum angles of the slopes sampled indicate a s i g n i f i c a n t degree of control exerted by both aspect and the p o s i t i o n of the streams. are a d d i t i v e .  Although the l a t t e r influence i s dominant, the two e f f e c t s North-facing  than south-facing  ones;  slopes i n the v a l l e y s as a whole, are steeper  t h i s i s i n agreement with the general hypothesis  concerning asymmetry i n non-periglaeial areas and indicates that the presently e x i s t i n g slope forms are i n adjustment with the contemporary climatic regime. The  other variables measured i n Manitoba also tend t o be  s i g n i f i c a n t l y influenced by both cross-stream and cross-valley controls, but i t i s noticeable that the variations i n the geometric c h a r a c t e r i s t i c s of the slope p r o f i l e s are more closely r e l a t e d t o the nature of the l o c a l erosional environment and those of the non-geometric variables, t o the aspect of the p r o f i l e s .  Only one variable, the height/length  integral, a  derived geometric index, i s s i g n i f i c a n t l y influenced by cross-stream controls alone.  S i m i l a r l y , the p l a s t i c i t y index, a non-geometric index,  i s influenced s o l e l y by the aspect of the slope.  Two variables —  the s i l t  index and the percentage of the slope occupied by the maximum angle section —  vary i n an apparently random manner.  On the whole, the variables investigated permit an accurate apportionment of v a r i a t i o n between the two major sets of controls and  78 show that, i n these v a l l e y s , the stream's p o s i t i o n i s the dominant influence over the form of the slopes, but that despite t h i s , the nature of the s o i l and vegetation cover depends primarily upon the aspect of the profile .  The s i t u a t i o n i n the Wyoming v a l l e y s i s by no means as clear cut. F i r s t l y , i t would appear that the differences i n present day  microclimate  between north- and south-facing slopes are, alone, i n s u f f i c i e n t to produce any marked v a r i a t i o n i n slope form, even though they do exert some general influence over the vegetation and s o i l .  Secondly, the streams i n t h i s area  although (or, perhaps more accurately, because) they are intermittent, exert a very strong influence over slope form, even i n the small, south-trending valleys.  In t h i s p a r t i c u l a r case the action of the meandering stream i s  s u f f i c i e n t l y strong to eliminate an i n i t i a l asymmetry imposed by the h i s t o r y of development of the drainage  net.  It i s only when an active stream and a north-facing slope are i n immediate juxtaposition that the effects of microclimate are translated i n terms of a d i s t i n c t set of slope forms.  This p a r t i c u l a r class of p r o f i l e s  not only has steeper absolute maximum and mean angles than the  corresponding  south-facing set, but also than the two groups of north-facing p r o f i l e s immediately up- and downstream from the apex of the meander bends.  This  example of interaction between the cross-stream and cross-valley controls, which produces a highly l o c a l i s e d asymmetry, quite unlike that found i n the Menitoba study area, r e s u l t s from the increased humidity  of the environment  of the north-facing cutbanks and proves to a f f e c t both the channel geometry and the amplitude of the meander pattern of the streams themselves.  F i n a l l y , the intensity of stream control over the form of the  79 adjacent slopes, i n these v a l l e y s , i s so pronounced that the l o c a l erosional environment i s not only the major determining factor as regards the geometry of the p r o f i l e s , hut also l a r g e l y influences the degree of vegetation cover.  CHAPTER IV.  PATTERNS OF VARIATION  This chapter discusses the r e s u l t s of two l e v e l s of regression and c o r r e l a t i o n analysis i n terms of the manner i n which the basins  and  the slopes studied function as geomorphic u n i t s . Multiple step-wise regression has been employed throughout.  As  the d i s t r i b u t i o n s involved cannot be assumed to be uniformly normal, i t was considered advisable to employ logarithmic transformations  of both the  dependent and independent variables i n every section of the analysis, IV;1  Inter-valley V a r i a t i o n This l e v e l of analysis was not employed with the Manitoba data,  as only three v a l l e y s were investigated.  In Wyoming, s i x east-trending  v a l l e y s with ephemeral streams were sampled, i n addition to four which lacked clearly-defined channels:  both types have been included i n t h i s  portion of the study, i n order to provide s u f f i c i e n t degrees of freedom f o r a multiple regression a n a l y s i s . The complete analysis of variance of the absolute maximum angles of the east-trending valleys with ephemeral streams, described i n Chapter I I I (see Appendix C : l ) , showed that a highly s i g n i f i c a n t source of v a r i a t i o n exists i n the  'between s i t e s ' category, that i s to say, between one sample  location and another.  A s i m i l a r s i t u a t i o n was  found i n the analysis of the  mean angles i n these v a l l e y s (see Appendix C s l l l ) .  These s i t e - t o - s i t e  81  variations r e f l e c t an observed d i s p a r i t y i n both degree and, more s i g n i f i c a n t , d i r e c t i o n of asymmetry i n the s i x major valleys —  a phenomenon  also found, though t o less s t r i k i n g l y i n the channel-less valleys —  as ,  shown i n Table XXIX. Table XXIX "  Valley-to-valley variations i n asymmetry, maximum angles, Wyoming.  :  Mean Asymmetry North-facing - South-facing  Valley Lonetree Creek A  14.95° -  Lonetree Creek B  3.25°  Goose Creek Goose Creek, t r i b u t a r y  -  Duck Creek, t r i b u t a r y B 1  -  0.38°  -  1.59° 2.42°  2 3 4  3.25° 6.54°  Duck Creek, t r i b u t a r y A  Lacking channels:-  7.58°  -  1.13° 1.59°  It i s important t o recognise the significance of these reversals of asymmetry:  the extremely l o c a l i s e d nature of slope over-steepening has  been discussed i n Chapter I I I , but i t now appears that, i n some cases i t i s the south-facing slopes which possess the steeper maximum angles. Undoubtedly t h i s i s a prime cause of the f a i l u r e of the analysis of v a r i ance t o demonstrate a s i g n i f i c a n t , cross-valley e f f e c t .  The mean  difference between north- and south-facing p r o f i l e s can be seen t o be largely a s t a t i s t i c a l f i c t i o n .  £»  o  t 3-0°  X  ~  VO.IIA£  of  rA«A»\  »wS^(v\«««.+ry  y  CO  ro  + 20% r*  X on y  =  69.68%  o  X  -7.o«  -3-3*  - A*"  II • • •  *  Sou+h-faxing steeper  slopes  N o r t t r fo».cfng steep*. •  slopts  0?S  */5° *  -  10* -2.00  FIGURE 17:1  <s  .1.50 Mta.*.  -  -o-$o  -1.00 difference.  In  ev^pofaction  —1  0.0 routes  -  +o-?o Ccy-/  Mean asymmetry, related t o differences i n vegetation cover and evaporation rates.  1  +1.00  \y  82  One possible cause of t h i s r e v e r s a l of asymmetry might be the r e l a t i v e ages of the v a l l e y s .  I f age i s r e f l e c t e d i n the size of drainage  area and degree of i n c i s i o n , then i t i s possible t o t e s t t h i s hypothesis by multiple regression.  Such an analysis was c a r r i e d out, with mean.'  asymmetry i n maximum angle as the dependent variable and four features of basin geometry (basin area, depth of v a l l e y , mean difference i n height of north- and south-facing p r o f i l e s and stream gradient) employed as the p  independent f a c t o r s .  The t o t a l c o e f f i c i e n t of determination,  R , produced  by the multiple c o r r e l a t i o n i s only 2 0 . 3 5 $ and none of the independent factors produces a s i g n i f i c a n t reduction i n the sum of squares of Y. I f the average asymmetry i n mean angles i s tested against the same four factors, R  r i s e s t o 3 8 $ , but again, no one variable i s s i g n i f i c a n t l y  associated with Y. However, when the investigation i s extended t o include the mean cross-valley v a r i a t i o n i n vegetation cover and i n evaporation r e s u l t s are improved.  rates, the  I t appears that 5^ $ of the observed mean asymmetry  i n maximum angles i s explained by the average cross-valley v a r i a t i o n i n vegetation cover of the maximum angle sections and, further, that the l a t t e r f a c t o r i s i t s e l f 70$ correlated with the differences observed i n evaporation  rates between the north- and south-facing profile's.  The  association of these three variables -- asymmetry, vegetation cover and evaporation rates —  i s shown i n Figure I V : 1 : negative  observations  indicate that the values f o r the south-facing slopes exceeded those from the north-facing p r o f i l e s .  !  How, the evaporation rates, which were measured at one crosssection within each v a l l e y and of slopes of lk° or l e s s , are representative of conditions i n the v a l l e y as a whole, rather than upon any p a r t i c u l a r  83 slope, l e a s t of a l l that of the maximum angle section.  They are, as  measured, quite independent of the asymmetry i n the maximum angles, and, as f a r as can he determined by the multiple regressions, appear t o be uninfluenced by v a r i a t i o n s i n basin geometry.  The observed differences i n  evaporation rates are, therefore, perhaps the closest approach t o a t r u l y independent variable i n t h i s study.  The interpretation of Figure IVsl:Is hot immediately c l e a r , but the main suggestion  i s that there i s ah o v e r - a l l association of those  v a l l e y s with steeper north-facing slopes and those i n which the northfacing p r o f i l e s showed lower evaporation r a t e s .  The r e l a t i v e l y  moister  the north-facing slopes, the steeper t h e i r average maximum angles. reverse, on the whole, i s also true:  The  namely, i n those cases where there  i s very l i t t l e difference i n evaporation rates between the two v a l l e y sides, the south-facing p r o f i l e s are the steeper.  A further and s t r a i g h t -  forward observation i s that the steepest north-facing slopes are less well-vegetated  than t h e i r south-facing  counterparts.  It i s suggested that the observed association between those v a l l e y s with steep north-facing p r o f i l e s and low evaporation rates from t h e i r southern sides, even i n mid-summer, cannot be e n t i r e l y due t o chance. What does appear inexplicable i s that there should be differences i n cross-valley v a r i a t i o n s of evaporation-rate, from v a l l e y t o v a l l e y , but t h i s v a r i a b i l i t y , although apparently unrelated t o the basic features of basin geometry, may be dependent upon purely l o c a l topographic  factors  whose s i g n i f i c a n c e i s not immediately apparent from a study of the 1:24,000 map series and which are, therefore, not amenable t o s t a t i s t i c a l examination,  ( i t should, perhaps, be emphasised that measurements of evaporation  were made i n s t r a i g h t , east-trending sections of each v a l l e y under nearly  8k uniform conditions of sun and wind,) Whatever the cause, the c o r r e l a t i o n between asymmetry and evaporation  exists and may provide some explanation of the steepening of  north-facing p r o f i l e s i n some v a l l e y s , hut not others.  However, i t i s con-  sidered t o be unwise t o place too much emphasis on t h i s r e l a t i o n s h i p alone, since i t can scarcely be extended t o account f o r the f a c t that, i n some cases, i t i s the south-facing slopes which are markedly steeper.  If the persistence of snow-banks leads t o increased s o i l moisture and hence, t o cutbank steepening,  i t i s clear that the conditions which are  l i k e l y t o lead t o the development of over-steepened north-facing p r o f i l e s are very s p e c i f i c and, therefore, u n l i k e l y t o be met equally i n a l l v a l l e y s at any one time.  I t i s suggested, then, that the steeper  south-facing  slopes do not r e s u l t from any s p e c i a l mechanism, but rather that t h e i r r e l a t i v e steepness i s due t o the fact that the corresponding, north-facing cutbanks are s t i l l i n the i n i t i a l stages of development. thesis i s acceptable,  I f t h i s hypo-  i t appears that the steepening of north-facing pro-  f i l e s i n t h i s area i s dependent, not only upon the l o c a l conditions of moisture a v a i l a b i l i t y around a meander bend, but also on the precise location of the meander t r a i n within each v a l l e y section.  This type of  asymmetry i s therefore extremely sporadic i n occurrence and quite unlike the valley-wide  asymmetry observed i n Manitoba.  It i s possible that the highly l o c a l i s e d development of steeper north-facing p r o f i l e s i n t h i s part of Wyoming i s a function of t h e i r comparatively short erosional h i s t o r y ; but i n view of the fact that there seems t o be no correspondence between the size of drainage area or depth of i n c i s i o n and the degree or d i r e c t i o n of asymmetry, there i s no evidence available t o support t h i s assumption.  Facing page - 85  Table XXX  Cross-stream and cross-valley variations i n R .  Category  Values of Worth-facing Total Stable  x 100 South-facing Total Stable  R  2  Pembina River, Manitoba  86.3$  84.0$  81.7$  80.1$  Gangplank, Wyoming:  87.8$  87.0$  87.9$  84.7$  83.5$  78.9$  67.9$  57.2$  ephemeral streams Gangplank, Wyoming: channel-less valleys Stream towards Total Stable  Stream away Stable Total  77.8$  72.6$  90.6$  88.7$  86.0$  82.6$  85.7$  84.7$  Pembina River, Manitoba  77.9$  75.6$  87.7$  85.4$  Gangplank, Wyoming:  81.1$  77.7$  77.2$  74.8$  93.9$  85.8$  97.2$  94.7$  Haute-Marne: basins of uniform l i t h o l o g y Haute-Marne: basins of mixed l i t h o l o g y  East-flowing Gangplank, Wyoming: South-flowing  85  i  T  <*  IV; 2 a)  Intra-valley V a r i a t i o n  Degree of 'organisation' of p r o f i l e s The maximum angle of slope i s representative of the nature of the  p r o f i l e as a whole and i t s steepness w i l l be causally related t o the other c h a r a c t e r i s t i c s of the p r o f i l e and also those of the adjacent  stream.  If the maximum angle i s employed as the dependent (Y) variable i n the regression analysis, and the other features of the p r o f i l e and the stream are considered t o be independent  (X) variables, then the reduction  in the sum of squares of I achieved by a multiple regression of a l l the X factors w i l l r e f l e c t the degree of association of Y and X and may be considered t o provide an estimate of the l e v e l cfffMteeaaTal 'organisation' of the slope-stream system.  An index of the r e l a t i v e e f f i c i e n c y of organisation  of the various categories of slopes i s provided by the c o e f f i c i e n t of o  multiple determination, R , p a r t i c u l a r l y by the values produced by the exclusion of a l l i n s i g n i f i c a n t independent variables from the regression equation.  p Table XXX l i s t s the t o t a l and stable values of R  obtained f o r  the cross-stream and cross-valley d i v i s i o n s of the analysis of the Manitoba and Wyoming data.  The cross-valley set has been augmented, f o r purposes of  comparison, by the i n c l u s i o n of data from the sandy limestones of the Plateau de Bassigny, Haute-Marne (Kennedy,  1965).  There seem t o be three situations i n which r e l a t i v e l y low values of the c o e f f i c i e n t of multiple determination w i l l be produced, a l l of which r e f l e c t increased indeterminacy^' of slope forms. (i)  The absence of a defined channel The stable value of R  2  obtained f o r the category of south-facing  86  .profiles i n the channel-less valleys i n Wyoming, 57-2$, i s lower than that for any other set of slopes.  The value f o r the north-facing p r o f i l e s i n  the same v a l l e y s i s lower than those for comparable slopes i n either Manitoba or the major, east-trending v a l l e y s i n Wyoming.  C l e a r l y the presence of an active stream channel exerts a considerable degree of influence over the manner i n which the v a l l e y sides develop, since the indeterminacy in such a marked fashion.  of forms i n channel-less v a l l e y s increases  The d i s p a r i t y i n the degree of organisation  exhibited by the north- and south-facing p r o f i l e s i n the  channel-less  v a l l e y s i s presumably a feature of t h e i r respective microclimatic environments : the moister conditions on north-facing slopes w i l l govern the nature of the s o i l and vegetation cover and also, to some extent, the rate and manner of down-wasting of the p r o f i l e s .  On the south-facing slopes, on the  other hand, the sparse vegetation cover w i l l increase the l i k e l i h o o d of the movement of material under the action of rainwash, the e f f e c t s of which w i l l be less predictable than those of creep.  The form of the  south-  f a c i n g slopes w i l l , therefore, be l a r g e l y dependent on the operation of small-scale, random forces and t h e i r angles w i l l r e f l e c t the length of time that dominant controls have been absent from these v a l l e y s . (ii)  The presence of a f l o o d p l a i n Although the t o t a l absence of a stream channel leads to a  reduction i n the degree of association between the various features of slope form and the maximum angle of the p r o f i l e , the presence of a f l o o d p l a i n within a v a l l e y seems t o produce a s i m i l a r , Tbutu^hsBrpnonnundedfEffect.  The c o e f f i c i e n t s of multiple determination  obtained f o r the  south-trending v a l l e y s In Wyoming are f a r higher than those from any  other  category and indicate that the components of randomly-induced v a r i a t i o n i n  87 slope form are"very small indeed.  These valleys are the only set studied  in which floodplains were not developed and a l l slopes were d i r e c t l y adjacent t o a channel. i  t  '  The e f f i c i e n c y of the same set of independent variables as predictors of the variations i n the maximum angles of .slopes i s f a r higher i n these small basins than i n the set of major, east-trending v a l l e y s i n  which floodplains are developed and i t i s clear that the growth of a f l o o d p l a i n reduces the degree of i n t e r n a l organisation of p r o f i l e s i n t h i s area. (ill)  The presence of an active, b a s a l stream The general increase i n the indeterminacy of the maximum angles  i n the categories of undercut p r o f i l e s r e s u l t s , not from an absence of any strong control, but from the fact that an active control i s exerted continuously or semi-continuously, with the r e s u l t that the less stable features of slope form, the maximum angle among them, are i n a state of constant re-adjustment.  Only upon cessation of b a s a l attack w i l l thessJbgipedde-el^p  a r e l a t i v e l y constant, c h a r a c t e r i s t i c form, the degree of organisation of which w i l l depend l a r g e l y upon the presence or absence of a f l o o d p l a i n .  One f i n a l , general point should be made:  a l l the v a l l e y s studied  (with the exception of those i n the Plateau de Bassigny) are of Recent age. The 2 0 $ or so of •unexplained v a r i a t i o n i n the maximum angl.es which i s rather uniformly present cannot be ascribed t o any 'indeterminacy' produced by the preservation of r e l i c t , Pleistocene or Pliocene forms, but must be attributed t o a combination of measurement error and omission, and t o the operation of random or small-scale forces.  That the l a t t e r source i s l i k e l y  to be more s i g n i f i c a n t than the former, at least i n the case of the Wyoming data, i s suggested by the very high c o e f f i c i e n t s of multiple determination  Max  i mwn  £» o p.  A n q l e  £3  p Leve| Stream  P r o f 11 « .  P r o f f I e.  Ke>a K +  &io b e d  r^et+erlal  r£% 878 Ji  w ! el +• K  Strtaw  9o veg. wax- ©.no^e.  Hew  Son  H«.(^V\+/la.ne(+^  FIGURE 17J2  Averse  OH  N = 96 0+ha.rs :  CD CO  bid  So f I  Nona Correlation set, north-facing slopes i n easttrending valleys with channels, Wyoming,  CD  88 obtained from the .analyses of the slope forms i n the small,  south-trending  valleys.  b)  The r e l a t i v e importance of the independent variables (i)  Nodality Figures IV:2 - h ( i n c l u s i v e ) i l l u s t r a t e the patterns of s i g n i f i c a n t  correlations observed i n three of the major categories of slopes studied. Those variables present i n the stable multiple regression equations are shown as forming Level I and the others are arranged at succesively lower l e v e l s according t o the directness with which they are associated with the maximum angle.  For the sake of c l a r i t y , l i n k s between variables at the  same l e v e l have been omitted.  In each of the three c o r r e l a t i o n sets shown, c e r t a i n variables other than the maximum angle emerge as possessing unusually complex connections with the other factors i n the a n a l y s i s .  Such variables may be  described as 'nodal,' and any change i n a nodal f a c t o r w i l l have wide implications i n terms of the organisation of the slope-stream  system as a whole.  In Figure I¥s2, which represents the category of a l l north-facing p r o f i l e s i n the major, east-trending v a l l e y s i n Wyoming, t h e nodal variable i s stream gradient:  i t Is clear that any change i n the other features of  the channel geometry w i l l influence the bed gradient, which w i l l i n turn e f f e c t the maximum angle of the p r o f i l e .  The negative r e l a t i o n s h i p between  bed- and maximum v a l l e y - s i d e gradient i l l u s t r a t e d , i s common t o a l l those v a l l e y s studied i n which floodplains were developed.  Only i n the s m a l l ,  30uth-trending basins i n Wyoming i s there evidence o f the d i r e c t association of these two variables which Strahler noted as being general  (1950).  In the class of s l i p - o f f p r o f i l e s i n Manitoba (Figure rVs3)> there  $ +r ea.  Q4K  FIGFORE  17:3  ars :  No  m  ne  Correlation set, a l l s l i p - o f f p r o f i l e s , Manitoba.  JiL  89 a r e t w o n o d a l v a r i a b l e s , t h e mean a n g l e a n d t h e h e i g h t / l e n g t h i n t e g r a l : any change  i n e i t h e r would r e s u l t  i n a complete r e - o r g a n i s a t i o n  m a j o r f e a t u r e s o f s l o p e f o r m , i n c l u d i n g t h e maximum  The c o r r e l a t i o n s e t p a t t e r n of  internal organisation  east-trending valleys metric variables  i n Wyoming,  at Level I  IV:b,  shown i n F i g u r e  representing  is  e x t r e m e l y complex and t h e t h r e e  a l l e x h i b i t a degree  h o w e v e r , t o b e e v e n more m a r k e d .  the  stream system the© the  the  of the s o u t h - f a c i n g p r o f i l e s i n the major  t h a t t h i s v a r i a b l e w o u l d b e a more s e n s i t i v e slope m  the  angle.  of n o d a l i t y .  t a n c e o f t h e e x t e n t o f v e g e t a t i o n c o v e r o n t h e maximum a n g l e slope appears,  of  maxtoffl  eagle  It  The  impor-  section  w o u l d seem, i n  geo-  of  fact,  i n d i c a t o r of changes i n t h e  itself, since  its relation  to  features of the channel geometry is more d i r e s t . (li)  Geometric  sad nea-geeaetria  variables  Sable XXXI l i e t i the frequency w i t h which the various independent v a r i a b l e s ooour i n the stable m u l t i p l e regression equations. I t i s c l e a r that the r e l a t i v e l y s t a b l e , geometric features of slope form are more c l e a n l y r e l a t e d t o the changing nature of the maximum angle than are the nen«geometric c h a r a c t e r i s t i c s of the p r o f i l e s .  Shis tendency i s p a r t i c u -  l a r l y marked i n the case of the Manitoba study area, I t i s suggested that the r e l a t i v e importance of geometric and non-geometric v a r i a b l e s r e f l e c t s the degree t o which the l a t t e r are Influenced by cross-stream c o n t r o l s .  In Manitoba, the non-geometric  features of the slopes are more d i r e c t l y r e l a t e d t o the nature of the l o c a l microclimate, than t o that of the e r o s i o n a l environment, whereas i n Wyoming the proportion of vegetation cover on the maximum angle s e c t i o n , i n p a r t i c u l a r , i s c l o s e l y governed by i t s steepness. The general importance of the geometric v a r i a b l e s of both analyses, and, i n p a r t i c u l a r , the length o f the  o N _ 96  p CD  M ax  1 duw  VO O  R = .tr-7/. a  0  Level  Mean a n q I ft  Stream a.nci I e  P r o f f le rvta.* <  r  <--d i u s  SO b e d mot+ev-io-l  bed  0  mod- e r i a. I  O-t-K& rs :  FIGURE 17:4  -  P«-<-f i I e lettq+K  a.ngje  HeigMVl-ng+h Sell integral "temperature,  D |o  be <_  N _ne  Correlation set, south-facing slopes i n easttrending v a l l e y s with channels, Wyoming.  Soil res i-s+c^nce  re.  a. rv*i  us i d -t-l"\  0  90 maximum angle section, even i n situations where cross-valley variations in microclimate have been shown to have a s i g n i f i c a n t influence upon the broad differences i n c h a r a c t e r i s t i c slope form, seems a clear i n d i c a t i o n .that the , p r o f i l e s of the slopes i n both groups of v a l l e y s are developed as  integrated  units and that short-term o s c i l l a t i o n s i n the nature of the l o c a l erosional environment w i l l be quite r a p i d l y absorbed by complementary alterations i n the i n t e r n a l organisation of the p r o f i l e s ;  by and large, these are  equilibrium forms. (iii)  Redundancy The  concept of redundancy i s a general one  i n multivariate  analyses of a l l types and concerns the i n c l u s i o n of the same ' b i t ' of information  in the measurement of two  a f f a i r s i s manifest when the sum  or more f a c t o r s .  Such a state of  of the i n d i v i d u a l reduction  i n the sum  of  squares of Y by the X variables i s greater than that achieved by a simultaneous consideration  of t h e i r joint e f f e c t s .  o  namely when R^ exceeds the sume of the r  p  The reverse s i t u a t i o n ,  values, represents a r e i n f o r c i n g  among the v a r i a b l e s , rather than redundancy.  It i s with the former  phenomenon that t h i s section deals. The reduction i n R^ between the general equations and those containing only s i g n i f i c a n t variables, i s small on the whole.  However, a  change of only 5 $ or so i s frequently associated with the elimination of the majority  of the independent variables.  If i t were always the same factors  which formed the stable equations, the others might safely be ignored i n further studies, with considerable t h i s i s not the case.  saving i n time.  Unfortunately, however,  Table XXXI shows that, i n the present instance,  reduction of the number of independent variables would be a highly hazardous procedure.  the  Facing page - 9 1  Table XXXI  a)  Frequency of Occurrence of Independent Variables i n Stable Multiple Regression Equations.  Manitoba Variable  $ length maximum angle H/L i n t e g r a l P r o f i l e height P r o f i l e length Average $ veg. P l a s t i c i t y index Mean angle S i l t index $ s o i l moisture Stream gradient $ lower concavity $ veg., max. angle b)  Range  Occurrence (out of 8 maximum) X X X X X X X X X X  2$ - 57$ 25$ - 82$ 12' - 71' 7 0 ' -974' 15$ - 94$  2.5 39 6 2$ 0.1° -  40  25° 57 44$ 1.5°  X X X X X X X X  X X X X X X X X X X X XXX XXX X X X X X  0$ - 9 1 $ 0$ -100$  Wyoming Variable  Range  Length maximum angle 5' P r o f i l e height 4' 30' P r o f i l e length $ veg., maximum angle 0$ Mean angle 3° S o i l temperature 52° 0.1° Stream gradient H/L i n t e g r a l 23$ Channel width 2.5' Dg^ bed material 3.4 mms. Channel area 0.4 sq.' DCQ bed material 0.1 mms. Hydraulic radius 0.01' D bed material 0.22 mms. 1 0  Average $ veg. S o i l resistance  - 185' - 118' - 6oo' -  90$  59° - 100° - 4.5° -  95$ 54'  -  15  -  135 7.0  -4.5' - 2.22  7$ c.  Occurrence (out of 12 maximum)  975,000  mms. sq.' mms. mms.  75$ ohms  X X X X X X X X X X X X X X X X  X X X X X X X X X X X X  X X X X X X X X X X  X X X X X X X  X X X X X X  X X X X X X  X X X X X XXX XXX X  91 In the Manitoba study area, a l l but two of the independent variables were represented i n at least one of the stable regression equations.  The four factors which are most c l o s e l y associated with the  maximum angle are those representing other features of the p r o f i l e  geometry  and the d i r e c t significance of the non-geometric features appears low, even though most of these variables represent a wide range of values.  The same  cannot be said f o r the bed gradient v a r i a b l e , whose small importance i n terms of the stable regression equations can best be explained by the very small range of gradients sampled  (0.1° - 1.5$), with  the r e s u l t that t h i s  variable was, e f f e c t i v e l y , held constant throughout the study area.  In Wyoming, a l l the independent f a c t o r s , including those which represent the channel geometry, emerge i n at l e a s t one stable equation. This Is i n part due t o the wider range of most of the factors i n t h i s sect i o n of the analysis (with the exception of s o i l resistance which r a r e l y f e l l below  900>000 ohms)j  the apparently small range of sizes i n the bed  material categories i s , t o some extent compensated for. by the logarithmic measurement scale employed.  Although some of these s i g n i f i c a n t associa-  t i o n s undoubtedly r e s u l t from mathematical, rather than geomorphic r e g u l a r i t i e s , the problem of eliminating variables from t h i s set would be d i f f i c u l t , p a r t i c u l a r l y i f i t were required t o f i n d a common, most-significant subset which would be equally representative of the Manitoba data. j  The bed gradient of the streams i n Wyoming also emerges as of greater importance i n r e l a t i o n t o the maximum angle, than i n Manitoba, possibly because of the wider range of gradients sampled, but also because of the absence of floodplains from the south-trending v a l l e y s . On the other hand, the importance of the height/length i n t e g r a l appears much lower i n the Wyoming v a l l e y s ;  t h i s i s not a r e s u l t of the  92 .  „te .  s  small range of the index over a l l , but of the s i m i l a r i t y of values obtained from any one erosional environment r e s u l t i n g from the exclusion of the f l o o d p l a i n from the measurements of slope length, c)  Summary This section of the analysis has served t o suggest that the  independent variables which were selected f o r these studies.are, on the whole, meaningfully  r e l a t e d t o the maximum angle of v a l l e y side slope  though some are more e f f e c t i v e controls than others. provide reasonably  Taken together, they  good 'explanations' of the v a r i a t i o n i n the l a t t e r  value, although the degree of uncertainty increases with the development of a f l o o d p l a i n and, more markedly, with the absence of a well-defined stream channel. The maximum angle does not appear t o be consistently r e l a t e d , i n a d i r e c t fashion, t o the gradient of the adjacent stream and t h i s appears to be a further r e s u l t of the formation of a f l o o d p l a i n . Moreover, the v a r i a t i o n i n the maximum angle i s more c l o s e l y described by that of other, stable, geometric variables than by the differences i n s o i l or vegetation. With the single exception of the channel-less v a l l e y s i n the Wyoming sample, the l e v e l of i n t e r n a l organisation displayed by variables i n a l l the categories of slopes i s high, and the number of completely isolated variables i n each c o r r e l a t i o n set i s small.  CKAPTEE V. V:l a)  DISCUSSION AND  CONCLUSION  M u l t i p l y - c o n t r o l l e d asymmetry Introduction Previous workers have generally assumed that asymmetry i n v a l l e y -  side angles r e s u l t i n g from microclimatic differences w i l l he either u n i formly present p. 71)  or absent, throughout an area.  have stated that:  (1957>  O i l i e r and Thomasson  "In western Europe . . . the south- and west-  f a c i n g slopes are usually steeper than those f a c i n g east or north  ..."  and the concensus of opinion among North American workers ( c f . Melton, i960) has been that the north-facing slopes w i l l generally be steepened. It i s usual to d i s t i n g u i s h two classes of asymmetry on the basis of format i o n under p e r i g l a c i a l and non-periglaclal climatic conditions.  When t h i s study was  i n i t i a t e d , i t was  therefore anticipated that  either the north- or the south-facing slopes i n east-trending valleys would prove to be uniformly steeper, i f cross-valley differences i n microclimate were operating e f f e c t i v e l y , or had once so operated within the area. addition, following Melton  In  (i960) i t was assumed that the influence of  variations i n the l o c a l erosional environment would be imposed upon any valley-wide, microclimatic e f f e c t s , i n a straightforward,  statistically  additive fashion.  Although the asymmetry which was  observed i n southwestern  Manitoba does not depart from the expected pattern, that found i n the s i x ,  Facing page - 94  Table XXXII  A)  Examples of Slope Asymmetry i n Areas of Non-periglacial Climate.  Areas Other Than The Central United States  Characteristics Southern Carpathians, Czech. Lithology Elevation Climate t Annual Ppt. Stream angles Mean maximum angles  Asymmetry  S o i l movement  Vegetation Source  Flysch 1,800-4,100 f t . B C  r / D  30-40 i n .  Areas S. E . Paris Basin, France Sandy limestone 850 f t . C C* r  Upper Pembina R., Manitoba Sandy t i l l 1,600 f t . C C  d  30.0 i n .  19.3 i n .  3.35°  0.36°  11.3 - 1 6 . 7 °  22.5°  17.6°  ? 'Preservation Pleistocene forms'  S-facing slopes 3.0°* steeper: streams toward N-facing banks  ?  xlOO, S-facing slopes Mixed forest Gerlach, 1963  N-faclng slopes 3 . 1 ° * steeper  Greater, W-facing slopes > 22° Rough grass & beech coppice Kennedy, 1965  Climates c l a s s i f i e d by the Thornthwaite  Rough grass & willows Kennedy, 1967  (1931) system.  9h east-trending valleys i n southeastern Wyoming, i s of a t o t a l l y d i f f e r e n t type.  In t h i s l a t t e r area, the effects of microclimate and l o c a l erosional  environment upon the form of valley-side slopes are not additive, but the two controls interact t o produce highly l o c a l i s e d steepening of certain north-facing v a l l e y sides.  Although i t s existence was t h e o r e t i c a l l y pre-  d i c t a b l e , t h i s study i s the f i r s t which has considered and documented the occurrence of t h i s type of l o c a l i s e d , multiply-controlled asymmetry.  b)  Control by moisture a v a i l a b i l i t y The three factors which have been suggested, both singly and  j o i n t l y , t o control the development of v a l l e y asymmetry, are i n s o l a t i o n , wind d i r e c t i o n and vegetation cover ( O i l i e r and Thomasson, 1957j> P«  7l)«  It i s advisable t o consider that a l l three w i l l act, t o some extent, i n any area and that they w i l l j o i n t l y influence the moisture a v a i l a b i l i t y of the micro-environment.  The available evidence was therefore examined t o  determine whether differences i n humidity are related t o the nature of asymmetry.  Table XXXII l i s t s some of the major features of seven recent studies of asymmetry i n Europe and North America i n areas of temperate climate, including the two discussed i n t h i s t h e s i s .  The data cover a  range of moisture regimes, as defined by the Thornthwaite t i o n (1931) •-- from 'humid' to 'semi-arid' —  'I' c l a s s i f i c a -  but are from roughly  comparable thermal provinces 'micro-thermal' t o t r a n s i t i o n a l  'taiga.'  From a study of t h i s data i t i s possible t o distinguish three types of asymmetry which may e x i s t at the present time, i n areas of nonp e r i g l a c i a l climate and moderately resistant rocks.  Facing page - 95 Table XXXII B)  AtfaaaciaXTKe Central United States  Charact er i s t i c s  Eastern Laramie Mts.,Wyo.  V i c i n i t y of Cheyenne, Wyo.  Gangplank, S.W. of Cheyenne, Wyo.  V i c i n i t y of Harrison, Kebr.  Lithology  Granite  Sandy conglom.  Sandy conglom.  Claystones, sandstones  Elevation  7,500 8,000 f t .  c.6,000 f t .  6,000 6,500 f t .  c.4,000 f t .  Climate  DC  D C  D C  D C  Annual precipitation  c.20.6 i n .  C.15 i n .  15.0 i n .  c.ll.k  Mean stream gradient  c. 1 . 0 °  ? (Low)  0.84°  (Low)  13.2° (mean angle)  30.0°  11.0° (mean angle)  Mean maximum angle (or as specified)  Asymmetry  d/ D  1  16.8°  N-facing slopes steeper*  S o i l movement  Vegetation Source  ?  d  N-facing slopes 0.6° steeper: streams towards Sfacing v a l l e y side  ?  d  N-facing slopes 2.92° steeper  Greater depths, N-facing slopes > 27°  d in.  N-facing slopes 4.0° steeper  (*)  ?  Sagebrush/ pine transition  Grassland  Grassland  Grassland  Melton I960  Hadley, 1961  Kennedy, 1967  Hadley, 1961  95 (i)  R e l i c t , reversed asymmetry The two European areas f o r which asymmetry studies are available  are both regions with large moisture surpluses and r e l a t i v e l y abundant p r e c i p i t a t i o n at a l l times of year.  Their l i t h o l o g i e s are not d i s s i m i l a r  from those investigated i n North America, and yet the asymmetry which i s presently found i n both areas i s almost c e r t a i n l y a Pleistocene 'hangover,* as the tendency i s f o r contemporary slopes.  In the Carpathians, Gerlach  conditions to f l a t t e n the south-facing  (1963) bas  shown evidence f o r higher  rates of down-wasting on the northern v a l l e y sides, although the rates are almost microscopic.  In the Plateau de Bassigny, Kennedy  (1965) found  a  s i g n i f i c a n t , reversed asymmetry i n v a l l e y s where the tendency of the streams i s t o cut, p r e f e r e n t i a l l y , against the base of the southern v a l l e y sides, suggesting that i n time the north-facing slopes may become the steeper.  Contemporary conditions, i f continued over a s u f f i c i e n t period  of time, should r e s u l t i n both areas i n the r e v e r s a l of asymmetry and the establishment of the 'normal,' non-periglacial type, but Oerlach's measurements of rates of s o i l movement i n the Carpathians would c e r t a i n l y suggest that t h i s a l t e r a t i o n would be a very long-term process.  It i s suggested that the extreme s t a b i l i t y of slope forms i n these two areas i s d i r e c t l y related t o the nature of t h e i r climatic regimes.  Although slow mass movements and, i n p a r t i c u l a r , creep, would  seem t o be r e l a t i v e l y favoured i n moist areas such as western Europe, a l l the available evidence points t o the conclusion that t h i s i s not the case. Apart from Gerlach's evidence (1963), confirmation i s available from a study by Kirkby  (1963) of comparative rates of s o i l creep i n two parts of the  B r i t i s h Isles.  The moister study area, i n the Galloway Peninsula, which  receives a r a i n f a l l of 68 inches a year, showed f a r lower rates of creep, over a three-year period than d i d control s i t e s situated i n Cambridgeshire,  96 where the annual p r e c i p i t a t i o n t o t a l i s 20 inches.  It seems that the  greater force of the d r i v i n g components which i n i t i a t e s o i l movement, tend , to be overcome by the joint resistance of well-developed  s o i l mantles and  deep-rooted vegetation In areas of humid temperate climate.  Further, the  material which i s moved t o the channels w i l l be small i n c a l i b r e and r e a d i l y removed by streams which flow a l l year round, with the r e s u l t that debris lenses at the base of south-facing slopes are u n l i k e l y to develop. (ii)  'Normal', valley-wide asymmetry Taking the data from Manitoba and from two investigations (Melton,  i960; Hadley, 1961) which have been carried out immediately to the west and east of the Wyoming area, we have a sample of three regions i n which the north-facing v a l l e y - s i d e slopes are observed to be uniformly steeper, by about 3 - h°, a l l of which l i e at the lower l i m i t of the zone of sub-humid climate (Thornthwaite  'II' revised water balance c l a s s i f i c a t i o n , 1955)  and  possess small, but s i g n i f i c a n t moisture surpluses i n the spring months which are produced by the coincidence of snow melt with peak r a i n f a l l . These areas are r e l a t i v e l y well-vegetated, but there Is evidence, i n a l l three, that the action of creep and the washing-out of material from the surface of the south-facing slopes i s s u f f i c i e n t to move the stream courses somewhat towards the southern v a l l e y sides ( c f . Hadley, 1961)0  The stream regimes i n these areas are intermittent to ephemeral, but are not characterised by the extremely regions.  'flashy' flow of true semi-arid  The evidence that the stream channels are being s h i f t e d southwards  by the growth of debris lenses, demonstrates that the supply of material from the slopes tends to exceed the capacity of the streams, which flow at low l e v e l s during the greater part of the above-freezing period.  Over a l l ,  one i s forced to the conclusion that d i f f e r e n t i a l slope processes i n these  97 areas are probably aided by the combination of the small, spring moisture surplus with the incomplete the channel processes.  vegetation cover, to a greater degree than are  The small volume of runoff r e s u l t s i n low-intensity  stream a c t i v i t y f o r the greater part of the water year.  (iii)  Localised 'normal' asymmetry The climate of the Cheyenne area i s t r u l y semi-arid, i n terms of  the Thornthwaite water balance c l a s s i f i c a t i o n (.1955).  The explanation of  the f a i l u r e of 'normal', valley-wide asymmetry to develop on the sandy conglomerates i n t h i s area (although i t i s found both on the weathered granites at elevations of 1,000  - 1,500  feet above the Ogallala, t o the  west and on the claystones and sandstones a similar distance below them, to the east) i s thought to r e l a t e to the paucity of available moisture i n t h i s p a r t i c u l a r area.  There i s very l i t t l e difference i n the r e l a t i v e erosional  resistance of the l i t h o l o g i e s involved, and the l o c a l i s e d nature of the asymmetry developed i n the Cheyenne area as a r e s u l t of the i n t e r a c t i o n of cross-stream and cross-valley controls must arise from a d i f f e r e n t i a l i n t e n s i t y i n the operation of erosional agents, rather than from the varying a b i l i t y of the materials to r e s i s t applied stresses.  The greater a r i d i t y of the climate i n the Cheyenne area seems to cause the balance between the e f f i c i e n c y of slope and stream processes to t i p i n favour of the l a t t e r .  Although the evidence  cannot be regarded  as  conclusive, i t does appear that the lack of any general moisture surplus, at any time of year, i n t h i s area^ leads t o the development of oversteepened, north-facing p r o f i l e s only when meander cutbanks become s u f f i c i e n t l y well-established to allow the formation and persistence of snow d r i f t s within them.  This process leads to the moistening of the surface  s o i l and an increase of void volume under unconfined  shear, which i n turn  98 aids further bank-cutting and the concomitant profile.  steepening of the whole  It seems l i k e l y that t h i s area l i e s at the l i m i t of conditions  conducive t o the development of cross-valley asymmetry, though t h i s does not imply that asymmetry cannot develop i n regions of greater a r i d i t y , i f other processes and controls predominate.  In the Cheyenne area, the r e s i s -  tance of the surface materials to small mass movements i s greater than the tendency of those materials t o creep, except i n very highly l o c a l i s e d zones of moisture retention.  I f l o c a l conditions do not favour the creation of a  saturated or near-saturated surface layer of s o i l , then the angle of slope w i l l be determined purely by the extent of basal sapping by streams (for the flash-floods i n these v a l l e y s have greater i n t e n s i t i e s , though lower f r e quencies, than the peak flows i n the more humid regions) p r i n c i p a l l y because • of the more rapid runoff from the poorly vegetated slopes.  c)  Summary In zones of moderate t o high humidity, the e f f i c i e n c y of slope  processes w i l l be low, as a r e s u l t of the well-developed s o i l and vegetation covers, unless these are disturbed, f o r example by c u l t i v a t i o n .  Cross-  v a l l e y asymmetry w i l l , therefore, be inhibited by the a b i l i t y of permanent or semi-permanent streams t o remove debris at roughly the same rate as i t i s supplied from the slopes.  In such circumstances, r e l i c t Pleistocene  asymmetry i s l i k e l y to be found at the present time, and t o p e r s i s t . In areas of lower humidity, the e f f i c i e n c y of stream processes w i l l be reduced by the low volume of stream flow f o r most of the year. Slope proceBses, on the other hand, are r e l a t i v e l y favoured because of the reduction In vegetation cover and strength of the s o i l mantle:  although  creep may be r e s t r i c t e d by the lack of moisture, the d i r e c t washing-out of f i n e , surface material during storms w i l l increase the volume of debris  99 moving t o the toe of the slope.  In such conditions, the gradual build-up  of lenses of material at the base of south-facing slopes w i l l be common and valley-wide asymmetry, which i s in-phase with the present climatic regime, will  develop. At the outer l i m i t s of the zone of sub-humid climate, asymmetry  w i l l develop only as a r e s u l t of l o c a l conditions which serve t o increase either the supply of debris from the south-facing v a l l e y side, or, as i n the case of the Wyoming study area, the s u s c e p t i b i l i t y of the north-facing p r o f i l e s t o bank-cutting.  I t seems necessary t o d i s t i n g u i s h t h i s type of  asymmetry from the more common, valley-wide form, found i n regions of greater general humidity, since i t i s by no means clear that the mechanisms involved are s i m i l a r . V:2  Relationship of Slopes and Streams Three subsidiary points concerning the nature of the r e l a t i o n s h i p  between slopes and the adjacent streams have emerged from t h i s study, with implications which seem s u f f i c i e n t l y wide-ranging t o warrant further investigation. ( i ) The r e l a t i o n s h i p between stream gradient and the maximum angle of the adjacent slopes i s not as uniformly d i r e c t as previously supposed, but i s dependent on the maturity of the v a l l e y and, most p a r t i c u l a r l y , the presence or absence of a f l o o d p l a i n . ( i i ) The development of a f l o o d p l a i n not only b l u r s the r e l a t i o n s h i p of slope- and stream gradients, but i s accompanied by an increase i n the random component of slope organisation.  Slopes i n v a l l e y s  lacking defined stream courses seem t o be even more l i k e l y t o develop under random influences, rather than under the control  100  of dominant processes which would tend to produce a greater degree of i n t e r n a l organisation among the components of slope form. ( i i i ) In certain, s p e c i a l cases, the form of a slope and the nature of the s o i l or debris movement upon i t , can and does influence the form of the adjacent stream, both i n cross-section and plan.  V:3  Conclusion This study seems t o have raised more problems than i t has solved,  which i s not necessarily a bad thing.  There i s a tendency f o r geomorpho-  l o g i s t s to generalise about geomorphic processes on the basis of very scant evidence and, more d i s t r e s s i n g l y , i n the absence of concrete data concerning the mechanisms by which the landscape functions.  Studies such as the  present one, which suggest that the nature of the interaction between a slope and the nearby stream i s both subtle and changeable, even within quite small areas, may perform a useful function i n that they demonstrate the l i m i t a t i o n s of our present knowledge and may serve to d i r e c t attention to what i s , i n the author's view, the most c r u c i a l problem i n the whole study of landscape development:  namely, the functional r e l a t i o n s h i p of the  planar and l i n e a r elements of the topography.  BIBLIOGRAPHY Anonymous, Reconnaissance S o i l Survey, Manitoba: Winnipeg, Manitoba.  Dept. of Agriculture,  Bindschadler, H., 1964, Hote on the Ascalon Series' P r o f i l e at Archer Weather Station: Unpublished. Wyoming S o i l Conservation Service. Budel, J . , 1953* 'Die "periglazial"-morphologischen Wirkungen des Eiszeitklimas auf der ganzen Erde': Erdkunde, Bd. 7, pp. 249-266. Burmister, D., 1951> Press, New York,  S o i l Mechanics, Volume I:  Columbia University  C u l l i n g , W. E. H,, 1965> 'Theory of Erosion on Soil-covered Slopes': Journal of Geology, v.73, pp. 230-254, Gerlach, T., 1963* 'Extension de Transformations des Versants Merldionaux de Haut Beskide a l'Epoque A c t u e l l e ' : Report of VI INQUA Congress, Warsaw, 196l: Volume I I I , iodz, (Abstract: Geographical Abstracts,  66A/$82).  Hack, J , T., 1965, P o s t g l a c i a l Drainage Evolution and Stream Geometry i n the Ontonagon Area, Michigan: U. S. Geological Survey Professional Paper 504-B. Hadley, R. P., 1961, 'Some E f f e c t s of Microclimate on Slope Morphology and Drainage Basin Development's Geological Survey Research, 196ls U. S. Geological Survey Professional Paper 421+-B, pp. B32-33, Halstead, E, C , 1959> Ground-water Resources of the Brandon Map-area, Manitoba: Geological Survey of Canada, Memoir 300. "~ Kennedy, B. A„, 1965? An Analysis of Factors Influencing Slope Development on the Charmouthien* Limestone of the Plateau de Bassigny (Haute-Marne J ~ France: Unpublished Regional Essay, Dept. of Geography, Cambridge University, Kirkby, M. J . , 1963, A Study of the Rates of Erosion and Mass Movements on Slopes, with Special Reference t o Galloways Unpublished Ph.D, d i s s e r t a t i o n , Cambridge University, Leopold, L, B. and J . P. M i l l e r , 1954, A P o s t g l a c i a l Chronology f o r Some A l l u v i a l Valleys i n Wyoming: U. S. Geological Survey Water Supply Paper 1261.  102 Leopold, L. B. and M. G. Wolman, 1957* River Channel Patterns: Braided, Meandering and S t r a i g h t : U. S. Geological Survey Professional Paper 282-B. Melton, M. A., i960, 'Intravalley Variations i n Slope Angles Related to Microclimate and E r o s i o n a l Environment : B u l l e t i n , Geological Society of America, v. 71, pp. 133-144. 8  ~  , 1965, 'Debris-covered H i l l s l o p e s of the Southern Arizona Desert - Considerations of t h e i r S t a b i l i t y and Sediment Contribution': Journal of Geology, v. 73, pp. 715-729.  Moore, P. E., 1959, The Geomorphic Evolution of the East Flank of the Laramie Range, Colorado and Wyoming: Unpublished Ph.D. t h e s i s , Dept. of Geology, University of Wyoming, Laramie. O i l i e r , C. D. and A. J . Thomassen 1957* 'Asymmetric Valleys of the C h i l t e r n H i l l s " : Geographical Journal, v. 123, PP. 71-80. Pearson, E. S. and H. 0. Hartley, 1951, 'Charts of the Power Function f o r Analysis of Variance Tests, Derived from the Non-central F - d i s t r i b u t i o n ' : Biometrika, v. 38, pp. 112-130. ~~ Rand, N. A., 1961, An Analysis of the Slopes of Some Small Basins on the Chalk and Hythe Beds of South England: Unpublished Regional Essay, Dept. of Geography, Cambridge University. Schumm, S. A., 1956, Badland Slopes': , 1967, Colorado':  'The Role of Creep and Rainwash on the Retreat of American Journal of Science, v. 254, pp. 693-706.  'Rates of S u r f i c i a l Rock Creep on H i l l s l o p e s i n Western Science, v. 155> PP. 56O-562.  Smith, H. T. U., 1949, 'Physical E f f e c t s of Pleistocene Climatic Changes in Nonglaciated Areas': B u l l e t i n , Geological Society of America, v. 60, pp. 1485-1516. Steel, R. G. D. and J . H. T o r r i e , i960, P r i n c i p l e s and Procedures of S t a t i s t i c s : McGraw H i l l Book Co. Inc., New York. Strahler, A. N., 1950> 'Equilibrium Theory of E r o s i o n a l Slopes, Approached by Frequency D i s t r i b u t i o n A n a l y s i s ' : American Journal of Science, v. 248, pp. 673-696; 800-814. , 1952, 'Dynamic Basis of Geomorphology': Society of America, v. 63, pp. 923-938. '  B u l l e t i n , Geological  , 1957, 'Quantitative Analysis of Watershed Geometry': actions, American Geophysical Union, v. 38, pp. 913-920.  Trans"~  Terzaghi, K. and R. B. Peck, 1948, S o i l Mechanics i n Engineering P r a c t i c e : John Wiley & Sons, Inc., New YorkT !  103 Thompson, D'A. W., 1 9 6 l , On Growth and Form; Cambridge University Press, Cambridge.  Edited, J . T. Bonner,  Thornbury, W. D., 1965, Regional Geomorphology of the United States; John Wiley & Sons, Inc., New York. Thornthwaite, C. W., 1931, 'The Climates of North America According to a New C l a s s i f i c a t i o n ' : Geographical Review, v. 1, pp. 633-655. Thornthwaite, C. W. and J . R. Mather, 1955, The Water Balance: Publications i n Climatology, v. VIII, no. 1, Laboratory of Climatology, Centreton, New Jersey. U. S. Weather Bureau, 1956, Summary of Hourly Observations, Cheyenne, Wyoming: Climatography of the United States No. 30-4b\ , 1961, Paper hO. , 1964  R a i n f a l l Frequency A t l a s of the United States: Technical and 1965,  v7T*> no. 13,  Climatic Summary, Wyoming:  v. 73,  no. 13,  and  A P P E N D I X  A  ROTES ON THE VARIABLES EMPLOYED IN THE ANALYSES  105 A:I 1.  THE VARIABLES OF THE MANITOBA ANALYSIS Maximum angle.  Measured i n the f i e l d with Abney l e v e l . Represents that section of the p r o f i l e of length 5 feet or more, with the steepest angle. In the absence of a r i v e r c l i f f , t h i s w i l l coincide with the Strahler maximum angle. Accuracy:  2.  Length maximum angle section. Measured i n the f i e l d with 100-foot tape. Expressed as $ t o t a l slope length. R e l a t i v e l y constant. Accuracy:  3.  Mean angle.  k. P r o f i l e length.  P r o f i l e height.  ±1.0°  Measured i n the f i e l d , at right angles t o the apex of the meander bends, orthogonal t o the contours. Base of p r o f i l e always the r i v e r bankj head taken either as the divide or that point where the slope down-valley along the interfluve equalled that down-profile. Accuracy:  ± 2.0 f t .  Computed from scale drawings of slopes ( 1 : 1 , 2 0 0 ) . Accuracy:  6,  ± 1.0 f t .  Height/length r a t i o of the p r o f i l e , derived from f i e l d measurements. Accuracy:  5,  — 0.5°  ± 2.0 f t .  Stream gradient. F i e l d measurement with Abney l e v e l , downstream from apex of meander bend. Only moderately accurate:  t. 50$  7, Length of lower concavity. Computed from scale drawings of p r o f i l e s . Defined as that section below the maximum angle segment, leading into a stream channel, on which the angle of slope increases upwards i n a regular fashion. Expressed as a $ of t o t a l slope length. Arbitrary and probably less accurate than the height/length i n t e g r a l . 8.  Height/length i n t e g r a l . The mean height of the p r o f i l e , expressed as fo t o t a l height (see I:3c). Accurate and sensitive t o differences i n l o c a l erosional environment.  106  9, 10.  Vegetation cover, maximum angle section. Vegetation cover on each Average vegetation cover. slope section was estimated ' by eye i n the f i e l d and expressed as $ t o t a l area. The average value f o r each slope represents the geometric mean. Approximate, but consistent.  11.  P l a s t i c i t y index.  12.  S i l t index.  Estimated by laboratory t e s t s of s o i l samples at f i e l d capacity: one sample was collected from the upper s i x Inches of the s o i l p r o f i l e on each maximum angle segment. The t e s t s were derived from Burmister (1951). Approximate, but consistent.  13.  S o i l moisture content. Obtained by oven-drying 100 gm. samples from each maximum angle segment, at temperatures of 100° F. Moisture expressed as $ wet weight of s o i l . Reasonably accurate.  A:II a) 1.  THE VARIABLES OF THE WYOMING ANALYSIS A l l Valleys Maximum angle.  As Manitoba. The Strahler maximum angle was separately defined f o r those p r o f i l e s i n east-trending valleys on which the absolute maximum angle represented the r i v e r c l i f f .  2.  Length maximum angle section.  As Manitoba.  Expressed i n feet, rather than as $ t o t a l slope length. 3.  Mean angle.  k„  P r o f i l e length. Measured i n the f i e l d orthogonal t o the contours. Head of p r o f i l e defined as i n Manitoba: base either stream bed or junction v a l l e y side and f l o o d p l a i n .  As Manitoba.  Accurate. 5.  P r o f i l e height. As Manitoba.  6.  Channel or v a l l e y gradient. As f o r Manitoba, f o r valleys with c l e a r l y defined cnannels. For other v a l l e y s , measured downv a l l e y from centre of c r o s s - p r o f i l e . Considered t o be more accurate and sensitive than the comparable variable f o r Manitoba.  10? 7.  Height/length Integral.  As Manitoba.  The exclusion of the floodplain from the measurement of the length of the s l i p - o f f p r o f i l e s reduced the value of t h i s v a r i a b l e , as there was l i t t l e v a r i a t i o n between the integrals from the two main classes of erosional environments. Accurate, but i n s e n s i t i v e . 8. Vegetation cover, maximum angle section. 9 . Average vegetation cover. 10. 11.  b) 12.  As Manitoba.  S o i l temperature. At-a-point readings made at depths of 6 inches on S o i l r e s i s t a n c e ? maximum angle sections, with S o i l Test meter and probes. Temperature data the more accurate: readings of resistance uniform and close t o the l i m i t of the instrument because of extreme heating and drying of the s o i l s . Variables Relating t o Channel Characteristics of Ephemeral Streams Channel cross-sectional area. Measured by planimeter from large-scale drawings of channel cross-sections, obtained from f i e l d observations. Reasonably accurate.  13.  Channel width.  Obtained from scale drawings and f i e l d notes. Height of bankful channel inferred from slope change and/or proportion of vegetation cover. Reasonably accurate.  Ik.  Hydraulic radius.  Obtained from scale drawings and the formula: %  =  Cross-sectional area Wetted perimeter  Reasonably accurate. 15. 16. 17.  channel material.  Obtained by mechanical sieving of a i r - d r i e d samples of 200 gms. i n weight, collected from D50 channel material, the surface of the channel beds. Sizes, i n mm., are those thW:.which 84$, :50$ and 10$ of D channel material. material was f i n e r , by weight. 1 Q  t  h  e  s  a  m  p  l  e  Accurate, but u n l i k e l y t o be t r u l y representat i v e of bed load.  A P P E N D I X  B  THE PRECIPITATION, RUNOFF AND DISCHARGE DISTRIBUTIONS, RHODES, MANITOBA:  1959 - 1964  109  B:l 1959  Pembina River at Rhodes, Manitoba  Cumulative percentage frequency, p r e c i p i t a t i o n (P)  ©  ©  Cumulative percentage frequency runoff ( R )  Xr-  a  Cumulative percentage frequency, discharge ( Q )  Annual t o t a l ; P = R s  23.76  inches  O.725 inches  110  B:2  i960  Pembina River at Rhodes, Manitoba Cumulative percentage frequency, p r e c i p i t a t i o n  0  *  Cumulative percentage frequency, runoff  0  *  (R)  Cumulative percentage frequency, discharge ( Q )  Annual t o t a l : P = R -  15.24 inches 2.52  inches  (P)  Ill  B:3 I961  Pembina River at Rhodes, Manitoba  •  •  Cumulative percentage frequency, p r e c i p i t a t i o n  0  o  Cumulative percentage frequency, runoff  x  *  Cumulative percentage frequency, discharge  Annual t o t a l P a R = Q -  13.77  inches  0,303 inches 1035.1  cusecs  i  (R) (Q)  (P)  112  1962  • &  x  Pembina River at Rhod.es> Manitoba  •  Cumulative percentage frequency, p r e c i p i t a t i o n Cumulative percentage frequency, runoff  0  x  Cumulative percentage frequency, discharge  Annual t o t a l ; P =  23.4-5 inches  R a  l„95 inches  Q =  (R)  3556.0  cusecs  (Q)  (P)  113 B:5 1963  Pembina River at Rhodes, Manitoba  Cumulative percentage frequency, p r e c i p i t a t i o n Cumulative percentage frequency, runoff ( R ) Cumulative percentage frequency, discharge  Annual t o t a l :~ P _» R «-  Q a  18,08 inches 1,56  inches  3063,0  cusecs  (Q)  (P)  114  B:6  1964  Pembina River at Rhodes, Manitoba  •  •  Cumulative percentage frequency, p r e c i p i t a t i o n  o  o  Cumulative percentage frequency, runoff ( R )  *  *  Cumulative percentage frequency, discharge  (P)  (Q)  Annual t o t a l  I00%-1  ibr-  1  1  «/"  F  M  1  A  I  1  1  M  -7  «J"  1  1  1  1  A  S  O  N  1  A P P E N D I X  C  THE ANALYSES OF VARIANCE  116 C:I a)  MAXIMUM ANGLES Manitoba SOURCE  Aspect Stream Position Interaction Error Total NOTE:  SUM OF SQUARES  243.36 1552.36 116.64 5286.64 7199.00  D.F.  MEAN SQUARE  F  1 1 1 96 99  243.36 1552.36 116.64 . 55.069  4.4* 27.9** 2.12  aspect and erosional environment e f f e c t s tested against a pooled error term: _ SSError + SSInteraction DFError T DFInteraction E  p  b)  Wyoming SOURCE  Aspect Stream Position Interaction Error Total (i)  409.79 36811.00 82.03 54644.18 91947.00  D.F.  MEAN SQUARE  l  409.79 36811.00 82.03 290.22  1 l  188 T9TT  A l l data, p r i n c i p a l e f f e c t s only: ephemeral, streams.  SOURCE Aspect Stream p o s i t i o n Interaction Error Total (ii)  SUM OF SQUARES  SUM OF SQUARES  1640.00 17780.00 1222.5 18242.25 38884.75  D.F.  1 1 1 60  F  1.41 137.4** 0.28  east-trending v a l l e y s with  MEAN SQUARE  1640.00 17780.00 1222.5 304.04  D i r e c t l y at or opposite the apex of meander bends: trending valleys with ephemeral streams.  F  1.342 14.55 4.021*  east-  117  SOURCE  Aspect Site x aspect Stream p o s i t i o n Aspect x stream Bend Aspect x bend Stream x bend Interaction Error Total  NOTE:  SUM OF SQUARES 409.79 21050.00 36811.00 82.03 1104,90 1331.60 771.50 1433070  28953.00 91947.00  D. F.  1 30 1 1 2 2 2 2 150 191  MEAN SQUARE 409.79 701,66 36811.00 82.03 552,46 665.79 385.75 716.84 193.02  F.  2.12 3.64** 190.71 0.42 2.86 3.45 2.00 3.71*  i n t e r a c t i o n s i g n i f i c a n t therefore i n d i v i d u a l means tested pair-wise by Duncan's t e s t ,  (iii)  A l l data, a l l e f f e c t s : ephemeral streams.  SOURCE Aspect Stream position Interaction Error Total  (iv)  SUM OF SQUARES 148.39 2264.37 958.15 5213.27  east-trending valleys with  D. F. 1 1 1 48  MEAN SQUARE 148.39 2264,37 958.15 108.60  b 5b'4.lb' J  South-trending v a l l e y s with ephemeral streams *  *  F 0.1 20.9 8.82**  118  C:II  STRAHLER MAXIMUM ANGLES Wyoming:  east-trending v a l l e y s with ephemeral streams  SOURCE  SUM OF SQUARES  Aspect S i t e x aspect Stream p o s i t i o n Aspect x stream Bend Aspect x bend Stream x bend Interaction Error Total NOTE;  ClIII  604.22 7856.OO  D.F.  MEAN SQUARE  P.  1  604.22  20168.00  30 1  261.87 20168.00  179.41 1029.40  1 2  514.72  5.78  636.70  2  725.ll  2 2  318.35 362.56  3.58 4.07  353.63  3.97*  707.27 13355.00  45262.00  150 I9T  179.41  6.79  2.94 226.51 2.02  89.037  i n t e r a c t i o n s i g n i f i c a n t , therefore i n d i v i d u a l means tested by Duncan's t e s t .  MEAN ANGLES Wyoming:  SOURCE  Aspect S i t e x aspect Stream p o s i t i o n Aspect x stream Bend Aspect x bend Stream x bend Interaction Error Total  east-trending v a l l e y s with ephemeral streams  SUM OF SQUARES 146.32 3007.80 3225.90 1.07 61.77 27.53 77.60  D.F.  MEAN SQUARE  F  1  146.32  30 1 1 2 2 2 2  100.26  7.19** 4.92**  3225.90  158.41**  89.33 3054.60  150  9691.90  19T  1.07 30.89 13.77 38.80 44.67 20.36  0.05 1.52 0.68 1.91 2.19  

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.831.1-0093734/manifest

Comment

Related Items