LONGITUDINAL PROFILES OF EPHEMERAL STREAMS
IN SOUTHEASTERN ARIZONA.
by
D ou glas S tu a r t Cherkauer
A T h e s is S u b m itted t o t h e F a c u lty o f t h e
DEPARTMENT OF GEOLOGY
I n P a r t i a l F u lf illm e n t o f t h e R equirem ents
For t h e D egree o f
MASTER OF SCIENCE
I n t h e G raduate C o lle g e
THE UNIVERSITY OF ARIZONA
19
6 9
STATEMENT BY AUTHOR
T h is t h e s i s h as b een s u b m itte d i n p a r t i a l f u l f i l l m e n t o f r e ­
q u ire m e n ts f o r an advanced d e g re e a t The U n iv e r s ity o f A rizo n a and i s
d e p o s ite d i n th e U n iv e r s ity L ib ra r y to be made a v a il a b le to b o rro w e rs
u n d er th e r u l e s o f th e L ib ra r y .
B r ie f q u o ta tio n s from t h i s t h e s i s a r e a llo w a b le w ith o u t s p e c ia l
p e rm is s io n , p ro v id e d t h a t a c c u r a te acknowledgment o f so u rc e i s made.
R eq u e sts f o r p e rm is s io n f o r e x ten d e d q u o ta tio n from o r r e p ro d u c tio n o f
t h i s m a n u sc rip t i n w hole o r i n p a r t may be g ra n te d by th e head o f th e
m ajo r d e p a rtm e n t:o r th e Dean o f th e G rad u ate C o lle g e when i n h i s ju d g ­
ment th e p ro p o sed u s e o f th e m a t e r i a l i s i n th e i n t e r e s t s o f s c h o la r ­
s h ip . I n a l l o th e r i n s t a n c e s , how ever, p e rm is s io n m ust be o b ta in e d
from th e a u th o r.
SIGNED:
V
CL
APPROVAL BY THESIS DIRECTOR
T h is t h e s i s h as been approved on t h e d a te shown below :
W illiam 3 . B u ll
P r o fe s s o r o f G eology
D ate
ACKNOWLEDGMENTS
T h is p r o j e c t c o u ld n ev er have b een com p leted w ith o u t t h e .
c o n tin u a l h e lp and en couragem ent, i n th e f i e l d and w ith th e d r a f t in g
and ty p in g , o f my w if e , K athy.
Mr. Thomas Haddock, J r . i n i t i a l l y
su g g e ste d th e t o p ic f o r s tu d y , and h i s su b seq u en t comments and id e a s
have b een o f g r e a t v a lu e .
Dr. W illia m B. B u ll o f f e r e d many u s e f u l
and tim e -s a v in g t e c h n iq u e s and s u g g e ste d im p o rta n t c o r r e l a t i v e
i n v e s t i g a t i o n s w h ile s e r v in g a s t h e s i s d ir e c t o r .
I n a d d it io n t o
t h e s e two men, Dr. John S tu r g u l r ev iew ed t h e m a n u scr ip t, making
many v a lu a b le comments.
The Departm ent o f G eology and th e " U n iv e r s it y Computer C en ter
p ro v id ed t h e n e c e s s a r y com puter tim e and program c o n s u lt a t io n .
iii
TABLE OF CONTENTS
.
Page
LEST OF ILLUSTRATIONS . .................................... ................................................ .... .
LEST OF T A B L E S ....................................................................... ....
ABSTRACT
v iii
........................................................... .................. ....
INTRODUCTION
......................................................
vi
ix
..................
1
Purpose . ............................................................... . . . . . .
.......................
L o c a t i o n .................................... .... ......................................................... ....
C o lle c tio n o f D ata .......................
P r e s e n ta tio n o f D ata ................................................
1
1
3
3
MEASUREMENTS.........................................................................................
4
S e le c tio n o f P a ra m e te rs f o r M easurem ent ..................................................
Map M e a s u r e m e n ts .................................................
D rainage A rea . . . . . . . .
...............................................................
C hannel L ength ..............................................................................................
C hannel G ra d ie n t .................................
C o n c a v i t y ...........................................................................................................
R e l i e f .......................................................................
F ie ld M easurem ents .....................................................
C hannel C r o s s - s e c tio n ............................... . . . ................................
Bed M a te r ia l S i z e ............................................
....................... . . .
A d d itio n a l F ie ld P a ra m e te rs . . . . . . .
P r e c i p i t a t i o n I n d e x ...............................
4
5
5
6
6
6
7
7
8
10
12
12
GEOLOGIC AND HYDRAULIC CONDITIONS IN THE CHANNELS STUDIED...................
1?
W hetstone M ountains ..............................................................................................
M ustang M o u n ta in s ..................................................................................................
S i c r r i t a s .............................................................................................
Summary o f Downstream R e la tio n s . : ...................................
17
21
26
32
INTERRELATIONS AMONG PARAMETERS LEADING TO A NATURAL SUBDIVISION
OF DATA . •.....................................................................................................................
36
CONCEPT OF THE EPHEMERAL STREAM PROFILE..........................................................
44
Review o f P e r t i n e n t Work on L o n g itu d in a l P r o f i l e s ...........................
C o n tro ls on th e L o n g itu d in a l P r o f i l e ......................................................
S ig n if ic a n c e o f th e P o in t o f C o n ca v ity Change . 1........................... .
44
46
48
IV.
V
TABLE OF CONTENTS— C ontinued
Page
Summary . . . . . . . . . . . . . . . . . . . . .
53
DEVELOPMENT OF EMPIRICAL EXPRESSIONS FOR THE PROFILES
54
TEST OF THE PROFILE EQUATIONS .................... . . . . . . .
63
CONCLUSIONS .......................................................................................... ;
71
......................................
........................
REFERENCES
. . . . . .
APPENDIX I
........................ ...................... ................................ ....
. .
76
APPENDIX I I .....................................................................................
. .
78
74
LIST OF ILLUSTRATIONS
Figure
Page
1•In d e x Map Showing L o c a tio n s M entioned i n T ex t .......................................
2
2.
V a r ia tio n o f P r e c i p i t a t i o n w ith E le v a tio n i n t h e S tu d y A rea .
14
3.
L o c a tio n Map f o r S tream s and S t a t i o n s i n t h e W hetstone
M ountains
........................
18
L o n g itu d in a l P r o f i l e s (A) and C o n c a v itie s (B) i n t h e
W hetstone M o u n ta in s ....................................................................
19
Change o f D rain ag e A rea, P a r t i c l e S iz e and W id th :d e p th R a tio
w ith C hannel L ength i n th e W hetstone M ountains . . . . .
20
L o c a tio n Map f o r S tream s and S t a t i o n s i n t h e M ustang
M ountains ......................................................... ...................................................
22
L o n g itu d in a l P r o f i l e s (A) and C o n c a v itie s (B) i n th e
Mustang M o u n t a in s .............................................................
24
Change o f D rain age A rea, P a r t i c l e S iz e and W idth:depth R a tio
w ith C hannel L ength i n t h e Mustang M o u n t a i n s ................... ....
25
L o c a tio n Map f o r Stream s and S t a t io n s i n th e S i e r r i t a
M ountains .............................................................................................................
27
L o n g itu d in a l P r o f i l e s (A) and C o n c a v itie s (B) i n th e
S i e r r i t a M o u n t a i n s ....................... .............................................................
30
Change o f D rain age A rea, P a r t i c l e S iz e and W idth:depth R a tio '
w ith C hannel L ength i n t h e S i e r r i t a M ountains ........................
31
R e la tio n o f Mean P a r t i c l e S iz e (A) and W id th :d e p th R a tio (B)
t o C hannel G r a d ien t . . . . . . . . . . . . . . . . . . .
37
R e la t io n o f D rain age Area (A) and A r o a s r e li e f 2 R a tio (B) t o
C hannel G ra d ie n t ...................................
38
R e la tio n o f Channel G ra d ien t a t a G iven D is ta n c e from th e
D iv id e t o B a sin R e l i e f and L ength ....................................................
39
R e la t io n B etw een Mean P a r t i c l e S iz e and W idth:depth R a tio • .
41
4.
56.
7.
8.
9.
10.
11.
12.
13«
14.
15»
vi
v ii
LIST OF ILLUSTRATIONS— C o n tin u ed
F ig u re
16.
17.
18.
19*
Page
R e la tio n o f C um ulative T r ib u ta r y D e n sity t o C hannel L ength
and C o n cav ity C h a n g e ................................................................... .... .
49
L o c a tio n Map f o r S tream s and S t a t i o n s i n C a ta lin a and
Tucson M ountains ..................................................................................... •
64
Com parison o f R e a l and P r e d ic te d P r o f i l e s i n C a ta lin a
M ountains .......................................................................
6?
Com parison Between R e a l and P r e d ic te d P r o f i l e s i n th e
Tucson M ountains ..............................................................
68
H ST OF TABLES
Table
Page
1 . E le v a tio n Zones f o r t h e P r e c i p i t a t i o n In d e x V a lu es . . . . . .
15
2 . Summary o f L o c a tio n s o f M ajor ch an g es i n t h e L o n g itu d in a l
V a r ia tio n o f P a ra m e te rs and T h e ir R e la tio n s t o Bedrock . .
33
3 . R e l i e f :le n g th R a tio s o f th e C o n ca v ity Segm ents . ...........................
40
4 . Com parison o f th e A c tu a l C hannel L en g th from D iv id e to
C o n ca v ity Change w ith Those P r e d ic te d from C um ulative
T r ib u ta r y D e n s ity ....................... . . . . . . . . . . . . . .
49
5 . C om parison o f P r o f i l e C o n c a v ity , R a te o f D rain ag e A rea
I n c r e a s e and R a te o f P a r t i c l e S iz e D ecrease . . . . . . .
52
6 . R e g re s s io n E q u a tio n s R e la tin g D rain ag e A rea, A, P a r t i c l e S iz e ,
Horn, W id th :d e p th R a tio , W/D, and G ra d ie n t, S, t o
C hannel L en g th , L ................................................................... ....
59
. 7 . C om parison o f R e a l and P r e d ic te d C o n c a v itie s . . . . . . . . .
v iii
61
ABSTRACT
The e x is te n c e o f two l o n g i t u d i n a l p r o f i l e segm ents o f d i f f e r e n t
c o n c a v ity i n ephem eral s tre a m s h e ad in g i n t h e m o u n ta in s o f s o u th e a s te r n
A riz o n a i s shown t o b e r e l a t e d t o t h e l o n g i t u d i n a l v a r i a t i o n o f d ra in a g e
a r e a . A, bed m a t e r i a l s i z e ,
and c h a n n e l w id th :d e p th r a t i o , W/D.
These p a ra m e te rs a p p ro x im a te d is c h a r g e , sed im en t lo a d and ro u g h n e s s,
w hich have b een fo u n d t o c o n t r o l th e p r o f i l e i n o th e r r e g io n s , b u t
w ere u n a v a ila b le f o r t h i s s tu d y .
I n c lu s io n o f b a s in r e l i e f , R, and l i t h o l o g y allo w ed developm ent
o f s t a t i s t i c a l l y s i g n i f i c a n t e q u a tio n s f o r b o th segm ents o f stre a m s
d r a in in g g r a n i t i c and se d im e n ta ry t e r r a i n s :
S e d im e n ta ry co n cav e:
S = ( 6 .6 x 1 0 -5 )R '8 0 D ;m ,'2 0 (w /D )'^
(D
^40
S e d im e n ta ry s t r a i g h t :
S = ( 1 .4 x 1Ct 3 ) r »3 8 ^ . 2 6
(2 )
G r a n itic co n cav e:
5 = ( 7 .6 x l0 ~ 6 )R1 *02]^nm‘ 2 8 (w /D )‘ 22
(3 )
G r a n itic s t r a i g h t :
s = (1.6 x 10™3)Re/j'2i^mi062
ix
w
P r o f i l e s o f s tre a m s w ith known l i t h o l o g y and r e l i e f i n two
a d d i t i o n a l m o u n tain ra n g e s w ere p r e d ic te d from th e e q u a tio n s w ith an
a c c u ra c y w ith in t h e l i m i t s o f a c c u ra c y o f th e f i e l d and map
m easurem ents.
P r e c i p i t a t i o n - e l e v a t i o n r e l a t i o n s have no a p p a re n t
e f f e c t on th e a c c u ra c y o f th e p r e d i c t i o n s o r on s tr e a m - p r o f ile
c o n c a v ity .
INTRODUCTION
Purpose
The lo n g it u d in a l p r o f i l e s o f t h e ephem eral strea m s d r a in in g
t h e m ou n tain s and a l l u v i a l v a l l e y s i n s o u th e a s te r n A rizon a a r e u n u su a l.
R ather th a n a c o n s ta n t r a t e o f d e c r e a s e o f g r a d ie n t downstream , or
c o n s ta n t c o n c a v ity , t h e s e p r o f i l e s have one c o n c a v ity from t h e d i v i d e .
t o a p o in t n ea r t h e m ountain f r o n t and a n o th e r , much lo w er c o n c a v ity
b elo w t h i s p o in t .
T h is s tu d y was u n d erta k en t o d eterm in e w hether t h e
change i n c o n c a v ity i s r e l a t e d t o h y d r a u lic and g e o lo g ic c o n d it io n s .
lo c a tio n
. The t h r e e m ountain r a n g e s s t u d ie d , th e W h etsto n es, M ustangs and'
S i e r r i t a s ( F ig . 1 ) , c o n ta in strea m s w ith segm ented p r o f i l e s .
The
W hetstone M ountains a r e lo c a t e d on t h e B enson, A rizo n a , q u ad ran gle
( 1 : 6 2 ,5 0 0 ) , some 45 m il e s s o u th e a s t o f T ucson.
Stream s on t h e e a s t s id e
o f t h e ran ge d r a in in g in t o t h e San Pedro R iv er w ere s t u d ie d .
The
Mustang M ountains a re im m ed ia te ly so u th o f th e W h etsto n es, s e p a r a te d
from th e n by R ain V a lle y .
They a r e mapped on t h e Mustang M ountains and
E lg in , A rizo n a , q u a d r a n g les a t 1 : 2 4 ,0 0 0 .
o r i e n t a t i o n s were m easured.
Two d r a in i n t o th e Babocom ari R iv e r , and
t h e t h ir d d r a in s i n t o R ain V a lle y .
i n t o t h e San P ed ro.
Three strea m s w ith d iv e r s e
B oth o f t h e s e strea m s i n tu r n f lo w
The S i e r r i t a s a r e lo c a t e d on th e Twin B u t t e s ,
A rizo n a , 1 :6 2 ,5 0 0 q u a d r a n g le, 25 m ile s so u th o f T u cson .
Three main and
fo u r s m a lle r strea m s d r a in in g e a s t t o t h e S an ta Cruz R iv er w ere s t u d ie d .
1
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INDEX MAP SHOWING LOCATIONS MENTIONED IN TEXT,
3
C o lle c tio n o f D a ta
M easurem ents w ere made on a c c e s s ib le s tre a m s .
S ta tio n s f o r
m easurem ent w ere s e l e c t e d a r b i t r a r i l y alo n g th e l e n g th o f each s tre a m ,
b u t an a tte m p t was made t o sp ace them u n ifo rm ly w ith in each p r o f i l e
segm ent.
G e n e ra lly , a b o u t th e same number w ere e s t a b l i s h e d above and
below th e change i n c o n c a v ity .
A lo n g e r sp a c in g i n t e r v a l was u s e d i n .
th e lo w -c o n c a v ity segm ents s in c e th e y a r e lo n g e r th a n th e h ig h -c o n c a v ity
seg m en ts.
F ig u r e s 3» 6 and 9 show t h e s t a t i o n l o c a t i o n s .
F ie ld work was done d u rin g th e w in te r and s p rin g m onths o f
1968 - 1 969 .
I n g e n e r a l, th e f u l l u p stre am segm ent and p a r t o f th e
dow nstream segm ent o f e a c h stre a m was w alk ed , w h ile th e re m a in d e r was
s p o t checked due t o t h e lo n g d is ta n c e in v o lv e d .
S in c e th e em phasis was
on d e te rm in in g th e c au se o f t h e c o n c a v ity ch an g e, th e f i e l d
i n v e s t i g a t i o n s w ere c o n c e n tr a te d aro u n d t h e a r e a o f ch an g e.
No s t a t i o n s
w ere e s t a b l i s h e d more th a n s i x m ile s from th e te r m in a tio n o f t h e h ig h c o n c a v ity segm ent.
D ata su p p le m e n ta l t o f i e l d m easurem ents were
o b ta in e d d i r e c t l y from to p o g ra p h ic m aps.
P r e s e n ta ti o n o f D ata
The d a ta was i n i t i a l l y h a n d le d g r a p h i c a l l y , and m ost o f th e
in f o r m a tio n f o r i n d i v i d u a l s tre a m s i s p re s e n te d i n t h i s m anner.
However, a s th e sam ple p o p u la tio n and th e number o f v a r i a b l e s i n c r e a s e s ,
i t becomes in c r e a s i n g l y d i f f i c u l t t o show t h e r e l a t i o n s g r a p h ic a ll y .
C o n se q u e n tly , th e d a ta was p ro c e s s e d by a com puter t o g e t s ta n d a rd
r e g r e s s io n r e l a t i o n s f o r th e more com plex s i t u a t i o n s .
MEASUREMENTS
S e le c t io n o f P a ra m e te rs f o r M easurem ent
S tu d ie s by L eopold and Haddock (1953)* Wblman (1955)* L eopold
and M ille r (1 9 5 6 ), Hack (1 9 5 7 ), L eopold and Y/olman (1 9 5 7 ), M ille r
(1 9 5 8 ), and B rush ( I 96 I ) have in d i c a t e d t h a t a s tr e a m 's l o n g i t u d i n a l
p r o f i l e i s a d ju s te d t o d is c h a r g e , v e l o c i t y , sed im en t lo a d , and c h a n n e l
ro u g h n e ss and shape a s w e ll a s l i t h o l o g y , r e l i e f and c lim a te .
W hile
many o f th e s e p a ra m e te rs can be r e a d i l y o b se rv e d i n ephem eral c h a n n e ls ,
th e r e l a t i v e in fr e q u e n c y o f flo w makes d i r e c t m easurem ent o f th e
h y d r a u lic f e a t u r e s , d is c h a r g e , v e l o c i t y , lo a d and ro u g h n e s s, to o
d i f f i c u l t f o r a co m p reh en siv e, s h o r t- te r m s tu d y .
Hence means f o r
a p p ro x im a tin g flo w p a ra m e te rs from th e d ry s ta g e were so u g h t.
L eopold
and M ille r (1956, p . 23) c i t e a s tu d y by H. H. Hudson (u n p u b lish e d )
w hich shows a c o n s ta n t r e l a t i o n e x i s t s b etw een d ra in a g e a r e a and
d is c h a rg e i n ephem eral s tr e a m s :
w here betw een + .7 and + .8 .
Q oC A *^.
The ex p o n en t v a r i e s - e l s e - -
I n p e r e n n ia l s tre a m s , th e r e l a t i o n i s a g a in
v e ry c o n s i s t e n t , b u t w ith an exponen t o f a b o u t +1’. 0 (L eo p o ld , Wolman
and M ille r , 1964, p . 2 5 1 ).
Hence d ra in a g e a r e a s h o u ld bo a good in d e x
o f d is c h a r g e .
T h is r e l a t i o n , how ever, i s c o m p lic a te d by two f a c t o r s .
F irs t,
th e c lim a te i n s o u th e a s te r n A rizo n a i s d i r e c t l y d ep en d en t on e le v a t i o n ,
so t h a t a stre a m flo w in g from h ig h m o u n tain s i n t o a r e l a t i v e l y lo w b a s in
w i l l r e c e iv e more r a i n f a l l and p ro b a b ly more r u n o f f i n i t s h e ad w a te rs
th a n i t w i l l a t low er p o i n t s alo n g i t s . p a t h .
S eco n d ly , when flo w o c c u rs
5
a c r o s s t h e a l l u v i a l p o r t i o n s o f a b a s i n , w a te r i s l o s t by b o th
i n f i l t r a t i o n and e v a p o r a tio n .
The e f f e c t o f th e f i r s t f a c t o r w i l l b e
in c lu d e d by r e l a t i n g p r e c i p i t a t i o n and e l e v a t i o n , b u t th e second i s
e x tre m e ly d i f f i c u l t t o d e te rm in e from d ry s tre a m s and w i l l b e d is c u s s e d
o n ly q u a l i t a t i v e l y i n t h i s p a p e r .
P u b lis h e d s tu d ie s o f t h i s phenomena
in c lu d e Babcock and G ushing (1 9 4 2 ), K eppel and R en ard (1962) and R enard
and K eppel (1 9 6 6 ).
Sedim ent lo a d s h o u ld a ls o b e r e l a t e d to d ra in a g e a r e a , a s th e
m a t e r i a l a v a i l a b l e f o r t r a n s p o r t i n c r e a s e s w ith a r e a .
L eopold and
Haddock (1953* p . 42) i n d i c a t e t h a t i n c h a n n e ls w ith c o a rs e bed
m a t e r i a l , su ch a s th o s e o f t h e s tu d y a r e a , ro u g h n e ss i s l a r g e l y a
f u n c tio n o f th e s iz e o f m a t e r i a l .
F i n a l l y , th e c r o s s - s e c t i o n a l shape
o f t h e c h an n e l i s r e l a t e d t o ro u g h n e s s, v e l o c i t y d i s t r i b u t i o n s and th u s
p ro b a b le sedim ent lo a d .
Hence d ra in a g e a r e a , p r e c i p i t a t i o n , b ed
m a t e r i a l s iz e and c h a n n e l shape w i l l be s u b s t i t u t e d f o r th e h y d r a u lic
p a ra m e te rs .
Map M easurem ents
D rainage Area
\
The d ra in a g e a r e a u p stre am from each o f t h e s t a t i o n s was
m easured from U .S .G .3 . to p o g ra p h ic maps u s in g a com pensating p o la r
p la n im e te r .
T h is in s tru m e n t i s a c c u r a te t o .01 s q u a re in c h e s , o r ab o u t
.01 sq u a re m ile s on 1 :6 2 ,5 0 0 maps and .001 sq u are m ile s on 1 :2 4 ,0 0 0
m aps.
G e n e ra lly o n ly one o r two m easurem ents were made a s th e
in s tru m e n t showed g r e a t c o n s is te n c y i n t h e v a lu e s m easu red .
c a s e s ,- v a r i a b i l i t y due to m easurem ent was l e s s th a n 5^*
I n m ost
6
Channel Length
C hannel le n g th s w ere m easured d i r e c t l y from th e to p o g ra p h ic
m aps, a llo w in g an a c c u ra c y t o ±100 f e e t on 1 :62,500 maps and ±$0 f e e t on
1 :2 4 ,0 0 0 maps.
M easurem ent v a r i a b i l i t y n e v e r ex ceed s 10$ n e a r t h e
d iv id e and i s g e n e r a lly l e s s th a n 2$.
C hannel G ra d ie n t
S tream g r a d ie n t was d e fin e d a s th e a v erag e c h a n n e l s lo p e betw een
t h e p o in t on t h e c h a n n e l t h r e e t o f i v e c o n to u r l i n e s above a s t a t i o n and
th e p o in t an e q u a l number o f l i n e s b elo w th e s t a t i o n .
I n c lu s io n o f
s e v e r a l c o n to u r i n t e r v a l s "produces an a v e ra g in g e f f e c t w hich sm ooths o u t
some o f th e l o c a l v a r i a t i o n and a ls o re d u c e s th e e r r o r due t o .
m easurem ent.
S in c e t h e g r a d ie n t i s sim p ly f a l l , o r v e r t i c a l d ro p ,
d iv id e d by c h a n n e l le n g th , t h e e r r o r w i l l be a p p ro x im a te ly th e same a s ,
o r s l i g h t l y l a r g e r th a n , t h a t f o r c h a n n e l le n g th a lo n e .
C o n cav ity
The l o n g i t u d i n a l p r o f i l e o f a stre a m i s th e r e l a t i o n betw een
f a l l , H, and l e n g t h , L.
p r o f i l e e q u a tio n , dH/dL.
G ra d ie n t i s sim p ly th e f i r s t d e r i v a t i v e o f t h e
Hack (1957) d e fin e d c o n c a v ity a s th e ex p o n en t
n i n th e power f u n c tio n r e l a t i n g g r a d i e n t , S, and stre am le n g th , L,
S = kLn .
G r a p h ic a lly , t h i s i s r e p r e s e n te d by t h e s lo p e o f th e l i n e
form ed when g r a d ie n t i s p l o t t e d a g a in s t l e n g th on lo g a r ith m ic
c o o r d in a te s .
I n e s s e n c e , n i s a f u n c tio n o f th e r a t e o f change o f
g r a d ie n t w ith l e n g t h , dS/dL , th e second d e r i v a t i v e o f t h e p r o f i l e
e q u a tio n .
C o n c a v ity , a s u sed i n t h i s p a p e r, w i l l r e f e r t o n , th e power
f u n c tio n e x p o n e n t.
The e r r o r s due t o m easurem ent o f b o th le n g th and
7
g r a d ie n t a r e th u s in c lu d e d i n c o n c a v ity .
However, th e in a c c u ra c y
r e s u l t i n g from f i t t i n g a l i n e t o a s c a t t e r o f p o i n t s o v e r r id e s th e s e
e r r o r s and l i m i t s d e te r m in a tio n o f c o n c a v ity to t h e n e a r e s t t e n t h .
R e lie f
R e l i e f i s d e f in e d a s t h e d i f f e r e n c e i n e l e v a t i o n betw een a
s p e c i f i e d p o in t on a stre a m and th e p o in t w here th e d ra in a g e d iv id e i s
m et by e x te n s io n o f t h e s tr e a m 's lo n g e s t headw ard t r i b u t a r y .
R e l i e f was
m easured to t h e n e a r e s t 25 f e e t on 25 f o o t c o n to u r i n t e r v a l maps and th e
n e a r e s t 50 f e e t on th o s e w ith c o n to u r i n t e r v a l s g r e a t e r th a n 25 f e e t .
The a c c u ra c y o f th e map e le v a tio n s i s w e ll w ith in th e s e l i m i t s s o , i n
e f f e c t , th e r e i s n e g l i g i b l e m easurem ent e r r o r in v o lv e d i n r e l i e f .
F i e ld Measurements
F i e l d m easurem ents w ere made a t t h e s t a t i o n s ch o sen from t h e
m aps.
An a tte m p t was made t o s e l e c t a r e p r e s e n t a t i v e 100 f o o t r e a c h
from a s t r a i g h t s e c tio n o f t h e c h a n n e l n e a r th e map l o c a l i t y .
I f pool
and r i f f l e p a t t e r n s w ere fo u n d , e q u a l numbers o f each f e a t u r e w ere
in c lu d e d i n th e s e c tio n .
Where th e c h a n n e l a l t e r n a t e d betw een a s in g le
c h a n n e l and b r a id e d r e a c h e s , th e s e c tio n chosen in c lu d e d b o th f e a t u r e s .
For co n v en ien ce i n f u l l y b r a id e d r e a c h e s , th e s e c tio n w ith th e n a rro w e s t
i s l a n d s was ch o sen to a llo w c o n t i n u i t y i n c h a n n e l w id th m easurem ents.
S in c e th e a c t u a l f i e l d m easurem ents w ere r a r e l y made a t p r e c i s e l y th e
map p o i n t , a s m a ll l o c a t i o n e r r o r i s added t o th e m easurem ent e r r o r
o f c h a n n e l le n g th .
.
8
Channel C r o s s - s e c t io n
To m easure a ch a n n el c r o s s - s e c t i o n , one m ust f i r s t d e f in e t h a t
c h a n n e l’ s banks i n a way t h a t w i l l be v a l i d f o r o th e r str e a m s.
If a
dominant f lo o d l e v e l , s im ila r t o th e b a n k f u ll s t a g e o f p e r e n n ia l str e a m s,
e x i s t s i n a c h a n n e l, i t sh o u ld le a v e d i s t i n c t t r a c e s on t h e v e g e t a t io n
and a llu v iu m o f t h e b a n k s.
B ecau se o f t h e i r lo w er fr e q u e n c y , h ig h e r
f lo o d s would b e r e p r e s e n te d by l e s s d i s t i n c t t r a c e s , w h ile s m a lle r , more
fr e q u e n t f lo o d s would le a v e t r a c e s b elo w th e b a n k f u ll l e v e l w hich w ould
be d e s tr o y e d by a b a n k f u ll f l o o d .
A pronounced f lo o d l e v e l d o es e x i s t
on t h e banks o f a l l t h e strea m s s t u d ie d , b u t i t becom es p r o g r e s s iv e ly
h ard er t o t r a c e u p stream .
I n g e n e r a l, th e m ost common marker i s th e
l e v e l o f v e g e t a t i v e f lo o d d e b r is ca u g h t on brush o r wedged betw een r o c k s
on t h e b an k s.
S in c e t h e m a t e r ia l f l o a t s , i t m ust mark t h e w ater
s u r fa c e a t some tim e d u rin g t h e f lo o d .
The s i g n i f i c a n c e o f t h e f l o a t i n g d e b r is l i n e s i s su p p o rted by
th e freq u en cy o f o ccu re n c e o f o th e r in d ic a t o r s a t th e same l e v e l .
Abrupt ch an ges i n v e g e t a t io n d e n s it y o r ty p e occu r a t th e f lo o d - d e b r is
le v e l.
O ften l e s s r e s i s t a n t p la n t s su ch a s m o sses or f i n e g r a s s e s grow
above t h i s l e v e l , b u t n o t b elo w i t .
s i g n i f i c a n t ch a n g es h e r e a l s o .
Bank m a t e r ia ls commonly show
Below t h e f lo o d - d e b r is l e v e l , f i n e sand
and o th e r o b v io u s f l u v i a l d e p o s it s occu r f r e q u e n t ly , w h ile above i t few
can b e fou n d.
In a d d it io n , t h e r e may be a c o lo r change i n th e f i n e
m a te r ia l com posing t h e banks w hich a g r e e s w ith th e f lo o d d e b r is .
U pstream , a s t h e s e in d ic a t o r s become l e s s fr e q u e n t, c e r t a in c a c t i appear
t o b e u s e f u l m ark ers.
I n p a r t ic u l a r , t h e agave seem s u n a b le t o s u r v iv e
b elo w th e b a n k f u ll l e v e l .
D efin ed on t h e b a s is o f t h e s e in d i c a t o r s , th e
9
b a n k f u ll l e v e l shows no p a r t i c u l a r r e l a t i o n t o t e r r a c e s .
I t can o c cu r
a t a t e r r a c e l e v e l , above i t , below i t , o r o c c a s io n a ll y , betw een two
te rra c e s .
However, a t s t a t i o n s w here th e b a n k f u ll s ta g e o c c u rs a t a
t e r r a c e l e v e l , th e c o in c id e n c e re m a in s c o n s i s t e n t th ro u g h o u t t h e .
re a c h s tu d ie d .
Once b a n k f u ll s ta g e was d e f in e d in d e p e n d e n tly on each b an k , a
l i n e was s t r e t c h e d t a u t betw een th e two p o i n t s p e r p e n d ic u la r to th e
d i r e c t i o n o f flo w .
As a f i n a l check on th e v a l i d i t y o f th e b a n k f u ll
p o s i t i o n , th e l i n e sh o u ld b e l e v e l i n s t r a i g h t r e a c h e s .
W idth was
m easured to th e n e a r e s t h a l f f o o t , and d e p th was m easured t o th e
n e a r e s t in c h a t one f o o t i n t e r v a l s alo n g th e l i n e .
I f th e c h a n n e l was
b r a id e d , th e n th e l i n e was s t r e t c h e d c o n tin u o u s ly a c r o s s a l l c h a n n e ls
p e r p e n d ic u la r t o th e o v e r a l l d i r e c t i o n o f flo w .
Those c h a n n e ls i n
w hich flo w o c c u rre d a t b a n k f u ll s ta g e w ere m easured and t o t a l c h a n n e l
w id th was th e sum o f t h e in d i v i d u a l c h a n n e l w id th s .
G e n e ra lly , th r e e
c r o s s - s e c t i o n s w ere m easured a t a r b i t r a r i l y ch o sen p o in ts a t t h e u p p er
and lo w er ends and th e m id d le o f th e 100 f o o t r e a c h .
A verage d e p th and
th e w id th :d e p th r a t i o w ere com puted f o r each c r o s s - s e c t i o n .
The mean
v a lu e o f w id th , d e p th and w id th :d e p th r a t i o f o r th e re a c h i s sim ply
th e a v erag e o f th e v a lu e s a t each p o i n t .
V a ria n c e o f means made on
re a c h e s where more th a n t h r e e c r o s s - s e c t i o n s were m easured i n d ic a te d a
sample o f th r e e g e n e r a lly had a v a r i a t i o n o f
a b o u t th e mean.
I n c r e a s in g th e sam ple s i z e w ould d e c re a s e th e e r r o r , b u t n o t
s i g n i f i c a n t l y u n t i l many more c r o s s - s e c t i o n m easurem ents were added.
S in c e t h i s s tu d y d e a ls o n ly w ith v e ry g ro s s r e l a t i o n s , g r e a t e r a c c u ra c y
was n o t deemed n e c e s s a r y , and th e sam ple s iz e was s e t a t t h r e e .
10
Bed M a te r ia l S iz e
'
P a r t i c l e s i z e d i s t r i b u t i o n was d e te rm in e d u s in g th e sam pling
m ethod s o t f o r t h by Wolman (195*0*
A g r i d was e s t a b l i s h e d i n th e
c h a n n e l bed by m aking a s e r i e s o f p a c in g t r a v e r s e s .
At e v e ry second
s tr id e * a sam ple was ta k e n by p ic k in g up th e f i r s t p a r t i c l e to u c h e d
when th e f i n g e r s w ere e x te n d e d o v e r th e t o e o f t h e b o o t.
m e d ia te a x is was m easured and r e c o r d e d .
The i n t e r ­
When one t r a v e r s e was
c o m p leted , th e n e x t was ru n i n th e o p p o s ite d i r e c t i o n and p a r a l l e l t o
i t . two s t r i d e s away.
To m in im ize th e sam pling e r r o r due t o o r ie n te d
d i s t r i b u t i o n s o f m a t e r i a l , t r a v e r s e s w ere ru n p e r p e n d ic u la r t o th e
arran g em en t o f m a t e r i a l s i z e s on th e b e d .
Thus i f c h a n n e l c o n f ig u r a tio n
was e s s e n t i a l l y p o o ls and r i f f l e s , t h e t r a v e r s e s w ere ru n p a r a l l e l t o
th e c h a n n e l b a n k s.
On t h e o th e r han d , c h a n n e ls w hich w ere dom inated by
g r a v e l b a r s o r b o u ld e r t r a i n s p a r a l l e l t o flo w w ere sam pled w ith
t r a v e r s e s p e r p e n d ic u la r t o t h e b a n k s.
T h is p ro c e d u re re d u c e d th e
p o s s i b i l i t y o f w e ig h tin g t h e sam ple to w ard g r a v e l, a s an exam ple, by
m aking one e n t i r e sam pling t r a v e r s e a lo n g th e le n g th o f a g r a v e l b a r .
S in c e th e m a t e r i a l i n m ost s tre a m s h a s a lo g -n o rm a l
d i s t r i b u t i o n , i t i s m ost c o n v e n ie n t t o re c o r d th e in te r m e d ia te a x is i n
a lo g a r ith m ic c l a s s i f i c a t i o n .
The W entworth p h i - s c a l e was u se d a s i t i s
th e m ost common and g e n e r a lly re d u c e d t h e d i s t r i b u t i o n t o a norm al o n e.
The p h i s i z e i s d e f in e d a s -lo g ? !)__ w here D
i s t h e p a r t i c l e 's
d ia m e te r i n m illi m e t e r s (F o lk , I 965 , p . 25 ) .
P a r t i c l e s i z e i s th o u g h t t o b e r e l a t e d t o b o th c h a n n e l ro u g h n e ss
and sed im en t lo a d .
B oth w ould b e m ost c l o s e ly r e l a t e d t o t h e p a r t i c l e s
11
on th e s u r f a c e o f th e channel- b ed .
VJblman’ s m ethod was ch o sen b e ca u se
i t a llo w s r e l a t i v e l y q u ic k , e a s y and a c c u r a te sam pling o f t h i s v e ry
f e a t u r e i n c o a rs e m a t e r i a l , and do es n o t r e q u ir e t r a n s p o r t i n g heavy
sam ples t o th e l a b .
R oughness m ig h t be c o n t r o l l e d m a in ly by t h e c o a rs e
f r a c t i o n o f th e b ed m a t e r i a l , r e p r e s e n te d b y
o r s i z e l a r g e r th a n 84$ o f th e p a r t i c l e s .
t h e 8 4 th p e r c e n t i l e ,
On th e o th e r han d , th e
m a te r ia l s iz e m ost r e p r e s e n t a t i v e o f t h a t b e in g moved d u rin g a f lo o d
w ould m ost l i k e l y b e a mean s i z e , s in c e th e m a jo r ity o f m a t e r i a l on th e
stre am bod i s t r a n s p o r t e d .
(^16 + ^50 +
Mean s i z e , d e fin e d by F o lk (1965) a s
and f$Q4 w ere d e te rm in e d f o r each s t a t i o n .
I t was
found t h a t t h e r e was alm o st a c o n s ta n t r a t i o betw een th e two s iz e
p a ra m e te rs .
Only i n t h e f a r t h e s t u p stre a m re a c h e s does t h i s r a t i o
ch an ge, owing t o th e p o o re r s o r t i n g o f m a t e r i a l t h e r e .
I n a d d itio n , t h e
d e v ia t io n s from th e r a t i o o f t h e s i z e p a ra m e te rs show no s i g n i f i c a n t
r e l a t i o n s t o th e o th e r p a ra m e te rs .
I t was c o n clu d ed t h a t th e two s iz e
m easurem ents a r e p ro b a b ly f u n c tio n s o f th e same c o n t r o l s and a r e n o t
b o th n e c e s s a ry .
C o n se q u e n tly , o n ly th e more g e n e r a l mean p a r t i c l e s iz e
w i l l be c o n s id e re d l a t e r i n th e p a p e r.
V a r ia tio n o f means i n d i c a t e s t h a t a sam ple o f 100 p a r t i c l e s
would g iv e a mean a c c u r a te t o w it h in 10$ a t m ost o f t h e s t a t i o n s
m easured, w h ile a sam ple o f 50 i s a c c u r a te t o w it h in 1 8$.
The in c r e a s e
i n a ccu ra cy w hich w ould r e s u l t from a sam ple la r g e r th a n 100 was n o t
deemed n e c e s s a r y f o r t h e g e n e r a l n a tu r e o f t h i s s tu d y .
s i z e o f 100 p a r t i c l e s was g e n e r a lly u s e d .
Thus a sam ple
In c a s e s o f e x tre m e ly good
s o r t in g , or where t h e ch a n n el bed had v e r y sm a ll a r e a l e x t e n t , o n ly 50
12
p a r t i c l e s w ere m easured.
As a r e s u l t , e r r o r o f m easurem ent n e v er
ex ceed s 18$ and i s g e n e r a lly a b o u t 10$.
A d d itio n a l F ie ld P a ra m e te rs
C hannel g r a d ie n t i n each 100 f o o t re a c h was a ls o m easured i n t h e
f i e l d u s in g a B runton compass a s hand l e v e l .
The r e s u l t i n g s lo p e s
showed g r e a te r v a r i a t i o n th a n th e map m easu rem en ts, b u t i n g e n e r a l t h e r e
was good agreem ent betw een t h e tw o.
No tr e n d s w ere found betw een t h e
d e v ia tio n o f f i e l d g r a d ie n t from map g r a d ie n t and th e o th e r c h a n n e l
p a ra m e te rs , so t h e d e v ia t io n a p p a r e n tly r e f l e c t s o n ly th e r e l a t i v e
in a c c u ra c y o f th e h a n d - le v e l m ethod.
C o n se q u e n tly , map g r a d ie n t was
u se d t o r e p r e s e n t th e g r a d ie n t a t each s t a t i o n .
G ross e s tim a te s o f t h e d e n s i t y o f v e g e ta tiv e co v er on th e
r e g io n a l s lo p e , c h a n n e l banks and bed w ere made a t each s t a t i o n .
In
a d d i t i o n , q u a l i t a t i v e o b s e r v a tio n s com paring th e s iz e and d i s t r i b u t i o n
o f m a t e r i a l on th e banks t o t h a t on th e bed w ere re c o rd e d .
P r e c i p i t a t i o n In d e x
S t u d ie s i n t h e C a ta lin a M ountains by L. J . B a tta n and C. Green
o f th e Department o f A tm ospheric P h y s ic s a t th e U n iv e r s it y o f A rizo n a
in d ic a t e d a c l o s e r e l a t i o n b etw een p r e c i p i t a t i o n and e l e v a t io n d u rin g
summer r a in s to r m s .
I n s o u th e a s te r n A rizo n a , summer r a i n f a l l i s more
p l e n t i f u l and in t e n s e th a n t h a t i n any o th e r se a s o n . * M onthly
p r e c i p i t a t i o n i n J u ly and A ugust e x c e e d s t h r e e in c h e s on th e a v era g e a t
th e s t a t i o n s s t u d ie d by Green and S e l l e r s (1 9 6 4 , p . 13) w h ile i t i s o n ly
about one in c h i n t h e w in te r m onths.
As a r e s u l t , m ost flo w s i n t h e
stream s s t u d ie d p ro b a b ly o ccu r i n th e summer.
A ll a v a il a b l e summer
13
p r e c i p i t a t i o n d a ta f o r s i t e s c lo s e t o th e s tu d y a r e a w ere p l o t t e d
a g a in s t e l e v a t i o n .
These d a ta in c lu d e d p r e c i p i t a t i o n in fo r m a tio n from
th e U n iv e r s ity o f A riz o n a ’ s S a n ta R ita E x p e rim en ta l Range (G reen and
M a rtin , 196?) and G reen and S e l l e r s ’ (1964) d a ta from th e Apache Powder
Co, and E lg in , B enson, C an elo , F a irb a n k s , F o r t Huachuca, P a ta g o n ia and
Tom bstone, A rizona ( F ig . 1 ) .
S e v e ra l o f th e p r e c i p i t a t i o n g a g es i n t h e
tow ns have b een moved th ro u g h o u t th e y e a r s to p o i n t s o f d i f f e r e n t
e l e v a t i o n s , g iv in g a d d i t i o n a l r e f e r e n c e p o i n t s .
T o ta l r a i n f a l l f o r
J u ly and A ugust o f each y e a r was d iv id e d by 62 t o g iv e a v e ra g e d a i l y
p r e c i p i t a t i o n com parable t o t h e B a tta n and G reen d a t a .
The r e s u l t s w ere
p l o t t e d a g a in s t e l e v a tio n on a lo g - lo g s c a le ( F i g .2 ) .
T h is p l o t shows a
r e l a t i o n e x i s t s such t h a t lo g p r e c i p i t a t i o n = -3 * 5 3 + *70 lo g e le v a tio n
w here p r e c i p i t a t i o n i s g iv e n i n in c h e s /d a y and e le v a tio n i s i n f e e t .
The c o r r e l a t i o n c o e f f i c i e n t o f ,83 h a s a s i g n if ic a n c e o f 99»5$*
The
d a ta a ro l i s t e d i n A ppendix I .
The C a ta lin a p o i n t s a r e d is p e r s e d th ro u g h o u t t h e m o u n ta in s, so
an a tte m p t was made t o d e te rm in e i f any d i f f e r e n c e i n p r e c i p i t a t i o n
o c c u rre d due t o t h e l o c a t i o n w ith r e s p e c t t o th e m o u n tain m ass.
P o in ts
on th e n o r th and so u th s id e s o f th e ra n g e a re d i f f e r e n t i a t e d on f ig u r e 2
and t h e r e . i s no t r e n d a p p a re n t t o t h i s w r i t e r .
C o n seq u en tly i t was
d e c id e d t h a t e le v a tio n i s a m a jo r f a c t o r i n c o n tr o llin g , p r e c i p i t a t i o n
and th e agreem ent o f tow ns around t h e s tu d y a re a w ith th e d a ta from th e
C a ta lin a s and S a n ta R i t a s im p lie s t h i s i s a r e g io n a l r e l a t i o n s h i p .
It
w ould a p p e a r t o be a v a l i d assu m p tio n t h a t a s i m i l a r r e l a t i o n e x i s t s i n
th o m ou n tain s o f th e s tu d y a r e a .
14
ELEVATION
(FEET)
IOOOO
4000
3000
MEAN DAILY PRECIPITATION (IN.)
KEY
FIG. 2.
SANTA R IT A S AND
COMMUNITY GAGES
•
CATALINAS:
NORTH S ID E
SOUTH S ID E
©
©
VARIATION OF PRECIPITATION WITH ELEVATION INTHE STUDY AREA
15
A p r e c i p i t a t i o n in d e x was d e r iv e d from t h e r e l a t i o n shown i n
f ig u r e 2 .
The p r e c i p i t a t i o n v a lu e a t 3250 f e e t was a r b i t r a r i l y
eq u ated w ith 1 .0 and a l l o th e r e l e v a t i o n s w ere g iv e n co rr esp o n d in g
v a lu e s (T ab le 1 ) .
The p u rp o se o f t h e in d e x was m e r e ly t o make t h e
f i g u r e s e a s ie r t o h a n d le .
However, t h e p rop er in d e x f o r a s t a t i o n i s
n o t t h a t f o r t h e s t a t i o n ’ s e l e v a t io n .
A l l r u n o f f a t a s t a t i o n comes
from p o in t s o f h ig h e r e l e v a t io n and th u s h ig h e r p r e c i p i t a t i o n .
T ab le 1 .
E le v a t io n Zones f o r t h e P r e c ip it a t i o n In d ex V a lu es
Bounding
e le v a tio n s
(in c lu s iv e )
P r e c ip ita tio n
in d e x
Bounding
e le v a tio n s
(in c lu s iv e )
P r e c ip it a t i o n
in d e x
7000 - 6600
1 .7
4499 - 4000
1.2
6599 - 6000
1 .6
3999 - 3500
1.1
5999 - 5500
1 .5
3499 - 3100
1.0
5499 - 5000
1 .4
3099 - 2600
0 .9
4999 - 4500
1 .3
2599 - 2100
0 .8
A more v a l i d in d e x v a lu e w ould b e t h a t f o r t h e e l e v a t io n w hich d iv id e s
th e a r e a d r a in in g t o a s t a t i o n i n h a l f .
S in c e h a l f t h e a r e a r e c e i v e s
more p r e c i p i t a t i o n and h a l f r e c e i v e s l e s s , t h i s m id -a r e a in d e x sh o u ld
approxim ate th e mean in d e x f o r t h e d r a in a g e a r e a .
The d iv id in g
e l e v a t io n can b e e s tim a te d by e y e from t h e map t o t h e n e a r e s t 100 or
200 f e e t d ep ending on th e co n to u r i n t e r v a l .
As a t e s t o f t h i s m ethod,
th e a r e a w it h in a b a s in betw een each p a ir o f a c c e n te d co n to u r l i n e s was
m easured.
From t h e s e v a lu e s th e e l e v a t io n d iv id in g th e d r a in a g e a rea
i n h a l f was computed f o r each s t a t i o n .
The mean p r e c i p i t a t i o n in d e x
o b ta in e d was t h e same a s t h e e s tim a te d v a lu e i n ea ch c a s e .
16
The e r r o r in h e r e n t i n th e p r e c i p i t a t i o n in d e x can n o t be
e v a lu a te d h e r e .
The r a i n f a l l d a ta f o r t h e v a r io u s p o i n t s w ere n ad e
on d i f f e r e n t in s tr u m e n ts , by d i f f e r e n t o b s e r v e r s , a t d i f f e r e n t i n t e r v a l s
o f tim e , and a l l have d i f f e r e n t p e r io d s o f r e c o r d .
I n a d d itio n , no
p o in ts a c t u a l l y w ith in th e d ra in a g e b a s in s s tu d ie d w ere a v a i l a b l e , and
th e s im p lif y in g assu m p tio n i s b e in g made t h a t t h e p r e c i p i t a t i o n w hich
e f f e c t s d is c h a rg e a t a p o in t i s e s s e n t i a l l y th e a v erag e p r e c i p i t a t i o n
f o r th e e n t i r e a r e a d r a in in g t o t h a t p o i n t .
However, th e in d e x i s o f
such a g e n e r a l n a tu r e t h a t a d e v ia t io n o f ± .1 a llo w s a ra n g e o f o v er
1000 f e e t i n e le v a tio n .
I n m ost c a s e s , t h i s sh o u ld be an a d e q u a te
ra n g e o f d e v ia t io n to in c lu d e th e c o n t r o l l i n g p r e c i p i t a t i o n , and i t
i s g e n e r a lly l e s s th a n a 10$ v a r i a t i o n on t h e p r e c i p i t a t i o n in d e x .
GEOLOGIC AND HYDRAULIC CONDITIONS IN THE CHANNELS STUDIED
S t a t io n s i n t h e w ash es a re i d e n t i f i e d w it h a s i x f ig u r e co d e,
such a s W15200.
The l e t t e r i s t h e f i r s t l e t t e r o f t h e name o f t h e
m ountain r a n g e , i n t h i s c a s e , 'W hetstone.
The f i r s t d i g i t i s a number
a r b i t r a r i l y a s s ig n e d t o each stream w it h in a r a n g e , and t h e f i n a l fo u r
d i g i t s a re t h e , e l e v a t io n o f t h e s t a t i o n .
In c a s e s w here s t a t i o n s on
t r i b u t a r i e s have b een u s e d , t h e f i n a l d i g i t w i l l b e r e p la c e d b y a "T".
The r a t e s o f change o f d r a in a g e a r e a , p a r t i c l e s i z e and w id th :d e p th
r a t i o w ith ch a n n el le n g t h r e f e r , a s d o e s t h e r a t e o f change o f g r a d ie n t
w ith le n g t h , t o t h e exp on en t o f le n g t h , L, i n r e l a t i o n s o f t h e form
A
iP,
Lq , and w/D oc Lr .
param eter in c r e a s e s downstream .
When t h e exp on en t i s p o s i t i v e , th e
A ll t h e n aesu ram en ts r e f e r r e d t o i n
t h i s s e c t io n a re l i s t e d i n Appendix I I .
W hetstone M ountains
Of th e t h r e e strea m s s t u d ie d ( F ig . 3)» W hetstone 1 d r a in s
lim e s to n e and s a n d sto n e , w h ile W hetstone 2 and 3 d r a in g r a n it o id ig n e o u s
rock s.
The sed im en ta ry r o c k s f r a c t u r e i n t o b lo c k s up t o t h r e e m e te r s i n
d ia m e te r .
Along i t s lo w er r e a c h e s , W hetstone 1 flo w s th rou gh c o a r s e
a llu v iu m d e r iv e d from t h e s e r o c k s w hich c o n ta in s fra g m en ts w ith a
maximum s i z e o f about a m e te r .
ch a n n el b a n k s.
C a lic h e cem enting i s common i n th e
The ch a n n el i s n ev er b r a id e d and i s en tren ch ed b etw een
W15400 and W14480 w ith a maximum d ep th o f 35 f e e t a t W14780.
17
19
A.
good
C = CONCAVITY CHANGE
10 X = EXAGGERATION
HORIZONTAL SCALE
ELEVATION (F E E T )
7000
—
0
10000 '
-
6000
5000
4000
3000
03
CHANNEL LENGTH (F E E T )
G R A D IEN T ( F T . / F T . )
'
KEY
WHETSTONE I
w hetstone
a
WHETSTONE 3
O *—
I0 3
CHANNEL LENGTH (F E E T )
FIG. 4 .
LONGITUDINAL PROFILES (A) AND CONCAVITIES (B)
IN THE WHETSTONE MOUNTAINS
©
F ig . 5 .
Change o f D rainage A rea, P a r t i c l e S iz e and W id th :d e p th
R a tio w ith Channel L ength i n th e W hetstone M ountains
A, B and C show th e v a r i a t i o n w ith c h a n n e l le n g th o f
d ra in a g e a r e a , p a r t i c l e s i z e and w id th :d e p th r a t i o
r e s p e c t i v e l y . The lo c a t i o n o f t h e c o n c a v ity change i s
superim p o sed on A, and t h a t o f t h e downstream l i m i t
o f b e d ro c k exposed i n th e c h a n n e l, l a b e l l e d "lo w est
c h a n n e l b e d ro c k ", i s p la c e d on B t o show th e r e l a t i o n
o f th e s e f e a t u r e s t o th e l o n g i t u d i n a l change o f
d ra in a g e a r e a and p a r t i c l e s i z e .
B = LOWEST CHANNEL
________ BEDROCK
WHETSTONE I
WHETSTONE 2
WHETSTONE 3
O
DRAINAGE AREA (t.
WHETSTONE 2
TRIBUTARIES
CHANNEL LENGTH (F E E T )
C = CONCAVITY
CHANGE
IO T
CHANNEL LENGTH (F E E T )
FIG. 5 .
-
CHANNEL LENGTH (F E E T )
CHANGE OF AREA%PA RTICLE S IZ E AND WIDTH*. DEPTH RATIO'W ITH CHANNEL LENGTH IN W HETSTONE MOUNTAINS
8
21
The g r a n it o id r o c k s g e n e r a lly f r a c t u r e t o fra g m en ts la r g e r th an
t e n c e n t im e t e r s , w hich i n tu r n w ea th er t o p a r t i c l e s o f fo u r t o e ig h t
m il lim e t e r s .
As a r e s u l t , t h e bed m a t e r ia l shows a n o t ic e a b l e
b im o d a lity tow ard t h e head o f b o th W hetstone 2 and 3*
L o ca l in t r u s io n s
by sm a ll d ik e s o f more m a s s iv e , f in e r - g r a in e d ro ck a re more r e s i s t a n t t o
w e a th e r in g th an th e g r a n i t i c r o c k s ,
The a llu v iu m b elo w t h e m ou n tain s
on b o th strea m s i s f in e r - g r a in e d th a n i n W hetstone 1 .
B ra id in g i s t h e
dom inant ch a n n el form downstream from W24200 and W34200.
Entrenchm ent
i s minor on W hetstone 2 , b u t i s a s much a s tw e n ty f e e t on W hetstone 3t
b etw een W34720 and 1734400, and a t 1)33800 where t h e ch a n n el i s c u t t in g
th rou gh a pronounced b l u f f p a r a l l e l i n g t h e San Pedro R iv e r .
F ig u r e 4 , showing t h e l o n g it u d in a l p r o f i l e s and t h e r e l a t i o n o f
g r a d ie n t t o ch a n n el le n g t h , i n d i c a t e s t h e l o c a t i o n o f t h e c o n c a v ity
change in each w ash.
F ig u r e 5 p o r tr a y s t h e lo n g it u d in a l v a r i a t i o n o f
d r a in a g e a r e a , p a r t i c l e s i z e and w id th :d e p th r a t i o , w ith l i n e s drawn t o
i n d i c a t e th e tr e n d s o f ch an ge.
G e n e r a lly , th e r a t e s o f change a re n o t
c o n s ta n t th ro u g h o u t t h e e n t i r e le n g t h o f t h e strea m .
In a l l c a se s,
t h e d a ta from t r i b u t a r i e s f i t s w e l l w it h in th e s c a t t e r o f p o in t s ,
in d ic a t i n g a s i m i l a r i t y o f r e l a t i o n s w ith th e m ain str e a m s.
Mustang M ountains
A l l t h r e e w ashes ( F ig . 6 ) t h a t w ere s t u d ie d i n t h e Mustang
M ountains d r a in sed im en ta ry and v o lc a n ic r o c k s .
Mustang 1 b e g in s i n
lim e s to n e and a t Ml 3200 flo w s i n t o a llu v iu m w hich a p p ea rs t o b e an
a l l u v i a l fa n .
The lim e s to n e f r a c t u r e s t o f a i r l y la r g e fragm en ts and
g e n e r a lly r e s i s t s w e a th e r in g .
Below M15200 t h e stream c r o s s e s
22
------- ~7n~r-
-
,
r ^ .J v /r .
CONTOUR
INTERVAL
SCALE
1: 6 2 ,6 0 0
50 FEET
FIO. 6 .
LOCATION MAP FOR STREAMS AND STATIONS IN
THE MUSTANG MOUNTAINS.
2 M ILE S
23
a r h y o l i t e o u tc ro p , flo w in g on t h e r h y o li te - a llu v i u m c o n ta c t.
The
r h y o l i t e c o n te n t o f th e bed m a t e r i a l b a r e ly re a c h e s 20$ a s t h e a llu v iu m
i s e s s e n t i a l l y a l l lim e s to n e .
I n t h i s a r e a t h e r h y o l i t e i s g e n e r a lly
m a ss iv e , b re a k in g i n t o l a r g e fra g m e n ts , a lth o u g h i t i s som etim es
h ig h ly f r a c t u r e d .
The d ra in a g e a r e a o f M ustang 2 i s d o m in a n tly lim e s to n e w ith m inor s a n d s to n e .
C o arse fra g m e n ts a r e p r e v a le n t.
At M25050, th e m ain
stream i s c u t t i n g th ro u g h a s m a ll fa n w hich o r i g i n a t e s i n one o f th e
t r i b u t a r i e s t o th e n o r th .
The m ain c h a n n e l ends on t h e s u r f a c e o f a
s m a ll, h e a v ily v e g e ta te d fa n a t 4860 f e e t e l e v a tio n .
At i t s u p p e r end,
th e fa n h as a w id th o f ?4 f e e t and a mean p a r t i c l e s i z e o f 6.5
m il l i m e t e r s , s i g n i f i c a n t l y s m a lle r th a n th e 25 m illi m e t e r s fo u n d a t
M24900, th e n e a r e s t s t a t i o n u p s tre a m .
At a d is ta n c e o f ab o u t 225 f e e t
dow nfan, th e w id th h as in c r e a s e d t o 95 f e e t and th e mean s iz e t o
35 m illi m e t e r s .
M ustang 3 d r a i n s a r e a s o f lim e s to n e , r h y o l i t e and m udstone.
The
lim e s to n e i s t y p i c a l l y r e s i s t a n t , b u t th e r h y o l i t e ra n g e s from h ig h ly
f r a c t u r e d to m a ssiv e and th e m udstone i s q u i t e weak.
t r i b u t a r y e n t e r s w hich c a r r i e s p r im a r i ly lim e s to n e .
At M34900, a m ajo r
The l e f t bank o f
th e s tre a m , t h e s id e from w hich th e m ain b ra n c h comes, i s 90$ r h y o l i t e ,
w h ile th e r i g h t s id e i s o n ly 60$ r h y o l i t e , w ith th e re m a in d e r b e in g
lim e s to n e and s a n d s to n e .
I n t h e b e d , th e b o u ld e rs a r e 60$ r h y o l i t e ,
w h ile th e g r a v e l i s o n ly 40$ r h y o l i t e .
The p e rc e n ta g e o f r h y o l i t e i n
b o th d e c r e a s e s r a p i d l y dow nstream and a t M34800 t h e b ed m a t e r i a l i s 60$
lim e s to n e and o n ly 25$ r h y o l i t e .
r e s i s t a n t th a n th e r h y o l i t e .
A p p a re n tly th e lim e s to n e i s more
24
ELEVATION (F E E T )
6000
5000
C = CONCAVITY CHANGE
10 X = VERTICAL EXAGGERATION
•
HORIZONTAL SCALE:
9
10000'
4000
P
CHANNEL LENGTH (F E E T )
G R A D IE N T ( F T . / F T . )
KEY
MUSTANG l
MUSTANG 2
MUSTANG 3
FIG. 7 .
LONGITUDINAL PROFILES (A) AND CONCAVITIES (B)
IN THE MUSTANG MOUNTAINS
F ig . 8 .
Change o f D rainage A rea, P a r t i c l e S iz e and W id th :d e p th
R a tio -with Channel L ength i n t h e M ustang M ountains
A, B and C show th e v a r i a t i o n w ith c h a n n e l le n g th o f
d ra in a g e a r e a , p a r t i c l e s i z e and w id th :d e p th r a t i o
r e s p e c t i v e l y . The lo c a t i o n o f th e c o n c a v ity change i s
superim p o sed on A, and t h a t o f th e dow nstream l i m i t
o f b e d ro c k exposed i n th e c h a n n e l, l a b e l l e d " lo w e st
c h a n n e l b e d ro c k " , i s p la c e d on B t o show th e r e l a t i o n
o f th e s e f e a t u r e s to th e l o n g i t u d i n a l change o f
d ra in a g e a r e a and p a r t i c l e s i z e .
B = LOWEST CHANNEL
. BEDROCK
M U STA N G l
MUSTANG 2
DRAINAGE AREA ( M l 2 )
MUSTANG 3
©
CHANNEL LENGTH (F E E T )
C = CONCAVITY
CHANGE
I04
CHANNEL LENGTH (F E E T )
FIG. 8 .
CHANNEL "LENGTH (FEET)
CHANGE OF AREA PARTICLE SIZE AND WIDTH: DEPTH RATIO WITH CHANNEL LENGTH IN THE MUSTANG MOUNTAINS
26
The a llu v iu m i n t h e h an k s o f t h e lo w er re a c h e s o f th e s e stre a m s
i s d o m in a n tly c o a rs e lim e s to n e and commonly i s cem ented w ith c a li c h e .
I t g e n e r a lly c o n ta in s more f i n e s th a n t h e bed m a t e r i a l .
o c c u r s , p ro b a b ly due t o t h e l a r g e m a t e r i a l s i z e .
on M ustang 2 .
No b r a id in g
E ntrenchm ent i s m inor
M ustang 1 i s i n c i s e d t e n f e e t a t Ml 5100 and Ml4700, b u t
v e ry l i t t l e e ls e w h e re , and t h e bed o f M ustang 3 i s f i v e t o t e n f e e t
below th e r e g io n a l s u r f a c e th ro u g h o u t m ost o f i t s le n g th .
F ig u re 7 p o r t r a y s th e c o n c a v ity change on t h e p r o f i l e s and on
th e g r a d i e n t - l e n g t h r e l a t i o n s .
The l o n g i t u d i n a l v a r i a t i o n s o f
p a ra m e te rs a r e shown on f i g u r e 8 .
A g ain , th e r a t e o f change o f each
p a ra m e te r g e n e r a lly changes a b r u p tly a t some p o in t alo n g th e
channel p r o f ile .
S ie rrita s
On t h e S i e r r i t a s tre a m s (F ig . 9 ) c a u tio n was ta k e n t o a v o id
s e l e c t i n g s t a t i o n s i n a r e a s a f f e c t e d by th e damming o f s to c k ta n k s .
The
f i l l i n g w hich o c c u rs u p stream i s g e n e r a lly o b v io u s i n t h e f i e l d .
O verflow from th e ta n k w i l l b e s e d im e n t- fre e and w i l l te n d t o remove th e
f i n e s t bed m a t e r i a l and d e c r e a s e w id th :d e p th r a t i o and stre am g r a d ie n t
by tr e n c h in g .
I f no o v e rflo w o c c u r s , th e c h a n n e l dow nstream w i l l
r e c e iv e w a te r o n ly from p r e c i p i t a t i o n b elo w t h e dam.
S tream s h ead in g
below th e m o u n ta in s, a n alo g o u s t o th o s e h ead in g b elo w th e dams, show
s i m i l a r p a r t i c l e s i z e s and g r a d i e n t s b u t s l i g h t l y s m a lle r w id th :d e p th
r a t i o s th a n t h e i r c o u n te r p a r ts h ead in g i n th e m o u n ta in s.
Thus, th e
t a n k s ’ e f f e c t on th e m easured p a ra m e te rs a p p e a rs t o b e s m a ll.
In e ith e r
s i t u a t i o n below th e dam, t h e e f f e c t s o f th e ta n k d is a p p e a r r a p i d l y
LOCATION MAP FOR STREAMS AND STATIONS IN TH E 3IE R R IT A MOUNT/
28
dow nstream and a r e g e n e r a lly gone a f t e r th e f i r s t m ajo r t r i b u t a r y
e n tr y .
Im m ed ia te ly below th e ta n k on S i e r r i t a 1 a t 4?00 f e e t , t h e
c h a n n e l c u ts t e n t o tw e n ty f e e t i n t o b e d ro c k .
S14525 i s lo c a t e d
betw een t h i s i n c i s i o n and t h e f i r s t m a jo r dow nstream t r i b u t a r y .
Throe
s t a t i o n s w ere m easured a t th e ju n c tio n w ith t h i s t r i b u t a r y , one above
th e i n t e r s e c t i o n on th e m ain s tre a m , S144MT, a n o th e r on th e t r i b u t a r y ,
S1444T, and t h e t h i r d on th e m ain s tre a m b elo w t h e ju n c tio n , S i4440.
,
P a r t i c l e s i z e in c r e a s e s from S I4525 t o S144MT, and th e n d e c r e a s e s below
t h e ju n c tio n , w h ile t h e m a t e r i a l i n th e undammed t r i b u t a r y , i s th e same
s iz e a s a t S i4525.
Had rem o v al o f f i n e s o c c u r re d , i t sh o u ld have b een
more e f f e c t i v e a t S i4525 th a n S144MT and a r e v e r s a l o f th e s i z e s found
would be e x p e c te d .
F u rth e rm o re , t h e d ro p i n w id th :d e p th r a t i o betw een
S i4750 and Si 4525 r e f l e c t s t h e i n f l u e n c e o f t h e b e d ro c k o u tc ro p s and n o t
th e manmade dam, f o r i t h a s s i m i l a r v a lu e s on th e u n d is tu r b e d t r i b u t a r y
and t h e main stre a m above t h e ju n c t i o n .
Thus th e e f f e c t o f th e ta n k
do es n o t e x te n d dow nstream i n t h i s c h a n n e l.
In d e e d , th e e f f e c t s o f
s h o r t- te r m f e a t u r e s su ch a s t h e ta n k s n a y n o t b e g r e a t enough to be
n o tic e d a t a l l i n t h e g r o s s r e l a t i o n s so u g h t i n t h i s s tu d y .
The
lo c a t i o n s o f th e o th e r ta n k s a r e shown on f i g u r e 9*
The S i e r r i t a . c h a n n e ls a r e flo w in g a c r o s s a b e d ro c k p ed im en t.
Bedrock c ro p s o u t i n th e c h a n n e l w a lls and on th e i n t e r f l u v e s w e ll down­
stre a m from th e l a s t c h a n n e l o u tc r o p s .
No e f f e c t on p a r t i c l e s iz e and
o th e r f e a t u r e s was n o tic e d .
B edrock i s g e n e r a lly p h a n e r i t i c ig n e o u s .
S i e r r i t a 1 and 2 flo w
th ro u g h a r e a s mapped by L o o ten s ( I9 6 5 ) a s p r im a r i ly q u a r tz m o n zo n ite and
29
g r a n o d io r it e .
Some f i n e r u n i t s in c lu d e w elded t u f f b r e c c i a s , f i n e
le u c o g r a n it e s and to u rm a lin e g r a n i t e s .
A ll f r a c t u r e t o fra g m e n ts up t o
a h a l f m o to r, b u t th e c o a r s e - g r a in e d ro c k s w e a th e r r a p i d l y t o f o u r to
e ig h t m illi m e t e r fra g m e n ts , w h ile t h e o th e r s a r e more r e s i s t a n t .
The
b ed ro ck i s d o m in a n tly c o a r s e le u c o g r a n it e (L o o te n s , 19&5) i n S i e r r i t a
At S35000 t h i s stre a m i s s t r u c t u r a l l y c o n t r o l l e d , flo w in g p a r a l l e l
t o a m ajo r j o i n t sy stem .
B ra id in g i s t h e dom inant c h a n n e l form b etw een S14250 and Si 4000,
from S25000 t o S24000 and a t 534250.
E lse w h ere t h e r e i s g e n e r a lly o n ly
one c h a n n e l. " No e n tre n ch m e n t o c c u rs a lo n g S i e r r i t a 2 .
S i e r r i t a 1 , on
th e o th e r h an d , i s u n d e rg o in g a c t i v e tr e n c h in g a t p r e s e n t a t S15000,
p ro b a b ly b e c a u se a d d i t i o n a l sed im en t r e s u l t i n g from a l o c a l b u rn h a s
f i l l e d th e c h a n n e l.
I n c i s i o n o f te n t o tw e n ty f e e t h a s o c c u rre d i n
b ed ro ck betw een 314-750 and 814-525, w ith th e stre am re m a in in g d e e p ly
e n tre n c h e d t o S i4250.
S i e r r i t a 3 shows i n c i s i o n o f f i f t e e n f e e t a t
S34-500, w hich d e c r e a s e s i n b o th d i r e c t i o n s .
As i n t h e o th e r r a n g e s , t h e p r o f i l e s and c o n c a v ity , to g e th e r
w ith lo n g i t u d i n a l r a t e s o f change o f p a ra m e te rs have b e en drawn
( F ig s . 10 and 1 1 ).
S i e r r i t a 5 i 6 and 7i t h r e e s m a lle r d ra in a g e s
h ead in g below t h e m ountain f r o n t , w ere exam ined t o d e te rm in e how such
s tre a m s w ould r e l a t e t o th o s e h e ad in g i n th e m o u n ta in s (F ig . 9 ) .
d a ta a r e p l o t t e d on f i g u r e s 10b, and 1 1 a, b an d c .
These
I n d i v i d u a l l y , e ac h
s t a t i o n f i t s r e l a t i v e l y w e ll i n t o t h e s c a t t e r o f p o i n t s on each p l o t ,
e x c e p t on g r a d ie n t v e rs u s l e n g th w here th e y a r e rem oved.
w i l l be e x p la in e d i n a s u b se q u e n t s e c t i o n .
T h is anom aly
30
6000
ELEVATION (FEET)
.
5000
4000
3000
C = CONCAVITY CHANGE
IOX = VERTICAL EXAGGERATION
HORIZONTAL S C A L E :
10000
?
2000
CHANNEL LENGTH (FEET)
SIERRITA I
TRIBUTARY
/
___________ /
<
T
/
A
__________________
GRADIENT (F T / F T )
m
:
KEY
-
-
!
,
«•
~
T
SIE R R IT A
I
S IE R R IT A
2
SIE R R IT A
3
S IE R R IT A
5 -7
T
-
1 1 1
I0 2
»
i
i
i i
i
i i
.
.
.
I0 3
.
.
!
?
.
)
I0 4
CHANNEL LENGTH (FEET)
FIG. 10.
LONGITUDINAL PR O F IL E S (A) AND CONCAVITIES ( 0 )
IN TH E S IE R R IT A MOUNTAINS
©
T '
F ig . 11.
Change o f D rain ag e A rea, P a r t i c l e S iz e and W id th :d e p th
R a tio w ith Channel L ength i n th e S i e r r i t a s
A, B and C show th e v a r i a t i o n w ith ch an n e l l e n g th o f
d ra in a g e a r e a , p a r t i c l e s i z e and w id th :d e p th r a t i o
r e s p e c t i v e l y . The l o c a t i o n o f th e c o n c a v ity change i s
superim posed on A, and t h a t o f th e dow nstream l i m i t
o f b e d ro c k exposed i n th e c h a n n e l, l a b e l l e d “lo w e st
c h a n n e l b e d ro c k ", i s p la c e d on B t o show th e r e l a t i o n
o f th e s e f e a t u r e s to th e l o n g i t u d i n a l change o f
d ra in a g e a re a and p a r t i c l e s i z e .
B = L O W E ST CH A N N EL
BEDROCK
SIERRITA I
SIERRITA 2
SIERRITA 3
AREA (M l
SIERRITA
5 -7
-
/ / \\
CHANNEL LENGTH (F E E T )
C = CONCAVITY CHANGE .
•CHANNEL LENGTH (F E E T )
FIG. II.
CHANGE OF AREA
'CHANNEL LENGTH (F E E T )
PARTICLE SIZE AND WIDTH: DEPTH RATIO WITH CHANNEL LENGTH IN THE SIERRITA MOUNTAINS
32
A ll t h r e e s tre a m s flo w i n a l l u v i a l m a t e r i a l d e riv e d from
g r a n itic ro c k s.
S tream s 5 and 6 do have some b e d ro c k c ro p p in g o u t i n
th e w a lls o f th e stre a m v a l l e y , p a r t s o f . t h e S i e r r i t a p ed im en t.
B ra id in g o c c u rs o n ly a t S63500,
However, none o c c u rs i n t h e stre a m b e d .
and o n ly a t th e same s t a t i o n i s bank m a t e r i a l v e ry d i f f e r e n t from b ed
m a t e r i a l , b e in g n o tic e a b ly c o a r s e r .
I f th e s e fo u r s t a t i o n s were c o n s id e re d a s b e in g on a s in g le
stre a m , th e c o n c a v ity and r a t e s o f change o f d ra in a g e a r e a , p a r t i c l e
s iz e and w id th :d e p th r a t i o w ith c h a n n e l le n g th w ould b e s i mi l a r t o t h e
dow nstream segm ents o f t h e o th e r s tre a m s .
C o n cav ity w ould be - . 1 .
Summary o f Downstream R e la tio n s
The change i n c o n c a v ity ( F ig s . 4 , 7 and 10) and t h e ch an g es i n
th e r a t e o f v a r i a t i o n o f p a ra m e te rs w ith c h a n n e l l e n g th ( F ig s . 5» 8
and 11) a lr e a d y have b e en n o te d .
o f th o s e f e a t u r e s .
T a b le 2 sum m arizes t h e m ost im p o rta n t
The c o n c a v ity o f th e p r o f i l e o f e ac h stre am ch an g es
from h ig h u p stre am t o low dow nstream .
I n e i g h t o f t h e n in e c a s e s , t h i s
change c o in c id e s c l o s e l y w ith a change i n t h e d r a in a g e a re a -c h a n n e l
le n g th r e l a t i o n (T ab le 2 ) .
D rain ag e a r e a in c r e a s e s more r a p i d l y w ith
le n g th i n th e h ig h - c o n c a v ity segm ents th a n i n th e low ( F ig s . 5a » 8a
and 1 1 a ).
The one anom alous c a s e , M ustang 3# r e s u l t s from th e e n tr a n c e
o f a m ajo r t r i b u t a r y a b o u t o n e - h a lf m ile dow nstream from th e c o n c a v ity
change, c a u s in g t h e h ig h e r r a t e o f in c r e a s e o f a r e a t o be m a in ta in e d
dow nstream beyond t h e c o n c a v ity ch an g e.
The r a t e o f d e c r e a s e o f p a r t i c l e s iz e dow nstream a ls o shows a
te n d e n c y f o r change ( F ig s . 5 b , 8 b , and 1 1 b ).
I n e i g h t o f th e n in e
33
T able 2 .
Summary o f L o c a tio n s o f M ajor Changes i n th e L o n g itu d in a l
V a r ia tio n o f P a ra m e te rs and T h e ir R e la tio n s t o B edrock'
The l e t t e r s p and q r e f e r t o th e e x p o n en ts i n A /X -lP
and
04
Stream
C o n c a v ity :
u p stre a m
dow nstream
L o c a tio n
Of
c o n c a v ity
change
( f e e t from
d iv id e )
L o c a tio n
o f change
of p
( f e e t from
d iv id e )
L o c a tio n
o f lo w e s t
channel
b e d ro c k
( f e e t from
d iv id e )
L o c a tio n
o f change
of q
( f e e t fro i
d iv id e )
4200
4200
4100
No change
4200
4200
4600
4400
6000
9000
5950
5700
13500
_ 12500
15000
15000
11000
11000
6550
6500
10000
10500
15250
16000
12000
13000
12700
12700
7500
7200
4300
4000
11000
•11000
7500
7000
- 1 .9
M ustang 1 .
-.6
t
-2 .4
M ustang 2
i
i
- .4
• -1 .0
M ustang 3
i
•
-1 .2
W hetstone 1
.
-.6
, -1 .2
W hetstone 2
t
- .7
r -1 .2
W hetstone 3
1
r - 1 .1
S ie rrita 1
l
-.3
r-1.0
S ie rrita 2
1 - .8
r-1.0
S ie rrita 3
L - .2
34
s tre a m s , p a r t i c l e s i z e d e c r e a s e s more slo w ly a n d /o r more c o n s i s t e n t l y
below t h e l a s t o u tc ro p o f b e d ro c k dow nstream th a n i t d o es above i t .
The
n i n t h s tre a m . M ustang 1 , shows e s s e n t i a l l y no d i f f e r e n c e i n p a r t i c l e
s iz e .d e c r e a s e above and below t h e l a s t b e d ro c k .
The r a t e o f d e c re a s e
below th e b ed ro ck te n d s t o b e s m a lle r i n g r a n i t i c c h a n n e ls th a n i n
th o s e d r a in in g s e d im e n ta ry and v o lc a n ic ro c k s .
The c o in c id e n c e o f t h e p a r t i c l e s i z e and c o n c a v ity ch an g es
depends on th e l o c a t i o n o f t h e l a s t o u tc ro p r e l a t i v e t o th e c o n c a v ity
change (T ab le 2 ) .
T hese two p o i n t s c o in c id e i n f o u r o f t h e n in e
c h a n n e ls , M ustang 1 , 2 and 3» and S i e r r i t a 1 .
Of t h e re m a in in g f i v e ,
th r e e s tre a m s , W hetstone 2 and S i e r r i t a 2 and 3» change c o n c a v ity b elo w
th e l a s t b e d ro c k .
The l a s t o u tc ro p o c c u rs dow nstream from t h e c o n c a v ity
change on b o th W hetstone 1 and 3» a lth o u g h t h e d is ta n c e s e p a r a tin g th e
two p o in ts i n W hetstone 1 i s l e s s th a n 1000 f e e t .
T h is d is ta n c e c o u ld
e a s i l y r e p r e s e n t o n ly t h e e r r o r i n h e r e n t i n t h e l o c a t i o n o f t h e
c o n c a v ity b re a k .
The l o c a t i o n o f a s t a t i o n w ith in t h e p o s s ib le ra n g e o f
lo c a t i o n h a s p ro b a b ly o n ly a c c e n te d th e in a c c u ra c y t h a t e x i s t s e lse w h e re
a s w e ll.
C o n sid e ra b le v a r i a t i o n o f c o n c a v ity o c c u rs w ith in b o th th e
h ig h -c o n c a v ity and th e lo w -c o n c a v ity seg m en ts, b u t th e two s o t s o f
v a lu e s have no o v e rla p (T a b le 2 ) .
P a r t o f th e v a r i a t i o n , p a r t i c u l a r l y
t h a t o f t h e h ig h - c o n c a v ity segm ent, r e s u l t s from l i t h o l o g i c d i f f e r e n c e s .
I n th e stre a m s i n s e d im e n ta ry r o c k s , t h e h ig h e s t c o n c a v itie s c o rre sp o n d
t o th e m ost r e s i s t a n t l i t h o l o g y , lim e s to n e , w h ile th e lo w e s t o c c u rs i n
th e stre a m w ith s u b s t a n t i a l r h y o l i t e .
The c o n s is te n c y o f c o n c a v itie s i n
th e g r a n i t i c c h a n n e ls p ro b a b ly i n d i c a t e s th e s i m i l a r i t y o f l i t h o l o g i e s . ,
35
W ith th e e x c e p tio n s o f M ustang 2 and W hetstone 3» w id th :d e p th
r a t i o i n c r e a s e s dow nstream t o a maximum v a lu e w ith in t h e lo w -c o n c a v ity
segment," below w hich i t d e c r e a s e s ( F ig s . 5 c , 8c and 1 1 c ).
W hetstone 3
i s anom alous i n t h a t t h e p r o f i l e becom es convex w here i t a p p e a rs t h e
maximum v a lu e w ould o c c u r .
Thus a more g e n e r a l f e a t u r e i s t h a t
w id th :d e p th r a t i o a c t u a l l y te n d s t o d e c r e a s e w ith d im in is h in g g r a d ie n t
i n th e dow nstream segm ent.
T h is f e a t u r e i s p ro b a b ly r e l a t e d t o a n
in c r e a s in g sed im en t c o n c e n tr a tio n dow nstream a s d is c h a r g e i s l o s t t o
in filtra tio n .
E i t h e r a s m a lle r w id th :d e p th r a t i o , s te e p e r g r a d i e n t ,
o r b o th , i s n e c e s s a ry t o c a r r y th e lo a d .
W id th :d e p th r a t i o i s l e s s c o n s i s t e n t i n t h e lo w -c o n c a v ity
segm ent, p a r t l y due t o t h e o c c u re n c e o f b r a i d i n g .
T h is c h a n n e l form
does n o t o c c u r i n t h e s e d im e n ta ry c h a n n e ls w ith c o a r s e bank m a t e r i a l .
P r e c i p i t a t i o n a l s o d e c r e a s e s r e g u l a r l y dow nstream .
T h is
f e a t u r e , how ever, r e s u l t s from p r e c i p i t a t i o n ’ s r e l a t i o n t o e le v a tio n
and th e f a c t t h a t th e s tre a m s flo w d o w n h ill.
INTERRELATIONS AMONG PARAMETERS LEADING TO A NATURAL SUBDIVISION OF DATA
I t w ould be v a lu a b le t o d e te rm in e w h e th er t h e d a ta can be
grouped i n a more u s e f u l m anner th a n by i n d i v i d u a l s tre a m s .
One means
t o t h i s end i s to lo o k f o r f a c t o r s w hich re d u c e t h e s c a t t e r on t h e
p l o t s o f v a r i a b l e s , p a r t i c u l a r l y th o s e in c lu d in g stre a m g r a d i e n t , th e
p rim a ry m easure o f th e stre a m p r o f i l e in v o lv e d .
The p l o t s o f g r a d ie n t
a g a in s t l e n g t h ( F ig s . 4 b , 7b and 10b) and d r a in a g e a r e a a g a in s t le n g th
(F ig s . 5a» 8 a and 1 1 a) i n d i c a t e t h a t i f t h e d a ta i s s e p a r a te d on th e
b a s i s o f c o n c a v ity seg m en ts, some o f t h e s c a t t e r w i l l d is a p p e a r .
F ig u re s 12a and 12b show th e s c a t t e r i s q u i t e l a r g e on th e
g r a d i e n t - p a r t i c l e s i z e and g r a d ie n t- w id th :d e p th r a t i o r e l a t i o n s .
Im posing l i t h o l o g y by d i f f e r e n t i a t i n g s e d im e n ta ry and v o lc a n ic p o i n t s
from g r a n i t i c p o i n t s c u ts t h e s c a t t e r a lm o st i n h a l f on each p l o t .
S e p a ra tio n i n t o c o n c a v ity seg m en ts, w here concave s ta n d s f o r h ig h c o n c a v ity and s t r a i g h t f o r lo w -c o n c a v ity , a d d s a s l i g h t im provem ent.
The g r a d ie n t- d r a in a g e a r e a r e l a t i o n (F ig . 1 3 a) shows a s c a t t e r
w hich i s n o t e lim in a te d by a p p l i c a t i o n o f e i t h e r l i t h o l o g y o r c o n c a v ity
segm ents.
I n f a c t , t h e g r a n i t i c p o i n t s form a b and i n th e c e n t e r ,
e n c lo s e d by p o i n t s from s e d im e n ta ry -v o lc a n ic c h a n n e ls .
i s a f u n c tio n o f r e l i e f .
T h is phenomena
W hetstone 1 , w ith t h e g r e a t e s t r e l i e f , h a s t h e
s t e e p e s t g r a d ie n t f o r a g iv e n a r e a , w h ile th e M ustang s tre a m s , w ith th e
lo w e s t r e l i e f s , show t h e g e n t l e s t s lo p e f o r a g iv e n a r e a .
I t was found
by t r i a l and e r r o r t h a t g r a d ie n t v a r i e s m ost c l o s e l y w ith A/R , w here
R i s th e t o t a l r e l i e f f o r th e p r o f i l e segm ent i n w liich a p o in t i s
36
3?
KEY
GRADIENT ( F T ./ F T ,)
SEDIMENTARY
©
CONCAVE
O
STRAIGHT
O
GRANITIC
CONCAVE
STRAIGHT
o
TRIBUTARIES
CONCAVE
T
STRAIGHT
10
MEAN PARTICLE S IZ E (MM)
w id t h : d e p t h
FIG. 12
r a t io
RELATION OF MEAN PARTICLE SIZE (A ) AND WIDTH: DEPTH RATIO ( B) TO
CHANNEL GRADIENT.
DOTTED L IN E S SEPARATE LITHOLOGIES
i
i
k i 1111
i
1 i i i i ii
n
GRADIENT ( F T /F T J
©
*
T
©
©
T
•
• •
-
.
©
©
o
e
0
-
• • »
0
y
* *
© O*
T
T
' t> °
e® 9 e
.T
°
-
e
* A * . ° *
»
° ° °©
* '
'
?
:
O
©
o
•
•
» 1 1 t ! f1
I0'2
I0*1
|,
GRADIENT (FT ./FT .)
DRAINAGE AREA (M l?)
© »
oo
I0*7
O Cp
1C6
AREA‘.R E L IE F 2 RATIO (Ml2. / F T 2 )
KEY
SEDIMENTARY
CONCAVE
STRAIGHT
FIG. 13.
GRANITIC;
o
o
CONCAVE
STRAIGHT
TRIBUTARIES
6
0
CONCAVE
STRAIGHT
T
T
RELATION OF DRAINAGE AREA (A) AND AREA: R ELIEF2
RATIO (B) TO CHANNEL GRADIENT
39
lo c a te d *
F ig u r e 13b shows t h e im proved f i t , and a ls o th e e f f e c t o f
im posing th e p r o f i l e segm ents on th e r e l a t i o n , f o r th e pro n o u n ced bend
i n t h e s c a t t e r f i e l d c o in c id e s w ith th e change i n c o n c a v ity .
The 'e f f e c t o f r e l i e f on th e a r e a - g r a d ie n t r e l a t i o n i s s t r i c t l y
g e o m e tric .
T ab le 3 shows t h a t th e r e l i e f :l e n g t h r a t i o s a r e q u i t e
s i m i l a r f o r t h e same segm ent on d i f f e r e n t s tre a m s .
Thus t h e p r o f i l e s
a r e concave-upw ard a r c s below t h e h y p o te n u se s o f s i m i l a r r i g h t
t r i a n g l e s (F ig . Vi-).
R/L = r ' / l 1
F ig . 1 4 .
R e la tio n o f C hannel G ra d ie n t a t a G iven D is ta n c e from th e
D iv id e to B a sin R e l i e f and L ength
The f i g u r e shows t h a t a t a g iv e n d is ta n c e "x" from th e d iv id e ,
th e g r a d ie n t i n th e s tre a m w ith th e g r e a t e r r e l i e f , (A ), w i l l be s te e p e r
b e ca u se th e ch o sen p o s i t i o n i s r e l a t i v e l y h ig h e r i n t h e p r o f i l e .
The
s i t u a t i o n i s th e same when t h e a r e a i s s u b s t i t u t e d f o r le n g th , a s a r e a
in c r e a s e s w ith l e n g th a t a c o n s ta n t r a t e i n each c o n c a v ity segm ent.
The r e l a t i o n o f w id th :d e p th r a t i o t o p a r t i c l e s i z e ( F ig . 15)
i n d i c a t e s a s e p a r a tio n o f p o i n t s due t o l i t h o l o g y .
However, t h i s
s e p a r a tio n i s m e re ly a r e s u l t o f t h e c o a r s e r m a t e r i a l and l a c k o f
b r a id in g e x i s t i n g i n s e d im e n ta ry s tre a m s , f o r th e s c a t t e r i s n o t
re d u c e d by im posing l i t h o l o g y on t h e p l o t .
A c tu a lly , th e r e l a t i o n o f
uo
T a b le 3*
R e l i e f :le n g t h R a tio s o f t h e C o n c a v ity Segm ents
H ig h -c o n c a v ity segm ent
L o w -co n cav ity segm ent
S tream
T o ta l
L ength
(fe e t)
T o ta l
R e lie f
(fe e t)
R e lie f:
L en g th
R a tio
T o ta l
L ength
(fe e t)
M ustang 1
4200
1025
.2 4
12100
350
.029
M ustang 2
4200
1075
.2 6
8200
275
.0 3 4
M ustang 3
6000
1050
.1 8
13700
350
.025
W hetstone 1
13500
2500
.1 9
66500
1400
.021
W hetstone 2
11000
1550
.1 4
39300
1100
.0 2 9
W hetstone 3
10000
1550
.1 6
42000
1250
.030
S ie rrita 1
12000
1250
.1 0
69200
1800
.026
S ie rrita 2
7500
1100
.1 5
78300
1900
.0 2 4
S ie rrita 3
11000
1150
.1 0
73600
1750
.0 2 4
S ie rrita 5
———
———
9500
250
.0 2 9
S ie rrita 6
————
———
13300
350
.0 2 6
16000
400
.025
S ie rrita 7
——~ —
T o ta l
R e lie f
(fe e t)
R e lie f:
L ength
R a tio
41
PARTICLE S IZ E (MM)
TTT
I
l
i
t
!
w id t h
: d e p t h r a t io
KEY
SEDIMENTARY
FIG. 13.
T R IB U T A R IE S
GRANITIC
CONCAVE
O
CONCAVE
•
CONCAVE
T
STRAIGHT
o
STRAIGHT
o
STRAIGHT
T
RELATION [BETWEEN MEAN PARTICLE SIZ E AND. WIDTH: DEPTH RATIO
42
th e s e p a ra m e te rs a p p e a rs t o b e c o n tin o u s a c r o s s l i t h o l o g i c b o u n d a rie s .
I n tr o d u c tio n o f p r o f i l e segm ents p ro d u ced l i t t l e
e ffe c t e ith e r.
Three s t a t i o n s on t r i b u t a r i e s above th e b re a k i n c o n c a v ity on
t h e i r tr u n k s tre a m s , and f i v e on th o s e below i t a r e shown on f i g u r e s
12a, 12b, 1 3 a, 13b and 15.
A ll a r e i n g r a n i t i c b e d ro c k a r e a s .
O nly i n
th r e e in s ta n c e s do th e y show a m arked d i f f e r e n c e from th e o th e r
s ta tio n s .
On p l o t s o f g r a d ie n t and w id th :d e p th (F ig . 1 2 a ), g r a d i e n t and
a r e a (F ig . 13a) and w id th :d e p th and p a r t i c l e s i z e (F ig . 15)» th e
t r i b u t a r i e s w hich e n t e r b elo w th e m o u n tain f r o n t f a l l o u t o f th e norm al
s c a tte r f ie ld .
A d d itio n o f r e l i e f moves th e n i n t o th e main f i e l d o f
g r a d ie n t v e rs u s A/R2 (F ig . 1 3 b ).
The re m a in in g two p l o t s i n d i c a t e th e s e
s tre a m s have a somewhat s m a lle r w id th :d e p th r a t i o th a n th e s tre a m s w hich
head i n th e m o u n ta in s.
The t h r e e s t a t i o n s on t r i b u t a r i e s e n te r in g above
t h e c o n c a v ity change f a l l w ith in t h e s c a t t e r on a l l p l o t s .
I t a p p e a rs
t h a t th e r e l a t i o n s w hich e x i s t among th e p a ra m e te rs a r e th e same on m ain
stream and t r i b u t a r y w ith t h e e x c e p tio n o f th o s e in v o lv in g w id th :d e p th
r a t i o on t r i b u t a r i e s w h o lly below t h e m o u n ta in s.
C o n se q u e n tly , t h e
s c a t t e r on p l o t s c a n n o t be a t t r i b u t e d t o a d i f f e r e n c e i n b a s in s iz e o r
o r d e r , and th e r e l a t i o n s w hich e x i s t among p a ra m e te rs a r e n o t due sim p ly
t o th e o v e r a l l s i m i l a r i t y o f t h e stre a m s sam pled.
The t r i b u t a r y d a ta
w i l l h e n c e fo rth he in c lu d e d w ith t h e o th e r s t a t i o n s .
The s c a t t e r o f t h e p l o t s i s re d u c e d p r im a r i ly by th e i n t r o ­
d u c tio n o f l i t h o l o g y and p r o f i l e seg m en ts.
R e l i e f shows an im p o r ta n t
e f f e c t , b u t s in c e t h e f i e l d o f p o s s ib le r e l i e f s i s i n f i n i t e , any u s e f u l
s e p a r a tio n o f p o i n t s w ould in v o lv e a r b i t r a r y g ro u p in g .
No n a t u r a l
g ro u p in g i s a p p a r e n t, so r e l i e f i s n o t c o n s id e re d a v a l i d p a ra m e te r
43
f o r c l a s s i f y i n g th e d a t a .
I n a d d itio n , th e re a re in d ic a tio n s th a t
c o n c a v ity i s a more s e n s i t i v e in d e x o f l i t h o l o g y th a n i s th e
c l a s s i f i c a t i o n o f ro c k ty p e u s e d h e r e .
However, th e stre a m s ch o sen f o r
t h i s s tu d y happen t o flo w th ro u g h ro c k s w hich f i t b e s t i n t o t h e two
v e ry b ro a d l i t h o l o g i e s u s e d .
S u b d iv id in g t h e s e d im e n ta ry ro c k s i n t o
lim e s to n e , s a n d sto n e and m udstone, f o r i n s t a n c e , would, a p p a r e n tly
produce b e t t e r r e l a t i o n s , b u t w ould r e q u i r e many a d d i t i o n a l sam ple s i t e s
i n each l i t h o l o g y .
The g e n e r a l n a tu r e o f t h i s s tu d y d id n o t w a rra n t
d e t a i l e d a n a l y s i s o f th e e f f e c t o f l i t h o l o g y on p r o f i l e s and th e
sam pling done i s in a d e q u a te t o e x te n d i t t o t h a t en d .
Thus t h e tw o fo ld
d i v i s i o n o f l i t h o l o g y i s a l l t h a t w i l l b e u n d e rta k e n .
I n c o n c lu s io n , t h e d a ta show a n a t u r a l f o u r f o l d s u b d iv is io n ,
th e h ig h -c o n c a v ity and lo w -c o n c a v ity p r o f i l e segm ents o f s e d im e n ta ry v o lc a n ic s tre a m s , a b b r e v ia te d s e d im e n ta ry concave and se d im e n ta ry
s t r a i g h t , a s w e ll a s g r a n i t i c concave and g r a n i t i c s t r a i g h t .
In tro ­
d u c tio n o f t h i s c l a s s i f i c a t i o n o f d a ta t o lo g - l o g p l o t s o f t h e
p a ra m e te rs m easured s i g n i f i c a n t l y re d u c e s s c a t t e r .
A ppendix I I
p ro v id e s a d e t a i l e d l i s t o f t h e d a ta u s e d i n t h i s s e c t i o n .
CONCEPT OF THE EPHEMERAL STREAM PROFILE
The d a ta p r e s e n te d th u s f a r show t h a t c h a n n e l g r a d ie n t i s , i n
f a c t , r e l a t e d t o d ra in a g e a r e a , c h a n n e l l e n g t h , p a r t i c l e s i z e and w id th :
d e p th r a t i o a s w e ll a s t o l i t h o l o g y and r e l i e f .
p la y i n d e te rm in in g t h e shape o f t h e p r o f i l e ?
What r o l e d o es e a c h
Does p r e c i p i t a t i o n have
any e f f e c t ? - Are th e s e r e l a t i o n s v a l i d i n o th e r m o u n tain ra n g e s?
To s e rv e a s an answ er t o th e s e q u e s tio n s , a m odel o f th e
l o n g i t u d i n a l p r o f i l e w i l l bo d e v elo p e d from th e r e l a t i o n s o b se rv e d i n
th e t h r e e m o untain r a n g e s .
T h is m odel w i l l b e u s e d t o p r e d i c t p r o f ile .-
form i n two a d d i t i o n a l m o u n tain r a n g e s , th e C a t a lin a and Tucson
M ountains, t o t o s t i t s g e n e r a l i t y .
T hese two ra n g e s w ere ch o sen f o r
t h e i r l i t h o l o g i e s and p ro x im ity t o T ucson, b u t a ls o b e ca u se th e y e x te n d
to e le v a tio n s w e ll below th o s e found i n th e t h r e e ra n g e s s tu d ie d .
As
a r e s u l t , t h e p r e c i p i t a t i o n i n t h e lo w e r re a c h e s sh o u ld be s u b s t a n t i a l l y
lo w er th a n i n th e o r i g i n a l n in e s tre a m s .
Review o f P e r t i n e n t Work on L o n g itu d in a l P r o f i l e s
A com plete re v ie w o f t h e developm ent o f th o u g h t on l o n g i t u d i n a l
p r o f i l e s was p r e s e n te d by W oodford (1
).
The id e a s w hich have b e en
in c o r p o r a te d i n t h i s p a p e r s t a r t w ith S h u l i t s (1 9 ^ 1 ), who d e v elo p e d an
e q u a tio n f o r th e p r o f i l e r e l a t i n g i t t o t h e dow nstream d e c r e a s e i n
p a r tic le s iz e .
M ackin (1948) co n ten d e d p a r t i c l e s i z e was n o t t h e s o le
c o n tr o l on g r a d i e n t , b u t t h a t r a t h e r d is c h a r g e , sed im en t lo a d and
p a r t i c l e s iz e a r e a l l im p o r ta n t.
45
However, stre a m g r a d ie n t h a s two im p o rta n t d im e n sio n s, i t s
a b s o lu te v a lu e , th e a c t u a l s lo p e a t a p o i n t , and i t s c o n c a v ity , th o
r e l a t i o n betw een th o s lo p e a t a p o in t and s lo p e s a t p o i n t s up and
dow nstream .
The c o n t r o l s on e a c h d im en sio n "need n o t be c o m p le te ly
i n t e r r e l a t e d , so i t i s im p o r ta n t t o lo o k a t b o th .
U sing d a ta from
gag in g s t a t i o n s th ro u g h o u t t h e w e s te rn U n ite d S t a t e s , L eopold and
Haddock (1953) co n clu d e d t h a t t h e a b s o lu te s lo p e i s im posed on a c h a n n e l
by th e e v e n ts w hich d e te rm in e th e v e r t i c a l and h o r i z o n t a l d is ta n c e s
th ro u g h w hich i t m ust flo w .
The p r o f i l e w hich c o n n e c ts th e two f ix e d
end p o in ts i s an a d ju s tm e n t t o t h e d is c h a r g e , sed im en t lo a d , p a r t i c l e
s iz e and r e l a t i v e e r o d i b i l i t y o f b a n k s and b e d .
L a te r w o rk e rs have e s s e n t i a l l y a g re e d w ith t h i s p o in t o f v iew .
Wolraan (1955) a rg u e d t h a t i n B randyw ine C reek , P e n n s y lv a n ia , s lo p e
c o u ld n o t be a d ju s te d sim p ly t o c a r r y th e p a r t i c l e s iz e s u p p lie d ,
b ecau se v e l o c i t y i n c r e a s e s dow nstream , i n d i c a t i n g o th e r f a c t o r s a r e
a d ju s t in g a l s o .
He c o n c lu d e d t h a t g r a d ie n t on any g iv e n ro a c h i s
p r im a r i ly a f u n c tio n o f th e d is c h a r g e and sed im en t lo a d s u p p lie d t o t h a t
re a c h .
Hack (1957) found i n t h e Shenandoah V a lle y t h a t S = 18( m/A)®*^,
where S i s c h a n n e l g r a d ie n t i n f e e t / m i l e , M i s m edian p a r t i c l e d ia m e te r
i n m il l i m e t e r s , and A i s d ra in a g e a r e a i n s q u a re m ile s .
d is c h a rg e i n h i s r e l a t i o n .
A rea r e p r e s e n t s
I n a d d itio n , th e c o n c a v ity o f a p r o f i l e i s
g r e a t e r when th e p a r t i c l e s i z e d e c r e a s e s dow nstream th a n when i t re m a in s
c o n s ta n t.
He f e l t , how ever, t h a t s lo p e was n o t e n t i r e l y a f u n c tio n o f
p a r t i c l e s iz e and d ra in a g e a r e a , n o tin g p a r t i c u l a r l y t h a t stre a m s i n
a r e a s o f s i m i l a r g e o lo g y a d ju s te d t h e i r p r o f i l e s i n th e same m anner.
M ille r (1 9 5 8 ), i n h i s s tu d y o f h ig h m o u n tain p e r e n n ia l stre a m s i n
46
New M exico, p o in te d o u t t h a t a c o m b in a tio n o f g e o lo g ic f a c t o r s may have
more c o n tr o l on s lo p e th a n h y d r a u lic f a c t o r s .
B rush (1 9 6 1 ), i n h i s work
w ith p e r e n n ia l s tre a m s i n P e n n s y lv a n ia , d e c id e d t h a t b e d ro c k in f l u e n c e s
a c h a n n e l’ s s lo p e and i t s p o s i t i o n i n s p a c e .
He co n clu d e d t h a t b e d ro c k
i s one p a ra m e te r a b s e n t from Hack’ s r e l a t i o n .
The s t u d i e s o f L eopold
and M ille r (1956) i n ep h em eral c h a n n e ls b elo w t h e m o u n tain f r o n t i n New
Mexico showed r e l a t i o n s among h y d r a u lic and g e o m e tric p a ra m e te rs s im ila r
t o th o s e found i n p e r e n n ia l s tre a m s .
They i n d i c a t e d t h a t f o r a g iv e n
r a t e o f in c r e a s e o f v e l o c i t y o r d e p th dow nstream , c o n c a v ity w ould be
h ig h e s t when ro u g h n e ss d e c r e a s e d m ost r a p i d l y dow nstream .
More r e c e n t l y , Schuram (1963* 1968) h a s em phasized t h a t a stre a m
may a ls o a d j u s t i t s l o n g i t u d i n a l p r o f i l e l a t e r a l l y by c h an g in g t h e
s in u o s it y o f i t s c o u r s e ..
S trea m s w ith a h ig h e r r a t i o o f su sp en d ed lo a d
t o bed lo a d , a r a t i o c o n t r o l l e d by c h a n n e l sh ap e , w i l l te n d t o b e more
sin u o u s th a n th o s e w ith low r a t i o s .
The in c r e a s e d s i n u o s i t y in c r e a s e s
c h a n n e l l e n g t h , th u s d e c r e a s in g th e g r a d ie n t and a f f e c t i n g th e p r o f i l e .
C o n tro ls on th e L o n g itu d in a l P r o f i l e
The p r e s e n t s tu d y i n d i c a t e s t h a t w h ile s i m i l a r r e l a t i o n s e x i s t
i n ephem eral c h a n n e ls d r a in in g from th e m o u n ta in s t o th e a l l u v i a l
v a l l e y s a s do e ls e w h e re , t h e p i c t u r e o f t h e l o n g i t u d i n a l p r o f i l e i s
c o m p lic a te d by th e e x is te n c e o f t h e c o n c a v ity c h an g e .
L ith o lo g y ,
r e l i e f , b a s e l e v e l and c lim a te a r e im posed upon e a c h stre a m sy stem .
The
im p o rtan c e o f th e f i r s t two h a s a lr e a d y b een i n f e r r e d from f i g u r e s . 12,
13 and I 5 .
L ith o lo g y , o r more g e n e r a lly g e o lo g y , w hich a ls o in c lu d e s
s t r u c t u r a l e f f e c t s such a s f r a c t u r i n g , c o n t r o l s t h e p a r t i c l e s i z e
•
4?
a v a il a b le f o r t r a n s p o r t , t h e r e s i s t a n c e o f m a t e r i a l t o e ro s io n an d , t o
some e x t e n t , c h a n n e l s h a p e .
T hese t h r e e f a c t o r s , to g e th e r w ith t h e
o u tc ro p p a t t e r n , a r e t h e p rim a ry c o n t r o l s o f c h a n n e l ro u g h n e s s.
T e c to n ic s c o n t r o l t h e v e r t i c a l and h o r i z o n t a l d is ta n c e s th ro u g h
w hich each stre a m m ust move by im p o sin g th e h e ig h ts o f and d is ta n c e s
betw een m o u n tain r a n g e s .
A r a n g e 's h e ig h t above t h e s u rro u n d in g v a l l e y s
i s a c t u a l l y , i t s t o t a l h e ig h t m inus t h e th ic k n e s s o f th e a l l u v i a l f i l l on
i t s fla n k s .
B oth a r e f u n c tio n s o f t e c t o n i c s .
The amount o f f i l l coming
from each ra n g e b o rd e rin g a v a l l e y , a g a in a t e c t o n i c f u n c tio n , d e t e r ­
m ines th e l o c a t i o n o f t h e th ro u g h -flo w in g s tre a m w hich s e r v e s a s l o c a l
b a se l e v e l i n e ac h v a l l e y .
The l o c a t i o n o f th e l o c a l b a se l e v e l
to g e th e r w ith t h e d is ta n c e betw een ra n g e s c o n t r o l s o v e r a l l stre a m le n g th .
The r e l i e f : l e n g t h r a t i o s th u s d e te rm in e d a r e l i s t e d i n T a b le 3*
C lim ate i s a f u n c tio n o f e l e v a tio n , a s p r e c i p i t a t i o n i n c r e a s e s
and te m p e ra tu re d e c r e a s e s w ith in c r e a s in g h e ig h t.
The amount o f
m o is tu re , to g e th e r w ith p r e v a i l i n g te m p e ra tu re , c o n t r o l s w e a th e rin g and
th u s sed im en t p r o d u c tio n .
d is c h a r g e .
P r e c i p i t a t i o n a ls o p ro v id e s th e stre a m w ith
Thus b o th t h e amount o f m a t e r i a l a v a i l a b l e f o r t r a n s p o r t and
t h e amount o f w a te r a v a i l a b l e t o t r a n s p o r t i t , t h e sed im en t lo a d and
d is c h a r g e , can b e e x p e c te d t o v a ry w ith e l e v a tio n .
N orm ally, th e n , r e l i e f and b a s e - l e v e l l o c a t i o n c o n tr o l a b s o lu te
s lo p e by im posing two end p o i n t s on a stre a m , w h ile c o n c a v ity r e f l e c t s
th e a d ju stm e n t o f t h e p r o f i l e t o l i t h o l o g y and c lim a te .
I t i s u n lik e ly
t h a t s i n u o s it y i s an im p o rta n t f a c t o r i n th e c o n c a v ity o f t h e p r o f i l e s
s tu d ie d a s t h e c o a r s e n e s s o f t h e bed m a t e r i a l and w id th o f th e c h a n n e ls
•
48
im ply bed lo a d i s th e dom inant lo a d ty p e ev ery w h ere.
The p r o f i l e s
s tu d ie d , how ever, have a t h i r d im p o r ta n t p o i n t , t h e c o n c a v ity ch an g e.
S ig n if ic a n c e o f th e P o in t o f C o n ca v ity Change
The fre q u e n c y o f t r i b u t a r y e n tr y i n t o th e m ain stre a m ch an g es a t
th e c o n c a v ity ch an g e.
A p a ra m e te r c a l l e d th e c u m u la tiv e t r i b u t a r y
d e n s it y was d e v elo p e d by d iv id in g t h e number o f t r i b u t a r i e s b etw een t h e
d iv id e and e ac h s t a t i o n by t h e c h a n n e l l e n g th t o t h e s t a t i o n i n
th o u sa n d s o f f e e t , g iv in g t h e a v e ra g e number o f t r i b u t a r y e n t r i e s p e r
th o u san d f e e t .
F ig u re 16 shows t h i s p a ra m e te r p l o t t e d a g a in s t c h a n n e l
le n g th i n two s e l e c t e d s tre a m s .
Mote t h a t th e r e l a t i o n u p stre am from
th e c o n c a v ity b re a k i s h ig h ly v a r i a b l e , b u t ..w ith a g e n e r a l t r e n d to w ard
in c r e a s in g d e n s it y dow nstream .
Below th e c o n c a v ity ch an g e, th e t r i b u ­
t a r y d e n s it y shows a c o n s i s t e n t d e c r e a s e .
N ote a l s o th e c lo s e p ro x im ity
o f th e c o n c a v ity b re a k t o t h e s t a r t o f t h e f i n a l d e c li n e o f c u m u la tiv e
tr ib u ta r y d e n s ity .
T a b le 4 shows t h a t t h e c o in c id e n c e o f th e s e two
p o in ts i s a g e n e r a l f e a t u r e .
The d e v ia t io n s a r e g e n e r a lly w ith in th e
l i m i t s o f a c c u ra c y o f t h e l o c a t i o n o f b o th p o i n t s .
T h is id e a i s
s u p p o rte d by th e te n d e n c y f o r t h e g r e a t e s t e r r o r s - t o o c c u r on th o s e
s tre a m s whore th e s t a t i o n s a r e m ost w id e ly sp a c e d .
The in c r e a s e d d i s ­
ta n c e betw een p o i n t s re d u c e s th e a c c u ra c y i n l o c a t i n g th e c h a n g e s.
The change i n t r i b u t a r y d i s t r i b u t i o n im p lie s a change i n
d ra in a g e p a t t e r n and d e n s i t y and b a s i n s h a p e .
Below th e c o n c a v ity
change, t h e t r i b u t a r i e s te n d t o ru n more p a r a l l e l t o th e m ain c h a n n e l
and th u s t o i n t e r s e c t i t l e s s f r e q u e n tly .
The b a s i n , i n t u r n , i s more
e lo n g a te p a r a l l e l t o t h e m ain c h a n n e l below th e c o n c a v ity change th a n i t
T ab le 4 . C om parison o f t h e A c tu a l C hannel L ength from D iv id e t o
C o n ca v ity C h an g e 'w ith Those P r e d ic te d from C um ulative
T r ib u ta r y D e n s ity
A ll d is ta n c e s a r e i n f o e t .
Stream
L ength from
d iv id e t o
c o n c a v ity
change
L ength
p r e d ic te d
from .
trib u ta rie s
D iff e re n c e
(p e r c e n t
of re a l
d is ta n c e )
D is ta n c e
betw een
bounding
s ta tio n s
14.
2410
Mustang 1
4200
*4800
M ustang 2
4200
4300
2 .4
970
Mustang. 3
6000
6000
0.
2000
W hetstone 1
13500
12000
11.
4070
W hetstone 2
11000
8600
22.
4140
W hetstone 3
10000
10000
0.
2930
S ie rrita 1
12000
14000
17.
5630
S io rrita 2
7500
4800
36.
3250
S ie rrita 3
11000
8500
23.
6830
ICT
CHANNEL LENGTH (F E E T )
MUSTANG 2
*
SIERR1TA 3
CONCAVITY CHANGE
FIG. 16.
®
C
RELATION OF CUMULATIVE TRIBUTARY DENSITY TO CHANNEL
LENGTH AND CONCAVITY CHANGE
50
i s above i t .
The d ra in a g e d e n s i t y a ls o te n d s t o b e lo w e r i n t h e down­
stre a m segm ent.
T hese f e a t u r e s i n d i c a t e t h a t th e lo w -c o n c a v ity segm ent
o f th e m ain c h a n n e l w i l l have lo n g e r re a c h e s i n w hich th e o n ly a d d itio n s
t o d is c h a rg e and sed im en t lo a d w i l l come from d i r e c t p r e c i p i t a t i o n i n t o
th e c h a n n e l and o v e rla n d flo w .
in c r e a s e g r e a t l y ,
As a r e s u l t , d is c h a r g e and lo a d w i l l n o t
L eopold, Wolman and M ille r (1 9 6 4 , p . 244) i n d i c a t e
t h a t S cx. (T*95 i n a dow nstream d i r e c t i o n i n ep h em eral c h a n n e ls , w here S
i s c h a n n e l g r a d ie n t and.Q i s d is c h a r g e .
Thus when d is c h a r g e re m a in s
c o n s ta n t, th e c h a n n e l w i l l te n d t o m a in ta in t h e same g r a d i e n t .
The e f f e c t o f b a s i n shape on stre a m p r o f i l e s i s a ls o r e f l e c t e d
i n th e r e l a t i o n o f d ra in a g e a r e a and c h a n n e l l e n g t h .
The change i n t h i s
r e l a t i o n a t th e b re a k i n c o n c a v ity h a s a lr e a d y b e e n i n d i c a t e d .
T a b le 5
shows t h a t d ra in a g e a r e a in c r e a s e s more r a p i d l y i n th e h ig h -c o n c a v ity
p r o f i l e segm ents.
I f t h e r e l a t i o n s b etw een d r a in a g e a r e a and d is c h a r g e ,
and d ra in a g e a r e a and sed im en t lo a d rem ain c o n s ta n t, th e n b o th d is c h a rg e
and sedim ent lo a d in c r e a s e more r a p i d l y i n th e h ig h -c o n c a v ity seg m en ts.
S in c e p r e c i p i t a t i o n h a s a c o n s ta n t r e l a t i o n w ith e l e v a t i o n , t h e u p stre a m
p r o f i l e segment, w ith i t s h ig h e r s lo p e , w i l l e x p e rie n c e a more r a p i d
d e c re a s e i n p r e c i p i t a t i o n dow nstream th a n th e lo w e r p r o f i l e segm ent.
Thus th e d e c re a s e i n p r e c i p i t a t i o n w ould te n d to c o u n te ra c t" t h e " in c r e a s e
i n a r e a downstream and re d u c e t h e r a t e o f in c r e a s e o f d is c h a r g e .
In
a d d itio n , i t w ould te n d t o d e c r e a s e t h e d i f f e r e n c e i n d is c h a rg e
r e l a t i o n s betw een th e two seg m en ts.
However, th e m ag n itu d e o f t h e a r e a
in c r e a s e p re d o m in a te s o v e r t h e p r e c i p i t a t i o n d e c r e a s e t o such an e x te n t
t h a t th e d is c h a rg e s h o u ld s t i l l i n c r e a s e more r a p i d l y th a n sed im en t lo a d
a s i s th e g e n e r a l c a s e (L eopo ld and H addock, 1953, P* 2 2 ).
The c h a n n e l ,
51
a d ju s t s w ith a d e c r e a s in g g r a d i e n t , c r e a tin g c o n c a v ity .
I n th e lo w -
c o n c a v ity r e a c h , th e i n c r e a s e o f d is c h a r g e i s p ro b a b ly o f f s e t b y
i n f i l t r a t i o n i n t o th e c h a n n e l b e d , c r e a t i n g an in c r e a s in g sed im en t
c o n c e n tr a tio n dow nstream .
S tream g r a d ie n t w ould h av e t o d e c r e a s e l e s s
r a p i d l y i n o r d e r t o t r a n s p o r t th e m a t e r i a l (M ackin, 1 9 4 8 ).
The more
c o n s ta n t s lo p e i s r e f l e c t e d by th e lo w e r c o n c a v ity .
The r a t e o f change o f p a r t i c l e s i z e w ith c h a n n e l l e n g t h , q , i s
d i f f e r e n t above and b elo w th e c o n c a v ity change i n e i g h t o f th e n in e
s tre a m s (T ab le 5)» I n e a c h c a s e q i s more n e g a tiv e i n th e u p stre a m seg ­
m ent th a n i t i s dow nstream .
Thus ro u g h n e ss i s d e c r e a s in g more r a p i d l y
i n t h e u p stream segm ent, w hich a c c o rd in g to L eopold and M ille r (1956)
and Hack (1957) s h o u ld r e s u l t i n a h ig h e r c o n c a v ity , a s i t d o e s.
T a b le 5 shows th e r e l a t i o n s among c o n c a v ity and r a t e s o f change
o f a r e a and p a r t i c l e s i z e .
T hese d a t a i n d i c a t e t h a t t h e v a r i a t i o n s o f
th e c o n c a v itie s o f th e lo w -c o n c a v ity segm ents a r e e x p la in e d b y d ra in a g e
a r e a and p a r t i c l e s i z e .
I n g e n e r a l, t h e g r e a t e r c o n c a v itie s a r e a s s o ­
c i a t e d w ith more r a p id ch an g es o f a r e a o r p a r t i c l e s i z e .
The h ig h -
c o n c a v ity segm ents show l e s s r e l a t i o n t o p a r t i c l e s i z e , b u t p a r a l l e l
more c lo s e ly d r a in a g e - a r e a i n c r e a s e s an d , a s s t a t e d e a r l i e r , l i t h o l o g y .
The r e l a t i o n o f w id th :d e p th r a t i o t o l e n g t h a ls o te n d s t o change
a t th e b re a k i n c o n c a v ity .
F ig u r e s 5C» 8c and 11c show t h a t th e r a t e o f
change o f w id th :d o p th r a t i o i s h i g h l y . v a r i a b l e , p a r t i c u l a r l y i n th e low c o n c a v ity seg m en ts.
A r e l a t i o n b etw een w id th :d e p th r a t i o and c o n c a v ity
e x i s t s i n th e h ig h - c o n c a v ity seg m en ts, b u t n o t dow nstream .
The g e n e r a l
d e c re a s e dow nstream i n th e lo w -c o n c a v ity segm ents p ro b a b ly r e f l e c t s
d e c r e a s in g d is c h a r g e .
52
T able 5*
Com parison o f P r o f i l e C o n c a v ity , R ate o f D rain ag e A rea
I n c r e a s e and R a te o f P a r t i c l e S iz e D ecrease
C o n ca v ity i s t h e ex p o n en t i n t h e r e l a t i o n b etw een c h a n n e l
l e n g th and- s tre a m g r a d i e n t , S = kLm. The r a t e s o f a r e a
and p a r t i c l e s i z e ch an g es a r e t h e c o rre sp o n d in g e x p o n en ts
i n th e r e l a t i o n s o f th o s e p a ra m e te rs w ith c h a n n e l le n g t h ,
A = jLP and D ^ = h i # .
H ig h -c o n c a v ity segm ent
Stream -
C o n c a v ity R ate o f R ate o f
(m)
a re a
p a rtic le
change
s iz e
(p )
change
'
L o w -co n cav ity segm ent
C o n ca v ity R ate o f R ate o f
(m)
a re a
p a rtia l
change
s iz e
(p )
change
(q)
(q)
- 1 .5
-.6
+ 2 .4
- .8
-.4
- 1 .0
+ 1 .6
+ .5
- .6
+ 1 .4
- 1 .2
W hetstone 1
- 1 .2
+ 1 .6
-2 .1
- .6
+1.1
- 2 .0
W hetstone 2
-1 .2
+ 1 .9
- 1 .3
- .7
W hetstone 3
- 1 .2
+ 1 .8
- .9
- .1
+ .8
-.4
S ie rrita 1
-1 .1
+ 1 .5
- .5
-•3
+ .8
- .8
S ie rrita 2
- 1 .0
+ 1 .8
- 1 .3
- .8
+ 1 .2
-.4
S ie rrita 3
- 1 .0
+ 1 .4
- 1 .3
- .2
+ .9
-.5
M ustang 1
-1 *9
+ 1 .8 :
M ustang 2
-2 .4
M ustang 3
+ 1 .2
.
- 1 .5
-.4
-.8
53
Summary
Each o f t h e s tre a m s s tu d ie d flo w s b etw een two im posed end
p o i n t s , th e d iv id e and th e m outh.
The p r o f i l e w hich h a s d e v e lo p e d t o
c o n n e c t th e s e p o i n t s c o n s i s t s o f two segm ents a d ju s t e d t o d i f f e r e n t s e t s
o f c o n d itio n s and c o n n e c te d a t th e p o in t o f c o n c a v ity ch an g e.
The
lo c a t i o n o f t h e c o n c a v ity ch an g e, w hich r e p r e s e n t s th e downstream
te rm in u s o f t h e h ig h - c o n c a v ity , o r u p s tre a m , segm ent, i s d e te rm in e d i n
each c a s e b y a change i n t h e r a t e o f in c r e a s e o f d ra in a g e a r e a .
A b so lu te c h a n n e l g r a d ie n t i s d e te rm in e d by t h a t p a r t o f th e b a s i n 's
t o t a l r e l i e f and l e n g t h c o n ta in e d above and below t h e c o n c a v ity ch an g e.
The c o n c a v ity i n e a c h p r o f i l e segm ent r e p r e s e n t s t h e a d ju stm e n t
o f c h a n n e l g r a d ie n t t o d is c h a r g e , sed im en t lo a d and ro u g h n e s s , w hich a r e
f u n c tio n s o f c lim a te and l i t h o l o g y .
They a r e r e p r e s e n te d p r im a r i ly by
d ra in a g e a r e a and p a r t i c l e s i z e , and t o a l e s s e r e x te n t by w id th :d e p th
r a t i o and p e rh a p s p r e c i p i t a t i o n .
Roughness-,• o r p a r t i c l e s i z e , i s
c o n tr o lle d by t h e l i t h o l o g y and l o c a t i o n o f b e d ro c k .
I t d e c r e a s e s more
r a p id ly above th e f i n a l b e d ro c k o u tc ro p i n th e c h a n n e l th a n i t d o es
below i t .
D isc h a rg e and sed im en t lo a d r e l a t e t o d ra in a g e a r e a , w hich
te n d s to in c r e a s e more r a p i d l y i n th e u p p e r p r o f i l e segm ent.
The
g r e a t e r r a t e s o f change o f a r e a and p a r t i c l e s i z e i n th e u p stre a m
segm ent c a u se a g r e a t e r c o n c a v ity t h e r e .
A g r e a t e r change i n c o n c a v ity
r e f l e c t s l a r g e changes i n a r e a and s i z e r e l a t i o n s .
DBVELOR'IENT OF EMPIRICAL EXPRESSIONS FOR THE PROFILES
I f t h e p ro p o se d m odel i s c o r r e c t , a .r e la tio n - b e tw e e n g r a d ie n t
and d ra in a g e a r e a , r e l i e f , p a r t i c l e s i z e , w id th :d e p th r a t i o and
p r e c i p i t a t i o n sh o u ld e x i s t w hich r e p r e s e n t s a m a th e m a tic a l e x p re s s io n
o f th e p r o f i l e and w i l l a c t u a l l y p r e d i c t p r o f i l e s e ls e w h e re .
The b e s t
f i t e q u a tio n s w ere so u g h t u s in g a s ta n d a r d m u ltip l e r e g r e s s io n ap p ro ach
(S n ed eco r, 1 9 5 6 ).
The s t a t i s t i c a l c o m p u ta tio n s w ere done on a CDC 6400
com puter u s in g a program w r i t t e n b y C h a rle s K. H uszar o f t h e U n iv e r s ity
o f A rizo n a Computer C e n te r.
The program i s d e s ig n e d t o m in im ize th e sum
o f s q u a re s o f d e v ia t io n s p a r a l l e l t o t h e a x is o f t h e d e p en d en t v a r i a b l e
r a t h e r th a n p e r p e n d ic u la r t o t h e l i n e o f b e s t f i t .
W hile th e l a t t e r
te c h n iq u e w ould have b e en more u s e f u l f o r t h i s p ro b lem , no a p p r o p r ia te
program was a v a i l a b l e , and t h e w r i t e r ’ s com puter e x p e rie n c e d id n o t
w a rra n t an a tte m p t a t d e v e lo p in g o n e .
The m ethod u s e d , how ever, i s
s a t i s f a c t o r y a s lo n g a s i t i s u se d c o n s i s t e n t l y .
The r e l a t i o n s w hich r e s u l t e d from d i r e c t r e g r e s s i o n a n a ly s is
o f th e raw d a ta w ere u n s a t i s f a c t o r y f o r two r e a s o n s .
F i r s t , th e
r e l a t i o n betw een d ra in a g e a r e a and t h e s q u a re o f r e l i e f (F ig 13b) m ust
be im posed on t h e d a t a , f o r i t w i l l n o t n e c e s s a r i l y r e s u l t from th e
l e a s t s q u a re s a n a l y s i s .
S e c o n d ly , th e s tre a m s sam pled w ere to o s i m i l a r
i n p r e c i p i t a t i o n v a lu e s t o a llo w developm ent o f a g e n e r a l r e l a t i o n
c o n ta in in g t h a t p a ra m e te r.
I n o th e r w o rd s, mil n in e stre a m s sam pled
s t a r t e d ro u g h ly i n th e same h ig h p r e c i p i t a t i o n zo n e, flow ed th ro u g h
54
55
s e v e r a l zones o f lo w e r p r e c i p i t a t i o n and ended i n s i m i l a r low
p r e c i p i t a t i o n z o n es.
As a r e s u l t , r e g r e s s i o n e q u a tio n s show o n ly t h a t
f o r th e stre a m s sam pled, s te e p g r a d i e n t s te n d t o o c c u r i n h ig h p r e c i p - '
i t a t i o n z o n e s.
T h is i s s t r i c t l y a r e f l e c t i o n o f t h e g eo m etry o f th e
stream p r o f i l e , w here s te e p e r g r a d i e n t s o c c u r a t h ig h e r e l e v a t i o n s , and
does n o t i n d i c a t e p r e c i p i t a t i o n ’ s t r u e e f f e c t .
The n in e sam ple s tre a m s
m ust be compared l a t e r t o s tre a m s i n v e r y d i f f e r e n t p r e c i p i t a t i o n zones
t o d e te rm in e t h i s e f f e c t .
As a r e s u l t o f th e s e f i n d i n g s , o n ly fo u r v a r i a b l e s w ere u s e d i n
th e r e g r e s s io n a n a ly s e s , g r a d i e n t , S , a r e a : r e l i e f ^ r a t i o , A/R^,
p a r t i c l e s i z e , D ^ , and w id th :d e p th r a t i o , W/D,
The e q u a tio n s , t h e
c o r r e l a t i o n c o e f f i c i e n t s and t h e i r s i g n i f i c a n c e f o r e ac h o f th e f o u r
d a ta s u b d iv is io n s fo llo w :
S e d im e n ta ry co n cav e:
S = ( 6 .6 x 10~ 5)R .80± .3*tT ]^.20± .22(,.f/D) .1 h i:.2 8
a .4 0 ± .1 ?
r. = .800
F = 1 8 .7 (9 9 .5 * )
S e d im e n ta ry s t r a i g h t :
S = ( l . h x 10""3)R*35b 1
08
A.1 9 ± .0 7
r = .7 9 5 (9 7 .5 2 ) ,
F = 9 -3 (9 9 .5 2 )
G r a n itic c o n ca v e :
s = (7.6 x i o~^)r^*025> i
"
:
r = .940 (9 9 2 ).
_
_
_
1o(yr/p).
_
F = 4 6 .0 (9 9 .5 2 )
14
56
G r a n itic s t r a i g h t :
S = ( 1 .6 x 1 o - ^ R ’ 42* - 1* ^ ’ 062^ ^ 6
r = .5 8 8 (9 9 ^ ) ,
F = 5 .7 6 " (9 9 ^ )
V fi.dth:depth r a t i o was e lim in a te d from t h e s t r a i g h t segm ents
b e ca u se i t was 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 , p ro b a b ly due t o th e g r e a t
v a r i a b i l i t y .in th e s e seg m e n ts.
I n g e n e r a l, th e re m a in in g v a r i a b l e s
exceed a s i g n if ic a n c e l e v e l o f 90$, i n d i c a t i n g t h a t t h e r e i s o n ly one
chance i n t e n t h a t a random v a r i a b l e c o u ld re d u c e t h e d e v ia t io n o f S
a s much a s th e y d o .
The m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t s ( r ) i n d i c a t e
th e c h an n e l g r a d ie n t i s c l o s e l y r e l a t e d to t h e s e p a ra m e te rs .
In
a d d itio n , th e F r a t i o s (S n e d e c o r, 1956 and Owen, 1962) show t h e
s ig n if ic a n c e
l e v e l o f a l l th e s e e q u a tio n s e x ce e d s 99$*
The F r a t i o i s
th e r a t i o o f th e mean s q u a re o f t h e d ep en d e n t v a r i a b l e , i n t h i s c a s e S ,
t o th e mean s q u a re o f t h e d i f f e r e n c e s b etw een r e a l S and t h e S p r e d ic te d
b y th e r e g r e s s i o n .
Thus a h ig h r a t i o i n d i c a t e s t h e r e g r e s s io n h a s
a good f i t .
D e v ia tio n s o f t h e g r a d ie n t s p r e d ic te d by t h e e q u a tio n s from t h e
r e a l o n es g e n e r a l ly a re t h e r e s u l t o f d i f f e r e n c e s i n c o n c a v it y .
Stream s
w ith h ig h e r th a n a v era g e c o n c a v ity have s t e e p e r g r a d ie n t s upstream and
g e n t le r on es downstream th a n t h o s e p r e d ic t e d .
S in c e c o n c a v ity
d if f e r e n c e s a re r e l a t e d t o l i t h o l o g y and b a s in sh a p e , m ost o f t h e
d e v ia t io n s from t h e e q u a tio n s a r e f u n c t io n s o f t h e s e two f a c t o r s .
E xtrem ely la r g e d e v ia t i o n s r e s u l t a t s t a t i o n s w here u n u su a l f e a t u r e s
su ch a s bed rock o u tc r o p s , a c t i v e t r e n c h in g , and u n u su a l ch a n n el w a ll
57
p r o p e r t i e s l i k e c a l i c h e cem en tin g te n d t o p ro d u c e u n u s u a l w id th :d e p th
r a tio s or p a r tic le s iz e s .
V e g e ta tio n seemed t o have no c o n s i s t e n t
e f f e c t on th e d e v i a t i o n s .
I n a d d i t i o n , w h ile d r a in a g e a r e a g e n e r a lly
in c r e a s e s w ith le n g th , i t d o e s so i n l a r g e in c re m e n ts a t e ac h m ajo r
trib u ta ry .
As a r e s u l t , a s t a t i o n im m e d ia te ly b elo w a t r i b u t a r y
ju n c tio n w i l l have a d ra in a g e a r e a w hich i s u n u s u a lly h ig h f o r i t s
lo c a tio n .
A s t a t i o n j u s t u p stre a m w ould b e u n u s u a lly lo w .
When t h e s e
v a lu e s a r e s u b s t i t u t e d i n t h e g e n e r a l e q u a tio n w hich assum es a u n ifo rm
r a t e o f i n c r e a s e , th e y p ro d u c e a d d i t i o n a l d e v i a t i o n s .
I f p r e c i p i t a t i o n e f f e c t s g r a d i e n t , a s tre a m w hich flo w s th ro u g h
zones o f lo w e r p r e c i p i t a t i o n th a n th o s e i n c o rre sp o n d in g p o s i t i o n s on
a n o th e r stre am s h o u ld te n d t o h ave a s te e p e r p r o f i l e .
T h is e f f e c t
w ould b e a p p a re n t i f t h e d e v ia t io n s showed t h e m odel p r e d ic te d g r a d ie n ts
to o g e n tle f o r t h e lo w e r p r e c i p i t a t i o n stre a m and to o s te e p f o r th e
h ig h e r one.
No such r e l a t i o n t o p r e c i p i t a t i o n was fo u n d , how ever.
I n a d d i t i o n t o e q u a tio n s (1 ) t o ( 4 ) , a s u i t e o f f u n c tio n s
r e l a t i n g e ac h v a r i a b l e t o t h e d i s t a n c e from th e d iv id e , L, was o b ta in e d
f o r each s u b d iv is io n (T a b le 6 ) .
The c o e f f i c i e n t n i n th e e q u a tio n s
S = kLn r e p r e s e n t s th e a v e ra g e c o n c a v ity f o r e ac h p r o f i l e segm ent.
N ote
t h a t i n each c a s e t h i s a v e ra g e c o n c a v ity i s much lo w e r th a n t h a t w hich
one w ould e x p e c t from t h e v a lu e s i n T a b le 5*
The r e a s o n f o r t h i s
a p p a re n t in c o n s is te n c y i s t h e u s e o f d i f f e r e n t m ethods t o o b ta in th e
b e s t f i t e q u a tio n s .
R e c a ll t h a t th e com puter m in im iz e s th e s q u a re s o f
d e v ia tio n s p a r a l l e l t o an a x i s .
On th e o th e r hand, t h e b e s t f i t l i n o s
d e te rm in e d g r a p h ic a ll y by eye r e p r e s e n t a m in im iz a tio n o f s q u a re s o f
58
d e v ia tio n s p e r p e n d ic u la r t o th e b e s t f i t l i n e .
The d i f f e r e n c e betw een
th e two l i n e s i n c r e a s e s a s sam ple s i z e d e c r e a s e s o r s c a t t e r i n c r e a s e s .
I n s i t u a t i o n s w here a v e r y s m a ll number o f d a ta p o in ts a r e
a v a i l a b l e , such a s i n d e te rm in in g c o n c a v ity •f o r a p r o f i l e segm ent w ith
o n ly fo u r t o e ig h t p o i n t s , th e l i n e f i t by eye i s p ro b a b ly j u s t a s v a l i d
a r e l a t i o n a s t h a t f i t b y co m p u ter.
T h is m ethod a llo w s some i n t e r ­
p r e t a t i o n o f th e s c a t t e r b a s e d on t h e r e l a t i o n o f one p r o f i l e segm ent t o
th e o th e r i n a s tre a m , th e c o n s id e r a tio n o f a b e r r a n t p o i n t s r e l a t e d t o
u n u s u a l c h a n n e l f e a t u r e s and t h e r e a l i z a t i o n t h a t t h e r e l a t i o n o f
g r a d ie n t t o le n g th becomes i n c r e a s i n g l y p o o r to w ard t h e d iv id e a s t h e
e r r o r i n m easurem ent o f b o th p a ra m e te rs i n c r e a s e s .
D ata p o i n t s c an b e
w eig h ted a c c o rd in g ly a s . t h e l i n e i s draw n, w h ile t h e com puter i s u n a b le
to i n t e r p r e t in f o r m a tio n i t h a s n o t r e c e iv e d .
v a lu e s have b een u s e d on i n d i v i d u a l s tre a m s .
C o n se q u e n tly , g r a p h ic a l
When more sam ple p o i n t s
a r e a v a i l a b l e , a s i n t h e f o u r f o l d s u b d iv is io n , t h e c o m p u te r's r e s u l t s
a r e more a c c u r a te and, i n t h e c a s e o f m u l t i p l e c o r r e l a t i o n , e a s i e r
t o o b ta in .
Thus a l l e q u a tio n s r e l a t i n g o n ly t h e f o u r s u b d iv is io n s a r e
com puter d e r iv e d .
Each v a r i a b l e on t h e r i g h t s id e s o f e q u a tio n s (1 ) t o (4 ) can be
r e p la c e d w ith an e x p r e s s io n i n te rm s o f le n g th (T a b le 6 ) .
R e lie f i s
c o n s ta n t f o r each s tre a m , and when i t s v a lu e i s s u b s t i t u t e d f o r R i n an
e q u a tio n , an e x p re s s io n i s p ro d u c e d f o r g r a d ie n t i n te rm s o f c h a n n e l
le n g th , p r e d ic te d e n t i r e l y by th e l o n g i t u d i n a l v a r i a t i o n s o f t h e o th e r
p a ra m e te rs .
For exam ple, i n t h e s e d im e n ta ry concave s u b d iv is io n ,
W idth: d e p th "
W id th :d e p th
ra tio
G ra d ie n t
8
H
(A
II
A
Is
x—
x-z
11
CO
O
H
G)
If
<
1
1^
1
!
0
CO
L
II
tti
•%>
a K-•
co
On
V\ k* in
If
11
qe
o
CM
IT»
4
11
M
n = 14
P a r tic le s iz e
vn ii
11 #
CO
^3*
o
S e d im e n ta ry s t r a i g h t
D rain ag e a r e a
R i s th e c o r r e l a t i o n c o e f f i c i e n t . The s u b s c r i p t s oni i t s v a lu e in d ii c a te th e
s ig n ific a n t c e . 2 = 99$, 1 = 93 $ ;and 0 i s l e s s th a n 9'5$. The number o f sam ples
i n e ac h su b d iv is io n i s g iv e n by ia.
R e g re ssio n i E q u a tio n s R e la tin g Dr a in a g e A rea, A, P a rt » ic le S iz e ,
R a tio , w/E i, and G ra d ie n t, S , t o C hannel L en g th , L
P r o f i l e segm ent
T a b le 6 .
59
N
%
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;
to
ii
ti
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11
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cm
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11
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8
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vr\
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°
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II
ti
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60
lo g S = - 1 .? 8 - .iH)log(A/R2 ) + .a O lo g E ^ + ,1*H og(w /D ).
S u b s t i t u t i n g from T ab le 5 p ro d u c e s :
lo g S = - I .78 + ,801ogR - ,4 0 ( - 8 .0 2 + 2.031ogL )
+ .2 0 ( 4 .0 6 - .7 llo g L ) + ,1 4 ( .5 5 + .441ogL)
lo g S = - .0 8 + .801ogR - .931ogL
S = -.8 3 R * 80 L” *9 3
(5)
For t h e re m a in in g t h r e e s u b d iv is io n s , t h e e q u a tio n s a r e :
S ed im en tary s t r a i g h t
S = -.2 9 R , 5 8 L*-e.50
( 6)
G r a n itic concave
S = -.1 1 R 1 , 02L“ *8^
(7 )
G r a n itic s t r a i g h t
S = -.0 3 8 R * 2f2L~*33
D e s p ite d i f f e r e n c e s i n t h e v a r i a t i o n o f a r e a s r e l i e f 2 r a t i o and
p a r t i c l e s i z e m t h l e n g th i n th e s e d im e n ta ry and g r a n i t i c concave
segm ents, th e e x p o n en ts o f l e n g th i n e q u a tio n s (5 ) and (7 ) a r e s i m i l a r .
These e x p o n en ts a r e t h e c o n c a v ity o f t h e p r e d ic te d p r o f i l e s .
Thus t h e
concave segm ents i n g e n e r a l have s i m i l a r sh ap e s r e g a r d l e s s o f l i t h o l o g y ,
b u t th e manner i n ■which th o s e c o n c a v itie s a r e a t t a i n e d d i f f e r s .
The
exponent o f le n g th f o r s e d im e n ta ry concave seg m en ts, - . 9 3 , g e t s -.8 1
from a r e a , - . 1 4 from p a r t i c l e s i z e and + .0 2 from w id th :d e p th .
+87$ , +15£ and -2 ^ r e s p e c t i v e l y .
These a r e
I n t h e g r a n i t i c concave seg m en ts, t h e
same t h r e e p a ra m e te rs c o n t r i b u t e - . 8 6 , -.1 5 and + .1 2 t o t h e ex p o n en t
- . 89 , +96$ , +17? and - 13$ r e s p e c t i v e l y .
61
The s t r a i g h t p r o f i l e segm ents a r e n o t a s s i m i l a r , r e f l e c t i n g th e
c o n s is te n t d if f e r e n c e s i n c o n c a v ity w hich s e d im e n ta ry and g r a n i t i c
c h a n n e ls show dow nstream .
I n th e s e d im e n ta ry s tre a m s , l e n g t h 's
exponent o f -.5 0 i s t h e sum o f - .2 9 from a r e a (5 8 /0 and -.2 1 from
p a r t i c l e s i z e (4 2 $ 0 .
On th e o th e r h a n d , p a r t i c l e s i z e shows much l e s s
e f f e c t i n t h e g r a n i t i c s tre a m s w here i t c o n t r i b u t e s o n ly -.0 3 (9 /0 t o
th e exponent o f - . 3 3 .
The re m a in in g - .3 0 (91$) i s c o n t r o l l e d by
d ra in a g e a r e a .
T a b le ?•
C om parison o f R e a l and P r e d ic te d C o n c a v itie s
P ro file
segm ent
P r e d ic te d
c o n c a v ity
A verage
re a l
c o n c a v ity
D iff e re n c e
S e d im e n ta ry concave
-.9 3
- 1 .0 '
-7 $
S e d im e n ta ry s t r a i g h t
- .5 0
-.5 6
-1 1 $
G r a n itic concave
- .8 9
G r a n itic s t r a i g h t
- .3 3
- 1 .0
-1 1 $
-.3 2
+3$
T ab le ? com pares th e c o n c a v i t i e s p r e d i c t e d b y l o n g i t u d i n a l
v a r i a t i o n s o f p a ra m e te rs i n e q u a tio n s (5 ) t o (8 ) w ith a v e ra g e v a lu e s f o r
com puter d e riv e d c o n c a v i t i e s o f t h e i n d i v i d u a l w ashes i n each
s u b d iv is io n .
I n each c a s e t h e d i f f e r e n c e i s w ith in th e l i m i t s o f
a c c u ra c y o f th e m easu rem en ts, w hich w ould a llo w f o r a v a r i a t i o n
o f 10 to 20$.
The e q u a tio n f o r t h e p r o f i l e , r e l a t i n g e l e v a t i o n and l e n g t h , i s
sim ply th e i n t e g r a l o f th e g r a d i e n t - l e n g t h e x p r e s s io n .
se d im e n ta ry concave a s an ex am p le, t h e c a l c u l a t i o n s a r e :
A gain, u s in g
62
s = -.83R*8()i f 93
(5 )
dH/dL » -.83R , 80L"*93
H « -.83R*80j i r ,93dL
H = «11.9 r *8 ol *°7 + C
(9)
The e q u a tio n s f o r th e re m a in in g s u b d iv is io n s a r e :
S ed im en tary s t r a i g h t
H = -.SSR*^3! / ^ 0 + c
(10)
G r a n itic concave
H « -R1*02!* 11 + C
(11)
G r a n itic s t r a i g h t
H = -*05?R*^2L*8^ + C
(12)
The i n t e g r a t i o n c o n s ta n t c a n b e d e te rm in e d f o r a g iv e n p r o f i l e
segment by s u b s t i t u t i n g th e v a lu e s o f H, L and R from one o f t h e
end p o i n t s .
TEST OF THE PROFILE EQUATIONS
Two stre a m s from b o th th e C a t a lin a and Tucson M ountains w ere
chosen f o r t e s t i n g t h e m odel ( F ig . 1 7 ).
B oth c h a n n e ls i n t h e C a ta lin a s
d r a in r e g io n s o f C a t a lin a G n e is s , a c o a r s e - g r a in e d ro c k re s e m b lin g
g r a n i t e i n c o m p o sitio n and some w e a th e rin g p r o p e r t i e s .
The Tucson
M ountain w ashes flo w th ro u g h a r e a s o f v a r i e d l i t h o l o g y , in c lu d in g
r h y o l i t e , s a n d s to n e , m udstone and lim e s to n e , t h e same l i t h o l o g i e s
found i n th e fo u r o r i g i n a l s e d im e n ta ry -v o lc a n ic s tre a m s .
The u n i t s i n
Tucson 3 a r e r e l a t i v e l y s o f t an d , u n l i k e th e s e d im e n ts i n t h e M ustangs
and W h etsto n es, w e a th e r t o san d s i z e fra g m e n ts .
The Tucson 2 b a s in , on
th e o th e r h an d , i s c ro s s e d by s e v e r a l r h y o l i t i c d ik e s , w hich have c au se d
some l o c a l motam orphism .
T h is f a c t o r , t o g e th e r w ith a to u g h e r sa n d s to n e
u n i t , c r e a t e s more r e s i s t a n t b ed m a t e r i a l .
Map and f i e l d d a t a f o r th e s e
fo u r stre a m s a re l i s t e d i n A ppendix I I .
P r o f i l e s w ere c o n s tr u c te d f o r e ac h stre a m u s in g e q u a tio n s
(9 ) t o (1 2 ) .
The p o s i t i o n o f t h e change i n c o n c a v ity was d e f in e d on th e
b a s i s o f t h e c u m u la tiv e t r i b u t a r y d e n s it y d is c u s s e d e a r l i e r .
The p o in t
w here th e d e n s i t y began i t s f i n a l d e c r e a s e dow nstream was u s e d , and i s
shown on F ig u re s 18 and 19 a s th e " p r e d ic te d b re a k " .
In th re e o f th e
fo u r c a s e s t h i s l o c a t i o n m ethod was v e r y a c c u r a t e , w h ile i n t h e f o u r t h ,
C a ta lin a 1 , th e in a c c u r a c y a p p a r e n tly d id n o t e f f e c t t h e r e s u l t s .
The c a l c u l a t i o n s in v o lv e d w i l l be d e m o n stra te d on C a t a lin a 2.
The c u m u la tiv e t r i b u t a r y d e n s it y i n d i c a t e d t h a t th e c o n c a v ity b re a k
63
3
FIG . 17.
LOCATION MAP FOR STREAMS AND STATIONS IN CATALINA AND TUCSON MOUNTAINS.
P
65
o c c u rs 11500 f e e t , L, from t h e d iv id e a t an e l e v a t i o n o f 2960 f e e t , H.
S in c e th e d iv id e i s 6000 f e e t h ig h , t h e u p p e r p r o f i l e segm ent h a s a
r e l i e f o f 3040 f e e t , R.
H = -R1 ,0 2 L*11 + C
(1 1 )
H = -3 6 1 0 1 /11 + C
At th e c o n c a v ity b re a k ,
2960 = -3 6 1 0 (1 1 5 0 0 )* 11 + C
2960 = -10150 + C
c = 13110
Thus f o r t h e concave segm ent,
H = -3 6 1 0 1 /11 + 13110
S u b s t i t u t i o n o f a.num ber o f a r b i t r a r y c h a n n e l le n g th s b etw een 0
and 11500 f e e t and c a l c u l a t i o n o f t h e c o rre s p o n d in g e l e v a t i o n s w i l l g iv e
s u f f i c i e n t d a ta t o p l o t th e p r o f i l e .
The com puted p r o f i l e s have n o t
been u se d betw een 0 and 1000 f e e t l e n g t h , how ever, s in c e g r a d i e n t ,
dfl/dL, ap p ro a ch e s i n f i n i t y o r v e r t i c a l a s L a p p ro a c h e s z e r o .
T h is i s
n o t th e c a s e i n t h e n a t u r a l c h a n n e ls , a s a c o n s i s t e n t c o n c a v ity i s n o t
m a in ta in e d t h i s c lo s e t o t h e d i v i d e .
I t was a ls o n e c e s s a ry t o d e f in e
b o th computed p r o f i l e segm ents a s p a s s in g th ro u g h th e c o n c a v ity b re a k
i n o rd e r t o in s u r e a c o n tin u o u s p r o f i l e .
F or th e s t r a i g h t segm ent o f C a t a lin a 2 , r e l i e f i s 660 f e e t , and
th e c h a n n e l le n g th and e l e v a t i o n a t t h e c o n c a v ity b re a k a r e I I 500 and
2960 f e e t r e s p e c t i v e l y .
H = -.0 5 ? R * if2L *67 + C
S u b s t i t u t i n g f o r R, L and H p ro d u c e s :
(1 2 )
66
2960 = -4 6 5 + C
C = 3425
T hus:
•H = -.8 8 L * 67 + 3425
A gain, s u b s t i t u t i o n o f a r b i t r a r y le n g t h s and c o m p u ta tio n o f
e le v a tio n s p ro d u c e s th e p o i n t s f o r t h e p r o f i l e p l o t t e d i n f i g u r e 18.
The re m a in in g p r e d i c t e d p r o f i l e s w ere o b ta in e d i n th e same m anner.
F ig u r e s 18 and 19 show c lo s e s i m i l a r i t i e s b etw een t h e com puted
and a c t u a l p r o f i l e s .
The maximum v e r t i c a l and h o r i z o n t a l s e p a r a tio n s i n
e a c h segm ent a re a ls o shown.
These d i s t a n c e s a r e a c t u a l l y c u m u la tiv e
e r r o r s , b u t th e y n e v e r ex ceed 15$ i n t h e co n cav e seg m en ts, w e ll w ith in
th e e r r o r from m easurem ents a lo n e .
The e r r o r s te n d t o be l a r g e r i n t h e
s t r a i g h t seg m en ts, g o in g up t o 20$, w hich i s p ro b a b ly beyond sim p le
m easurem ent e r r o r .
I n e a c h c a s e , how ever, t h e d e v ia t io n from th e m odel can b e
e x p la in e d on th e b a s i s o f t h e l i t h o l o g y , b ed m a t e r i a l o r b a s in sh a p e .
C a t a lin a 1 , w hich shows t h e p o o r e s t f i t i n th e concave segm ent, i s i n
g n e is s below numerous s te e p c l i f f s .
L arge b ed m a t e r i a l i s m a in ta in e d
f a r dow nstream , and t h e r a t e o f p a r t i c l e s i z e d e c r e a s e i s t h u s lo w .
a r e s u l t , c o n c a v ity i s lo w e r th a n e x p e c te d i n t h e m o d el.
In th e
s t r a i g h t seg m en ts, t h e p r e d i c t e d p r o f i l e i s g e n t l e r and l e s s concave
th a n th e r e a l one i n C a t a lin a 1.
F i e l d i n v e s t i g a t i o n s c o n firm e d t h a t
th e p a r t i c l e s iz e d e c r e a s e s more r a p i d l y i n t h e s t r a i g h t segm ent th a n
i s u s u a l f o r g r a n i t i c s tre a m s , due t o th e m a in te n a n c e o f l a r g e b ed
m a t e r i a l f a r dow nstream i n t h e co n cav e segm ent o f C a t a lin a 1 .
The
As
67
CA TALINA I
M‘
• REAL PROFILE
o PREDICTED PROFILE
4 X = VERTICAL EXAGGERATION _
600C -
MAXIMUM ERROR
V ERTICA L
17%
H O RIZONTAL 2 5 %
4000MAX. ERROR
VERT.
15%
HORIZ. 1 2 %
PREDICTED
L
BREAK
30C C -
5000
10000
15000
CHANNEL LENGTH
20000
25000
CATALINA 2
• REAL PROFILE
GOOD*
”
PREDICTED PR O FILE
4X = VERTICAL EXAGGERATION
5000 _
MAXIMUM ERROR
VERTICAL
7%
HORIZONTAL 6 %
3000-
MAX. ERROR
VERT.
10 %
HORIZ. 4 . 5 %
PREDICTED
BREAK
2000
5000
lOOOO
15000
20000
.CHANNEL LENGTH
FIG . 18.
COMPARISON OF REAL AND PREDICTED PROFILES
IN CATALINA MOUNTAINS
25000
68
TU CSO N 2
3500
•
REAL PROFILE
®
PREDICTED PR O FIL E
ELEVATION (FEET)
. 0X = V E R T IC A L E X A G G E R A T IO N
MAXIMUM ERROR
VERTICAL
12 .5
HORIZONTAL 18%
M AX.ERROR x
2500
VERT.
H0R1Z.
14%
94%
5000
• 10000
15000
20000
m
CHANNEL LENGTH (FEET)
4000
TU C SO N
3
*
REAL PR O FIL E
°
PREDICTED P R O F IL E
ELEVATION (FEET)
8 X = VERTICAL EX A G G ERA TIO N
MAXIMUM ERROR
VERTICAL
1 2 .5 %
HORIZONTAL 18 %
3000
PREDICTED
X
BREAK
MAX. ERROR
2500
VERT.
HORIZ,
0 .3 %
7 .7 %
5000
10000
15000
20000
CHANNEL LENGTH (FEET)
F IG . 19.
C O M PA R ISO N BETW EEN R EA L AND PR ED IC TED P R O F IL E S
IN TH E T U C SO N M OUNTAINS
69
computed p r o f i l e f o r C a t a lin a 2 shows l i t t l e d e v ia t io n from th e a c t u a l
p r o f i l e , b e ca u se th e s tre a m shows a r a t e o f p a r t i c l e s i z e d e c r e a s e
s im ila r to th e g r a n i t i c s tre a m s i n t h e W h etsto n es and S i e r r i t a s ,
Tucson 3 a ls o shows a c lo s e r e l a t i o n b etw een r e a l and p r e d i c t e d
p r o f i l e s i n th e concave segm en t, due t o a r a t e o f p a r t i c l e s i z e d e c r e a s e
s i m i l a r to t h e o th e r s e d im e n ta ry s tre a m s .
M ost o f t h e d e v ia t io n
betw een th e Tucson 2 r e a l and p r e d i c t e d p r o f i l e s r e s u l t s from t h e
s tre a m ’ s flo w in g a lo n g th e f l a n k o f a h i l l b etw een 2950 and 2600,
T h is
s i t u a t i o n c r e a t e s an u n u s u a lly lo w r a t e o f a r e a i n c r e a s e w hich r e s u l t s
i n th e low c o n c a v ity i n t h a t p a r t o f t h e segm ent.
B oth Tucson M ountain
s tre a m s a r e l e s s concave th a n t h e p r e d i c t e d p r o f i l e s i n t h e i r dow nstream
segm ents due t o a low r a t e o f p a r t i c l e s i z e d e c r e a s e com pared t o th e
o th e r s e d im e n ta ry s tre a m s .
The Tucson s tre a m s flo w a t e l e v a t i o n s a lm o st t o t a l l y below a l l
• s t a t i o n s on th e o r i g i n a l n in e s tre a m s .
Thus i f p r e c i p i t a t i o n i s a
f a c t o r , i t sh o u ld have some e f f e c t on t h e p r o f i l e s o f th e s e s tre a m s .
A lo w e r p r e c i p i t a t i o n s h o u ld r e s u l t i n a s m a lle r d is c h a r g e f o r a g iv e n
d ra in a g e a r e a , w hich i n t u r n w ould r e q u i r e a s te e p e r g r a d ie n t t o
tra n s p o rt m a te ria l.
However, e x a c tly t h e o p p o s ite i s t h e c a s e .
On b o th
p r o f i l e s , t h e g r a d ie n t p r e d i c t e d from th e m odel i s s te e p e r th a n t h e
r e a l g r a d ie n t.
A p p a re n tly p r e c i p i t a t i o n h a s no e f f e c t on t h e p r o f i l e s , o r i f i t
h a s an e f f e c t , i t i s so m ino r t h a t th e s tu d y was n o t p r e c i s e enough t o
d e te c t i t .
I t c o u ld i n f a c t b e overshadow ed by t h e o th e r f a c t o r s
a f f e c t i n g g r a d ie n t.
I t i s a ls o p o s s i b l e t h a t th e t o t a l summer
70
p r e c i p i t a t i o n d o e s n o t r e l a t e - t o h y d r a u lic f a c t o r s su ch a s d is c h a r g e .
A more im p o rta n t p a ra m e te r m ig h t b e a v e ra g e sto rm i n t e n s i t y , w hich c o u ld
i n f a c t be r e l a t i v e l y c o n s ta n t th ro u g h o u t t h e s tu d y a r e a .
d a ta w ere a v a i l a b l e t o e v a lu a te t h i s p o s s i b i l i t y .
In s u ffic ie n t
However, i f t h i s w ere
th e c a s e , storm d is c h a r g e s p e r u n i t a r e a w ould b e t h e same a t a l l
e l e v a tio n s .
The o n ly e f f e c t o f t h e g r e a t e r t o t a l p r e c i p i t a t i o n a t
h ig h e r e le v a tio n s th e n w ould b e t o te n d t o in c r e a s e r a t e s o f w e a th e rin g .
The t e s t h a s t h u s shown t h a t e q u a tio n s (9 ) th ro u g h (1 2 ) d e r iv e d
from th e l o n g i t u d i n a l v a r i a t i o n s o f d ra in a g e a r e a , p a r t i c l e s i z e and
w id th :d e p th r a t i o can b e u s e d t o p r e d i c t p r o f i l e s when r e l i e f , l i t h o l o g y
and t r i b u t a r y d i s t r i b u t i o n a r e known.
F u rth e rm o re , i t h a s v e r i f i e d t h e
p ro p o se d m odel o f th e s e e p h em eral s tre a m p r o f i l e s a s two segm ents
a d ju s te d t o d i f f e r e n t s e t s o f c o n d itio n s .
D e v ia tio n s o f t h e p r e d i c t e d
p r o f i l e s from t h e r e a l on es c a n b e e x p la in e d by u n u s u a l l o n g i t u d i n a l
changes o f th e p a r t i c l e s i z e .
P r e c i p i t a t i o n , a s m easu red b y 't h e in d e x
r e l a t i n g i t t o e l e v a t i o n shows no d i s c e r n i b l e e f f e c t .
CONCLUSIONS
The l o n g i t u d i n a l p r o f i l e s o f ep h em eral s tre a m s d r a in in g from th e
m ou n tain s to th e a l l u v i a l v a l l e y s i n s o u th e a s te r n A riz o n a a r e a d ju s te d
t o fo u r m ajo r in d e p e n d e n t v a r i a b l e s , r e l i e f , .l o c a l b a s e l e v e l , l i t h o l o g y
and c lim a te .
R e l i e f and l o c a l b a s e l e v e l , th e m outh o f t h e s tre a m ,
d e te rm in e th e v e r t i c a l d ro p a c h a n n e l m ust u n d erg o and th e d is ta n c e i n
w hich i t m ust do i t .
on th e sy stem .
I n e s s e n c e , t h i s im p o ses t h e maximum c h a n n e l s lo p e
The p a th t h e c h a n n e l fo llo w s t o c o n n e c t t h e d iv id e and
t h e m outh, th e p r o f i l e , i s a d ju s t e d t o th e l i t h o l o g y and c lim a te , w hich
d e te rm in e th e d is c h a r g e , sed im en t lo a d and ro u g h n e s s .
T hese h y d r a u lic
f e a t u r e s have b een a p p ro x im a te d i n t h e d ry s ta g e by d ra in a g e a r e a , bed
m a te r ia l s iz e and w id th :d e p th r a t i o .
P r o f i l e a d ju s tm e n t t a k e s t h e form o f two segm ents o f d i f f e r e n t
c o n c a v ity c o n n ec te d a t th e p o in t o f c o n c a v ity c h an g e .
The l o c a t i o n
o f t h i s p o in t i s d e te rm in e d by a change i n th e r a t e o f i n c r e a s e o f
d ra in a g e a r e a w ith c h a n n e l l e n g t h , w hich i s r e f l e c t e d by a change i n th e
number o f t r i b u t a r i e s e n te r in g p e r u n i t d is ta n c e and d ra in a g e d e n s i t y .
The d i f f e r e n t c o n c a v itie s r e f l e c t t h e e x is t e n c e o f two d i f f e r e n t s e t s o f
h y d r a u lic r e l a t i o n s i n e ac h c h a n n e l.
A more r a p i d in c r e a s e o f d ra in a g e
a r e a and d e c re a s e o f p a r t i c l e s i z e to g e th e r w ith a g e n e r a l in c r e a s e o f
w id th :d e p th r a t i o p ro d u ce a h ig h e r c o n c a v ity i n th e u p stre am segm ent
th a n downstream w here th e r a t e s o f change o f a r e a and p a r t i c l e s i z e a r e
s m a lle r and w id th :d e p th r a t i o i s v e ry i n c o n s i s t e n t o r d e c r e a s e s .
■71
In
72
each c a s e , d ra in a g e a r e a , w hich r e p r e s e n t s d is c h a r g e and sed im en t lo a d ,
i s t h e dom inant c o n t r o l .
E q u a tio n s w ere d e v e lo p e d r e l a t i n g g r a d ie n t t o d r a in a g e a r e a ,
r e l i e f , p a r t i c l e s i z e and w id th :d e p th r a t i o i n e a c h o f th e f o u r
s u b d iv is io n s :
S e d im e n ta ry concave
S = ( 6 .6 x 1 0 -5 ) R
» ^ ( W
/ D
) " 14± . 28
(D
a .4 0 ± .1 ?
S e d im e n ta ry s t r a i g h t
S = ( 1 .4 x 1 0"3 )Re38d:,1Z,'Ehm*2 6 1 ,0 8
( 2)
G r a n itic s t r a i g h t
,.5 1 ± .0 5
A
G r a n itic s t r a i g h t
S = ( 1 .6 x 10 -3 )R '4 % t' 1 4 ^ . 062±. 0$6
(4 )
a .2 1 ± .0 7
Each p a ra m e te r, e x c e p t r e l i e f , was th e n r e p la c e d by an e q u a tio n
r e l a t i n g i t t o c h a n n e l l e n g t h i n a p a r t i c u l a r s u b d iv is io n .
An
e x p re s s io n f o r g r a d ie n t i n te rm s o f le n g th and r e l i e f r e s u l t e d .
I t was
u s e d t o p r e d i c t p r o f i l e s i n m o u n tain ra n g e s o th e r th a n th o s e from w hich
th e o r i g i n a l d a ta was c o l l e c t e d by s u b s t i t u t i o n o f t h e known r e l i e f and
a r b itr a r y channel le n g th s .
V a r ia tio n b etw een t h e r e a l and p r e d ic te d
p r o f i l e s was g e n e r a lly w ith in th e l i m i t s o f a c c u ra c y im posed by th e
73
e r r o r o f m easu rem en ts.
M ost o f t h e v a r i a t i o n was e x p la in e d by
l i t h o l o g i c , o r p a r t i c l e s i z e , d i f f e r e n c e s , w h ile th o v a r i a t i o n o f
p r e c i p i t a t i o n among th e ra n g e s showed no a p p a re n t e f f e c t .
T here may
n o t b e enough v a r i a t i o n i n p r e c i p i t a t i o n to a llo w d e t e c t i o n o f an
e f f e c t , o r r a i n f a l l i n t e n s i t i e s may b e s i m i l a r th ro u g h o u t t h e e le v a tio n
ra n g e s tu d ie d .
S u f f i c i e n t d a ta f o r a d e c is io n w ere n o t a v a i l a b l e .
Thus t h e p r o f i l e s i n th e ep h em eral c h a n n e ls s tu d ie d a r e a d ju s te d
t o d is c h a r g e , sed im en t lo a d and ro u g h n e ss a s i s t h e c a s e i n p e r e n n ia l
s tre a m s and i n th e ep h em eral s tre a m s s tu d ie d by L eopold and M ille r
(1 9 5 6 ).
The change i n c o n c a v ity w hich o c c u rs i s p r im a r i ly a f u n c tio n
o f a change i n th e r a t e s o f d is c h a r g e i n c r e a s e and ro u g h n e ss d e c r e a s e .
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f lo o d s i n a . t y p i c a l d e s e r t w ash, P in a l C ounty, A riz o n a : Am.
Geophys. U nion T r a n s ., v . 23 , p . 4 9 -5 6 .
B a tta n , L o u is J . , and G reen, C h r is tin e R ., D ata on summer p r e c i p i t a t i o n
. i n t h e S a n ta C a t a lin a M o u n tain s, Pima C ounty, A riz o n a ,
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B ru sh , L ucion M ., J r . , 1961, D rain ag e b a s i n s , c h a n n e ls and flo w
c h a r a c t e r i s t i c s o f s e l e c t e d s tre a m s i n c e n t r a l P e n n s y lv a n ia :
U. S . G co l. S urvey P r o f . P ap er 282-F , p . 145-181.
F o lk , R o b ert L . , 1965» P e tro lo g y o f S ed im en tary R o ck s:
A u s tin , T ex as, 159 p .
H e m p h ill’ s ,
G re en , C h r is tin e R ., and M a r tin , S . C la rk , I 967 , An e v a lu a tio n o f
p r e c i p i t a t i o n , v e g e ta tio n and r e l a t e d f a c t o r s on th e S a n ta R ita
E x p e rim e n ta l Range: U n iv e r s ity o f A riz o n a I n s t i t u t e o f
A tm ospheric P h y s ic s T e c h n ic a l R e p o rts on M eteo ro lo g y and
C lim a to lo g y o f A rid R e g io n s, n o . 1?» p . 1 -8 2 ,
__________________ __ , and S e l l e r s , W illiam D. ( e d i t o r s ) , 1964, A rizo n a
C lim a te : U n iv e r s ity o f A riz o n a P r e s s , T ucson, 503 P»
Hack, John T . , 1957* S tu d ie s o f l o n g i t u d i n a l stre a m p r o f i l e s i n
V ir g in i a and M aryland: U. S . G eo l, S u rv ey P r o f . P ap er 294-B ,
97 p .
H u szar, C h a rle s K ., A g e n e r a liz e d s te p w is e m u l t i p l e r e g r e s s i o n a n a l y s i s :
U n iv e r s ity o f A riz o n a Computer C e n te r, Tucson ( d i t t o e d i t i o n f o r
lim ite d d is tr ib u tio n ) .
K eppel, R o b e rt V ., and Reward, K. G ., 1962, T ra n s m is sio n l o s s e s i n
ephem eral stre a m b e d s : J o u r n a l o f P ro c e e d in g s o f Amer. Soc. o f
C i v i l E n g in e e rs , v . 8 8 , no . HY3, p . 5 9 -6 8 .
L eopold, Luna B ., and H addock, Thomas, J r , , 1953, The h y d r a u lic geom etry
o f stre a m c h a n n e ls and some p h y s io g ra p h ic im p lic a tio n s :
U. S. G e o l. Survey P r o f . P ap er 252, 57 P*
____________, and M i l l e r , John P . , 1956, E phem eral s tre a m s h y d r a u lic f a c t o r s and t h e i r r e l a t i o n t o t h e d r a in a g e n e t :
U. S . G eo l. S urvey P r o f . P ap er 282-A , p . 1 -3 7 .
74
75
_________________ , Wolman, M. G ordon, and l-S ille r, Jolin P . , 1964, F l u v i a l
P ro c e s s e s i n Geom orphology: W. H. Freem an and C o ,, San
F r a n c is c o , 522 p .
L o o te n s, D ouglas J . , 1965, S t r u c t u r e and p e tro g ra p h y o f t h e e a s t s id e o f
t h e S i e r r i t a M o u n tain s, Pima C ounty, A riz o n a : u n p u b lis h e d
d o c t o r a l t h e s i s , U n iv e r s ity o f A riz o n a , 224 p .
M ackin, J . H oover, 1948, C oncept o f t h e g ra d e d r i v e r :
A m erica B u l l . , v , 5 9 , p . 4 6 3 -5 1 2 .
G e o l, S oc.
M i l l e r , Jo h n P . , 1958, High m o u n ta in s tre a m s ; t h e e f f e c t s o f g eo lo g y on
c h a n n e l c h a r a c t e r i s t i c s and b ed m a t e r i a l : New M exico S t a t e
B ureau o f M ines and M in e ra l R e s o u rc e s, Memoir 4 , 51 P»
Owen, D onald B ., 1962, Handbook .o f S t a t i s t i c a l T a b le s : A ddison-W esley
P u b lis h in g C o ., I n c . , R ead in g , M a s s a c h u s e tts , 580 p .
R en ard , K enneth G ., and K eppel, R o b e rt V ., 1966, H ydrographs o f
ephem eral s tre a m s i n t h e s o u th w e s t: J o u r n a l o f P ro c e e d in g s o f
Amer. S oc. o f C i v i l E n g in e e rs , v . 92, n o . HY2, p . 3 3 -5 2 .
Schumm, S ta n le y A ., 1963, S in u o s ity o f a l l u v i a l r i v e r s on th o G re a t
P l a i n s : G e o l. S oc. A m erica B u l l . , v . 7 4 , p . 1089-1100.
____________________ , 1968, R iv e r a d ju stm e n t to a l t e r e d h y d ro lo g ic
re g in o n - H urrum bidgee R iv e r and p a lc o c h a n n e ls , A u s t r a l i a :
U. S. G eo l. S urvey P r o f . P ap er 598, p . I - 65 .
S n e d e co r, G eorge ¥ . , 1956, S t a t i s t i c a l M ethods:
P r e s s , Ames, Iow a, 534 p .
Iow a S t a t e C o lle g e
S h u l i t s , Sam uel, 1941, R a tio n a l e q u a tio n o f r iv e r - b e d p r o f i l e :
Geophys. U nion T r a n s ., v . 22, p . 6 2 2 - 631 .
Am.
Wolman, M. G ordon, 1954, A m ethod o f s a m p lin g . c o a r s e r i v e r - b e d m a t e r i a l :
Am. G eophys. U nion T r a n s ., v . 35 , n o . 6 , p . 9 5 1-956.
________ , 1955, The n a t u r a l c h a n n e l o f Brandyw ine C reek ,
P e n n s y lv a n ia : U. S . G e o l. S urvey P r o f . P ap er 2 ? 1 , $6 p .
W oodford, A. 0 » , 1951, S tream g r a d i e n t s and M onterey S ea V a lle y :
G e o l. S oc. A m erica B u l l . , v . 62, p . 799-852
A P P E N D IX I
PRECIPITATION DATA USED TO DERIVE THE PRECIPITATION INDEX»
S ta tio n
Name
Mean
D ailySummer
R a in fa ll
( in c h e s )
E le v a tio n
(fe e t)
S a n ta R i t a E x p e rim e n ta l Range
S ta tio n
Name
.1 0
.13
.0 9
.0 8
.1 2
3920
4520
3300
3080
3880
18
130
131
140
149
D e s e rt Rim
E rio p o d a
F lo r id a S t a t i o n
F o re st S ta tio n
G ra v e lly R iv e r
.0 9
.10
.1 4
.1 2
.0 9
3400
3740
4300
4160
3040
Huefano
Hughes S t a t i o n
M u h len b erg ia
N o rth e a s t
N orth w est
.10
.0 8
.0 9
.0 9
.0 8
3880
P a rk e r S t a t i o n
Road
R obinson
R odent
R u elas Ranch
.1 2
.1 0
.1 3
.1 0
.11
4320
S outhw est
W ater R e te n tio n
W ater S p rin g
W hitehouso
.1 0
.0 9
.1 0
.1 2
3360
3660
3720
3880
3440
3280
2960
.0 9
.10
.1 0
.11
.0 9
4260
3800
3480
3480
3540
152
155
161
163
164
.1 0
.0 8
.0 8
.0 8
.0 9
4020
3240
3190
3160
166
169
173
184
185
.1 0
.11
.0 9
.1 0
.0 9
3960
4100
- 3690
3720
3490
192
205
.0 8
.1 0
.0 9 '
.0 9
.1 0
3300
3040
3450
■ 3600
. 3720
229
.1 4
I 87
- 188
191
3640
4200
3560
4560
76
E le v a ti
(fe e t)
(G reen and M a rtin , 1967)
Box
Brown Ranch
C h o lla S t a t i o n
D e s e rt
D e s e rt G ra ss
3120
Mean
D a ily
Summer
R a in fa ll
(in c h e s )
.
3120
4200
77
Mean
D a ily
Summer
R a in fa ll
( in c h e s )
S ta tio n
Name
E le v a tio n
(fe e t)
C a ta lin a M ountain E x p erim en t
1
2
3
4
5 ‘
Mean
D a ily
Summer
R a in fa ll
( in c h e s )
E le v a tio n
(fe e t)
(B a tta n and G reen , u n p u b lis h e d )
.1 8
.1 8
.1 6
.1 7
.1 4
.9 1 5 0
4450
5800
16
17
18
19
20
.1 6
.1 2
.1 2
.11
.11
7050
4680
4820
3840
3950
21
22
23
24
25
.1 0
.0 ?
.1 8
.1 5
.0 9
4960
.0 7
.0 9
.0 9
.0 7
.08
3740
3650
3350
3025
27
28 .
29
.0 9
.0 9
.0 8
2920
.0 7
.0 9
.11
.1 0
.1 6
4200
4500
6
7
8
9
10
11
12
13
14
15
5000
2960
Community R ain Gages
Apache Powder Co.
C anelo
F a irb a n k
F o r t Ruachuca
P a ta g o n ia
Tombstone
S ta tio n
Name
.10
.1 4
.10
.1 2
.1 4
.1 3
9000
7920
8400
5980
3400
8400
6800
2720
2?00
2740
*
(G reen and S e l l e r s , 1965)
3690
4985
336?
4664
4044
4540
Benson
Benson
E lg in
E lg in
E lg in
.0 9
.0 9
.1 3
.1 0
.1 3
3575
3640
4900
478O
. 4730
A P P E N D IX I I
FIELD AND MAP DATA FOR THE MUSTANGS, WHETSTONES AND SIERRITAS
The a b b r e v ia ti o n s u s e d t o h ead t h e colum ns a r e :
-
E le v .
A rea
E le v .
A rea
A/R^
L
S
W
D
W/D
Djnui
D34
A/R2
- e le v a tio n o f s ta t io n i n f e e t
- d ra in a g e a r e a i n s q u a re m ile s
- d ra in a g e a r e a : r e l i e f 2 r a t i o x 10°
- c h a n n e l le n g th from th e d iv id e i n f e e t
- c h a n n e l g r a d ie n t i n f e e t / f e e t
- c h a n n e l w id th i n f e e t
- c h a n n e l d e p th i n f e e t
- c h a n n e l w id th :d e p th r a t i o
- mean b e d p a r t i c l e s i z e i n m illi m e t e r s
- 8 4 th p e r c e n t i l e o f b ed m a t e r i a l i n m i lli m e t e r s
L
S
W
D
W/D
Dg^
P
M ustang 1
5600
5500
5300
.0 0 4
.010
.016
.0 2 4
5200
.033
5100
.086
.1 3 7
5400
5000
4900
4800
4700
4625.
--------------------------.0 2 4
--------.0 8 2
.1 3 0
.363
2 .5 9
. 417 --------. 633
4.52
1 .3 0
9 .2 9
.58
680
890
1080
1390
-------- ------ -------.4 9 ' - — ...............................
.4 3
-------- ------ -------.27.
15.
.9
1?.
1830
2580
3770
6180
.20
.092
.062
.033
9180 . 033
12960 . 020
1 6270 . 020
-------...........
-------133.
-------- ---........... ......
-------- ---1024. 1.5
..................................................................................
12.5
2 .6 4 ;9
40.
147. 1 .4
18.
1 .5
12 .
37.
85 . 1 .4
2 2 .5
1 .4
17.
20 .
43 . 1 .4
-------26 .
13.
------
1 .2
.?
-------23 .
19 .
-------17 .
5 .0
-------60 .
13.
---1 .4
1 .3
M ustang 2
5800
5700
5500
5400
.0 0 4 — - —
. 010 ---------.0 1 3 ---------. 01?
.015
5300
.0 3 3
5200
5100
5050
.064
.167
.405
---------
.055
.1 4 4
5.34
680 .6 4 5
.53
840
1240
1450
.4 9
.36
I 750 .27
2310 .12
3470 "059
4440 .037
'
............ ................. ...... ........... ..........
-------- ---------- ------ .................. ......................
— — ..... .......................................................... —
6.0
.6 3
9 .5
97.
355. 1*5
-------- ------6.0
.4 ?
1 9 .5
1 .5
19.0
1 .4
78
-------13.
13.
15 .
-------53.
60 .
30 .
-------166.
256
111 .
---1 .4
1 .4
1 .4
79
E le v .
A rea
o o o
O O VO
.547
.665
A/R2
L
7 .2 4
8 .8 0
6160
8660
10160
.681
S
.033
.030
.027
W
D
w/ d
4m
d84
P
2 7 .5
1 1 .5
1 .7
.5 7
18.
20 .
21 .
25.
43.
64.
1 .4
1 .4
20 .
21 8 .
1 .5
13.
25.
355.
1 .5
M ustang 3
5800
.008
5700
.020
5600
5500
•.097I
.0 6 9
5400
5300
.0 8 6
.1 1 3
.129
.167
5200
51 oo
5000
4900
1.67
4800
4?00
1 .8 9
2 .1 0
.018
.078
.151
.540
1 3 .6 '
1 5 .4
17.1
750
1125
.3 4
.2 3
1625
2250
.21
.13
3000
3660
10.5
1 .2 5
1 2 .5
1.1
4370
.1 5
.1 6
.1 3
5245
.080
1 3 .0
.8 5
16.
37.
159.
1 .5
7245
.032
10459
14935
19685
.028
1 9 .5
2 3 .5
1 8 .5
1 .2
.9 3
1 .3
16.
32.
15.
23.
13.
11.
97.
37.
30.
1 .4
1 .4
1 .4
53.
333.
1 .7
69.
1 .7
W).
74.
49.
69.
1 .6
1 .6
1 .6
1 .5
1 .5
1 .5
1 .4
1 4 ?.
1 .6
1 .5
1 .5
1 .4
.020
.019
8 .6
W hetstone 1
6800
6600
6400
• 01
.0 ^
.0 8
.1 4
6200
6000
5800
5600
.1 9
• 57
.6 3
.8 6
.1 3 3
3650
4620
5350
6000
5400
4?80
1 .0 5
1.81
3 .1 9
4 .0 ?
.168
.289
1 .6 8
2 .1 7
§O §O O§
7200
5 .2 7
5 .5 9
1 0 .2 9
2 .7 8
5200
5000
490
1060
1710
2630
.0 9 2
2.96
5 .4 5
.5 5
.3 5
.2 5
.21
.2 0
.25
1 6 .0
2.11
8 .0
.15
1 6 .5
1 .6 4
10 .
7790
9990
14060
204?0
. 10
.0 6 2
.0 4 2
.0 3 4
23.0
23.0
26.0
1 .6 5
1 .1 0
1 .0 4
1 .0 0
14.
16. .
26.
29.
26030
30310
37540
.031
31.0
2 0 .5
3 4 .0
.7
.9
1 .0 5
45.
23.
32.-
6 .0
.019
.021
4 .0
26.
48.
43.
19.
18.
30.
65.
15.
15.
4 .5
5 .0
209 .
11 .
11 .
.2 9
2 8 .5
8 .0
11.
19.
20.
21.
7.5
W h etsto n e 2
OOOO
OOOO
VAx—O 00
xnv'vvrv.d-
.0 4
.2 4
.30
.71
.0 1 7
.100
.1 2 6
.2 9 6
1710
.2 6
7.5
4150
5075
.11
1 0 .5
2 0 .5
-8005
.11
.0 4 3 — 31.5
.4 0
.6 0
.71
.4 7
80
D
W/D
E le v .
Area
a/ r 2
L
S
W
4600
4400
4200
4000
1.41
1 .7 8
1 .9 6
2 .8 8
1.11
1.41
1 »55
12145
17675
.045
.035
37-5
8 8 .0
5 1 .5
4 2 .5
• 43
-55
.3 2
.3 8
88.
160.
160 .
115.
4 .5
7 .0
.2 5
• 52
18.
17.
T r ib u ta r y 1
5700
.02
5400
.0 3
5200
•.0
V 7
f
T r ib u ta r y 2
4600
. 23 .
2.27
.008
.013
23685
32135
1220
2030
2690
.026
.022
.41
.33
.21
d3 4
- 4 .0
3 .5
2.0
1 .5
19.
35.
6.0
5 .5
4 .0
3 .5
P
1 .4
1 .4
1 .4
1 .3
256 .
1.6
21 8 .
1 .5
'
.998
7650
.0 4 2
20.0
.4 5
45.
3 .5
5 .0
1 .3
W hetstone 3
5800
.01
1220
5600
.0 3
1790
1r 7 V
45
. 27f
2850
3900
.12
.11
1 4 .5
.9
16.
5 .0
64.
1 .5
5690
.067
1 5 .0
.8 5
18.
3 .0
16.
1 .5
76.0
.8
95.
1 .5
3 .0
1 .4
4 1 .0
6 0 .0
9 5 .5
9 3 .0
.49
.2 9
.1 4
.1 4
88.
210.
700.
665 .
1.0
2 .5
2 .5
2 .0
1 -5
1 .4
1 .3
1 .3
1 .3
13.
22.
"46.
17.
23 .
9.5
5400
.07
5200
.09
.033
5000
.19
4800
4?20
4600
.6 9
1.22
1.31
.6 2 2
4400
4200
4000
3800
1.78
2 .2 6
2 .4 8
5 .6 8
.907
1 .1 5
1 .2 6
.090
9760
7 1 • o?6
v^u
2.90
12690
.037
16100
.0 2 8
24230
31060
37070
42620
.0 2 8
.028
.0 3 4
.035
1 .0
1.0
1.0
S ie rrita 1
5250
.0 4
.15
.3 5
.096
.230
.65
.416
.685
4000
1 .0 7
.71
1 .8 8
2 .5 5
3750
3425
3 .3 7
4 .7 5
5000
4750
4525
4440
44 mt
4250
.4 5 4
.578
.7 8 9
1 .4 ?
9
T r ib u ta r y 1
4440
.3 6
.026
1470
2610
4320
8960
.2 2
8 .0
.23
13.0
.0 7 9
. 044-
2 0 .0
9 -5
.6 3
.61
.4 6
.7 3
9770
9770
.0 4 5
.045
15300
.032
23750
.0 3 3
1 9 .5
1 2 .0
4 2 .0
37-5
.6 8
.6 6
.2 3
• 51
34150
48950
.0 2 4
.023
3 6 .0
7150
.0 6 4
1 0 .0
8 .0
12.
74.
37.
44.
69.
1 .5
1 .4
1 .4
1 .4
30.
18.
185.
74,
12.
24.
2 .0
3 -5
69.
89.
3 .5
6 .5
1 .4
1 .4
1 .3
1 .3
1 .0 8
34.
1.0
3 .0
1 .2
.6 8
15.
316.
1 .4
15.
/
81
E le v .
A rea
a/ r 2
L
S
W
D
W/D
4mm
D84
P
97.
85.
10.
1 .5
1 .5
1 .4
S ie rrita 2
5500
5250
4925
4750
.02
.11
.56
4500
4250
4000
3825
.8 5
1 .2 2
2 .1 6
3 .0 2
3750
3 .3 9
.017
.091
.207
970
2270
4710
7960
.3 4
.1 3
.081
nAR
4 .5
7 .5
2 2 .5
.3 9
.4 4
.2 2
12.
20.
110.
21.
21.
4 .5
.213
.305
.540
.755
11370
16570
23560
31060
.060
.0 4 2
.0 2 8
.020
3 4 .0
3 9 .0
1 2 8 .5
56 .O
.2 3
.2 8
.3 4
155.
140.
420.
87.
3 .0
3 .5
2 .0
2 .5
35610
021
12.
16.
4 .5
.8 2
.66
5 .0
7 .5
4 .5
4 .5
1 .4
1 .3
1 .3
1 .2
S ie rrita 3
4750
4500
.0 2
.0 5
.2 0
.6 2
.038
.151
4250
4000
3750
3500
1 .4 5
1 .7 6
2 .7 5
3 .5 6
5250
5000
890
.4 6 9
2190
3320
838O
.2 0
.2 3
.1 0
.0 6 2
.4 7 3
• 575
.8 9 8
1 .1 6
15210
.0 2 7
23320
32760
43320
7 .0
.4 2
10.0
.47
1 7 .5
.3 7
23.
23.
50.
.030
.025
7 3 .0
2 9 .5
2 3 .5
.0 2 2
27.0
.2 2
.1 8
.2 4
.2 4
400.
165.
100.
98.
4 .0
3 .0
2 .5
2 .5
6 .0
4 .5
5 .2
4 .5
1 .3
1 .3
1 .2
1 .2
.2 6
85.
3 .0
5 .0
1.1
.2 ?
.3 2
76.
110.
1 .5
2 .0
3 .0
4 .5
1.1
1.1
.41
56.
1 .5
3 .0
1.1
49.
91.
20.
1 .4
1 .4
1 .4
S ie rrita 5
3550
2 . 5I
.1 9
6800
.0 2 4
2 0 .5
S ie rrita 6
3500
3400
.3 4
.5 9
2.78
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