Analysis of the Soil Conservation Service Project Formulation Program - Hydrology
by Orrin Albert Ferris
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in Civil Engineering
Montana State University
© Copyright by Orrin Albert Ferris (1968)
Abstract:
The ability of the Soil Conservation Service method to accurately predict the peak discharge of a
rain-caused runoff event on Montana watersheds is studied. Runoff hydrographs are developed for
actual and hypothetical storms by using a computer program entitled "Project Formulation Program Hydrology", previously written for the Soil Con- x serration Service, to effect solutions of the SCS
runoff prediction equations.
The actual storm of June 16, 1965 on Duck Creek watershed near Brockway, Montana is simulated.
The basin characteristics for Duck Creek and the storm characteristics of the June 16, 1965 storm are
described for use with the computer program," which then constructs the predicted runoff hydrograph
as calculated using SCS synthetic hydrograph criteria. The agreement between the calculated runoff
hydrograph and the actual known hydrograph is not close. Possible reasons for this discrepancy are
discussed. Chief among them is the fact that the various equations (used to simulate runoff
hydrographs) are sensitive to the various parameters and variables (describing the basin and storm
characteristics) when applied to storms of low rainfall excess.
Hypothetical storms are also described to the computer program to demonstrate the way in which they
could be used to predict peak discharges on a watershed from a storm of a given frequency.
I It is concluded that the SCS method is a logically organized procedure that has been effectively
programmed for computer solution.
Furthermore, successful use of the method requires careful definition of watershed and storm
parameters. /O -Z J
CV-
ANALYSIS OF THE SOIL CONSERVATION SERVICE
PROJECT FORMUIATION PROGRAM - HYDROLOGY
uy
ORRIN ALBERT FERRIS
's
A t h e s is subm itted t o th e Graduate F acu lty in p a r t ia l
f u lf illm e n t o f the requirem ents fo r the degree
o f'
MASTER OF SCIENCE
in
C iv il Engineering
Approved:
Head, Major Deparbment
Chairman, Examining Committee
T
MONTANA STATE UNIVERSITY
Bozeman, Montana
June, 1968
iii
ACKNOWLEDGMENTS
The author w ishes t o express h is a p p re c ia tio n t o a l l who have spent
tim e and e f f o r t in h elp in g complete t h is stu d y .
S p e c ia l thanks goes t o
Theodore T. W illiam s fo r h is te c h n ic a l h elp and encouragement in a l l
phases o f t h is stu d y.
The author a ls o w ishes t o thank Dr. W illiam Hunt and Dr. Thomas
Hanson fo r t h e ir review and valu ab le c r it ic is m s o f th e rough d ra ft of
th e t h e s i s .
A ssista n c e in gath erin g and p ro cessin g f i e l d data from Gary
Lewis i s a ls o a p p recia ted .
Taping o f many rough d r a fts was n ecessa ry t o complete t h i s t h e s i s .
The author w ishes t o express h is g r a titu d e fo r th e ty p in g o f th ese d r a fts
and th e f i n a l copy t o h is w ife , Sharon Iynn.
The f in a n c ia l support o f t h is work was provided by th e Montana S ta te
Highway Department and the' United S ta te s Bureau o f Public Roads through a
grant t o Montana S tate U n iv e r sity a t Bozeman, Montana.
A p o rtio n o f th e
computer s e r v ic e s was provided by th e Montana S ta te o f f ic e o f the S o il
C onservation S e r v ic e , U nites S ta te s Department of A g r icu ltu r e .
iv
TABLE OF COBTEHTS
C h a p te r I
INTRODUCTION
C h a p te r I I
LITERATURE REVIEW
o o o e o n o e o e e o e o o o e o A p e e o e e o o e o f r C i e o o o o o t f
E l s t o r x c a l Eycirolo^jyr
tlOCle 3. Ill EyilrO lO ^y
C h a p te r I I I
I
............ .............. ...................
4
o« ooooooci ooo« oobo « ooooo « dqo
4
o e c e o o o e e o o o B B < i » o o o o 6 C a o B t i ‘o e » e e
SO IL CONSERVATION SERVICE RUNOFF' PREDICTION METHOD
Proposed Use o f SCS Method
T
10
e p c p c e o c i o f l e s o c i o o o e
U nxt H y d ro g ra p h T iie o ry ©©©©©©©©©©*© ©©o©.© ©©©©©©© 12
S y ste m S y n t h e s i s a n d A n a l y s is
©©©©©© «©©.©©©.©»©© © 13
. F u n c t io n i n g o f a G e n e r a l S y n t h e s i s M ethod . . . . . .
14
R a i n f a l l E x c e ss o . * . . . . . . . . . . . . . . . . . . . . . * . . . .
14
S to rm R u n o ff
1 9
© © © a © © © © © © © © © © © © © © © © © © © © © © © © © © © ©
F lo o d R u n o ff ©o©©©©.©©©©©©©©©©©©©©©©©©©©©©©©©
C h a p te r IV
■C h a n n e l F lo o d R o u tx n g ©©©©©©©©©©©©o©©©©©.©©©©©©©
24
R e s e x v o ir F lo o d Rouoxng ©©©o©©©©©©©©©©©©©©©©©©©©
23
S y stem s C l a s s i f i c a t i o n o f SCS Mhthod ©©©,© ©©. »©,
29
SOIL COBSERVATIOE SERVICE PROJECT FORMULATION
PROlaR/VM.=“HYDROLOGY e e e o o « * e & o o o o o o e o o © o o e o © 0 6 © a o
PFP Subroutine Arrangement
o o o e
33
e o o o B o o o o e e c o o e c o o o e e
36
Tabular Data ©©©©©©©©©©©©©©©©©©©©©©©©©©a©©©©©©©©
36
Standard C ontrol ©©©©©©©©o©©©©©©©©©©©©©©©©©©©©*©
39
ExecuGxve C ontrol ©©©©©©©©©©©©o©©©©©©©©©©©©©©©©©
42
Examples of ExecutIvc Control .................. ..
Chapter V
24’
. PREPARATION OF WATERSHED DATA .............................
Subwatershed Areas and Channel Lengths
c o o c o e o o o
43
46
48
V
TABLE OF CONTESTS ( C o n t . )
S tag e-A rea and, S ta g e -D is ch arg e R e la tio n s h ip s . , .
Friction Slope
C hapter VI
O. 0 0 0 0 » 0 6 0 < f 0 0 0 6 6 6 0 0 - s 0 0 0 6 c » 0 6 0 e 0
4-9
Aone oL Transxticn 66oooooe66ooeoooeoDOtieooo6
49
fanning's Roughness Coefficient .... .......
50
Bydr U,lXC Rad XUS eesoDooooooeoOfrococeeoosoooo
53
-V-. *1 v i /v t «-t
TTi^ >i - r -i v--i-„-i'
Computer S o lu tio n-i o f M anning's
E quation' . . . ^. .
93
T e s tin g th e R e l i a b i l i t y o f JVhnning1s E q u atio n
$4
Curve Numbers and A ntecedent M oisture C o n d itio n s
57
Txme.o f Concenoratxon . . . . . . . . . . . . . . . . . . . . . . c . . .
59
Storm Dam . . . . . . . . . . . . . . . o . . . . . . . . . . . . . . . / . . . . . .
61
Summary . . . . . . . . . . . o . . . . . c . . . . . . . . . . . .
62
ACTUAL AND HYPOTHETICAL STORtS . . . ,i e o o e e o o e o o o o o e o i s o
A c tu a l Storm o f June 16, 1965
H y p o th e tic a l Storms .
C hapter VlL
L8
63
o f r o o o o o e o o o e o e o e e d
63
■ 5 6 0 t i 0 0 o e 6 6 e e e o o o < o e o d o o o o
65
A c tu a l R unoff Hydrograph . . . . . . . . . . . . . . . . . . . . . .
66
Computer Runs Completed
e c o e o C d ^ c e o e c e e o e e o o e e e e
68
B o e o o o e o o o o o o e e o o o e d o o o o - e o o f r C b ® * *
Tl
A c tu a l Storm E v alu avion . . . . . . . . . . . . . . . . . . . . . . . .
71
Computer R e s u lts . o . . . . . . . . . . . . . . . . . . . . .
72
H y p o th e tic a l Storm E v a lu a tio n
74
RESULTS .................. ..
e o * 0 » » 0 0 0 6 - 0 0 » 0 0 6 8 0
» d o e o o o o e » e e o o o
78
t o o f l c e e c o c e e o o o o v d e c e
78
P r e p a r a tio n o f th e In p u t Data . . l. o o o e e o f ' e o e o o e
79
C h ap ter V l11 DISCUSSION
The Storm of June 16, 1965
^
vi
TABLE OF CONTENTS ( C o n t . )
The' SCS M e th o d ...............................................................
8l
Be sign-Type Storms ..................................................................
83
Program Use By Montana S ta te Highway................
84
C h ap ter IX CONCLUSIONS ........................................................... ............................
86
C h ap ter X RECOMMENDATIONS AND SUMMARY.....................................................
88
Summary ..........................................................................................
89
.............................................. ................................... ................................
90
A.
S o lu tio n o f R unoff
91
B.
H ydrologic S o il Types ...................... ..............................
92
C.
R unoff Curve Numbers f o r H ydrologic S o il Cover Complexes .................................
93
APPENDIX
D.
E q u a t i o n .................................
Computerized S o lu tio n o f Manning's E q u a tio n ......... ' 94
LITERATURE CITED
99
vii
LIST OF TABLES
Table I
Types o f A ntecedent Moisture C onditions ............................
T able I l
EXlamplg tif E x ecu tiv e C o n tro l Ob Samble WatordhdA . „ , ,
T able I I I
Table IV
20
44
C a le u ld tio n o f com posite curve Number on a
Sample W a te r sh ed .............................................................................
58
Summary o f Computer Runs Completed ......................................
69
v iii
LIST OF FIGURES
F ig u re
1
Block Diagram D e p ic tin g S o il C o n se rv a tio n S e rv ic e
BUnOfT FreQiCGiOIl MetlioT C Q o e a o e o o o e e o e c o o o G o o o o o o
o c o o o e Q t
11
2
A djustm ent o f Curve Number Value f o r Types o f AMC ,
3
C on v o lu tio n o f R a i n f a l l Excess i ( T ) and
In s ta n ta n e o u s U nit Eydrograpb u(t™ f ) . . . . . o . . . . . . . . . . . . . . 21
k
R e la tio n s h ip betw een ^ u and IC oeootocoe^ooooiaocfet. ooocoooo 28
5
Schem atic of P r o je c t F o rm u la tio n Program O p eratio n ........... .. 34
6
S u b ro u tin e Scheme f o r S o il C o n se rv a tio n ServiceP r o je c t F o rm u latio n Program -H ydrology
......... ......................... 37
7
Sample W atershed w ith C orresponding S tan d ard C o n tro l
f o r th e S o il C o n se rv a tio n S e rv ic e P r o je c t F o rm u latio n
Program oo&#toc*oo@6oeoo*aooODec@oocaoooGoooo«ocoocoeooowa 40
8
Duck Creek W atershed
9
T y p ic a l P la n View and C ro s s -s e c tio n o f a
M eandering Stream .................... e e e e o o o e e o c e e
20
o o o o o c o o o o o e o e c e o o e o o e o a e e o e o o e o e o e e o
e o o c o o A o e e o o e o o o o
47
51
IO
E ast Fork o f Du.ck Creek R atin g Curve
1.1
Duck Creek R atin g Curve
12
I s o h y e ta l Map o f June 16, 1965 Storm on Duck Creek
W atershed eocoocecoooeoooeoocooecocGOoeooeeooeoeGOceeooeoc 64
13
A c tu a l Runoff Hydrograph of th e June 1.6, 1965 Storm
on th e Duck Creek W atershed f r o c o f r o o o o o e o e c o f r f l f l f l o o e c o o o e e o o 67
14
A c tu a l and C a lc u la te d R unoff Hydrograph - Duck Creek
W
15
a t e r s h e d
o e o o s o o o o f r o o e t -
c c e o f r c o
O f l O O f l f l O f l f r f l O O O O C e O f l C O C O »■ 6 O O O f l f l C t r C
0. 56
o o e o o o o e e o o o o c e e o e o o o o e e e o o o o e o c o o o o e c o c o o e o o o o o
Example o f Peak D ischarge D esign C hart . o d o o o f r o o
e ‘« o o f l o o o
55
fJ j
. . 75
Ix
ABSTRACT
The a b i l i t y o f th e S o i l C onservation Service method t o a ccu ra tely
p r e d ic t th e peak d ischarge o f a rain -cau sed ru n off event on Montana
w atersheds i s stu d ie d . Runoff hydrographs are developed fo r a c tu a l and
h y p o th e tic a l storms by using a computer program e n t it le d "Project For­
m ulation Program - Hydrology", p r e v io u sly w r itte n fo r th e S o il Con­
s e r v a tio n S e r v ic e , t o e f f e c t s o lu tio n s o f th e SCS ru n off p r e d ic tio n
eq u a tio n s.
The a c tu a l storm o f June l 6 , 1965 on Duck Creek watershed near
Brockway, Montana is sim u la ted . The b a sin c h a r a c t e r is tic s fo r Duck
Creek and the storm c h a r a c t e r is tic s o f the June 16, 1965 storm are d e s­
crib ed fo r use w ith the computer program," which then co n stru cts the pre­
d ic te d runoff hydrograph as c a lc u la te d using SCS s y n th e tic hydrograph
c r i t e r i a . The agreement between th e c a lc u la te d runoff hydrograph and
th e a c tu a l known hydrograph i s not c lo s e . P o ssib le reasons fo r th is
discrepan cy are d is c u s se d . ' C hief among them i s the fa c t th a t the various
equations (used t o sim ulate ru n off hydrographs) are s e n s it iv e to the
variou s parameters and v a r ia b le s (d esc rib in g the b a sin and storm charac­
t e r i s t i c s ) when ap p lied t o storms o f low r a i n f a l l e x c e s s .
H yp oth etical storms are a ls o d escrib ed t o the computer program to
demonstrate th e way in which th ey could be used to p r e d ic t peak d i s ­
charges on a watershed from a storm o f a g iv en frequency.
I t i s concluded th a t th e SCS method i s a lo g ic a lly organized pro­
cedure th a t has been e f f e c t i v e l y programmed fo r computer s o lu tio n .
Furthermore, s u c c e s s fu l use o f the method req u ires c a r e fu l d e f in it io n
o f watershed and storm param eters.
Chapter I
IHTRODUCTIQH
In u n d a tio n o f r i v e r flo o d p la in s by o c c a s io n a l flo o d
d is c h a rg e s has been a t h r e a t t o th e l i f e and p ro p e rty o f man
s in c e th e dawn o f c i v i l i z a t i o n . Man has long sought means
o f p r e d ic tin g flo o d s and a v e r tin g t h e i r d an g er. Modern m an's
need f o r q u a n t i t a t i v e in fo rm a tio n co n ce rn in g flo o d flo w s
becomes even more p r e s s in g a s he a l t e r s n a tu r a l w aterways
w ith s t r u c t u r e s , re a lig n m e n ts , and d iv e r s io n s .
A m ajor problem c o n tin u a lly fa c e d by highway d e s ig n e r s , urban
p la n n e r s , and w atersh ed management e n g in e e rs i s t h a t o f d e te rm in in g th e
fre q u e n c y o f peak flo o d d is c h a rg e s from stre a m and r i v e r b a s in s .
For
la r g e r i v e r b a s in s ( i n e x cess o f 100 sq u are m ile s ) flo o d fre q u e n c y i n ­
fo rm a tio n i s g e n e r a lly a v a il a b le by v i r t u e o f long te rm re c o rd s of p r e ­
c i p i t a t i o n , s tre a m flo w , e t c . , which have been c o lle c te d by v a rio u s
p u b lic a g e n c ie s ( in c lu d in g th e U. S. E nvironm ental S cience S e rv ic e s •
A d m in is tra tio n , G e o lo g ic a l Survey, B ureau o f R eclam atio n , A g ric u ltu re
R esearch S e rv ic e , and o t h e r s ) .
For w atersh ed s s m a lle r th a n 100 square
m iles in a re a th e r e i s g e n e r a lly a sh o rta g e o f h y d ro lo g ic d a ta .
Only
w ith in th e p a s t few y e a rs has s i g n i f i c a n t r e s e a r c h been d ir e c te d tow ard
a s tu d y o f flo o d fre q u e n c ie s on b a s in s o f t h i s s i z e .
The "D rainage C o r r e la tio n R esearch P r o j e c t ”, which was. i n i t i a t e d by
th e D epartm ent o f C iv il E n g in eerin g and E n g in eerin g M echanics, Montana
S ta te U n iv e rs ity , Bozeman, Montana, i n 1963, a d d re sse s i t s e l f t o th e'
problem o f p re d ic tin g , th e fre q u e n c y w ith which a peak d is c h a rg e o f g iv e n
t
m agnitude may he e x p ec te d on s m a ll w a tersh e d s in Montana.
This in v e s t i­
g a tio n i s sponsored by th e Montana S ta te ' Highway Departm ent and th e U. S.
B ureau o f P u b lic Roads.
The work i s b e in g done under th e d i r e c t i o n of
2 *"
Theodore T. W illiam s, A ss o c ia te P r o fe s s o r o f C i v i l E n g in eerin g and En­
g in e e r in g Ivfechanics a t Montana S ta te U n iv e rs ity .
The- D rainage C o r r e la tio n R esearch P r o je c t is a two phase s tu d y :
a ) t o d eterm in e flo o d freq u e n cy r e la tio n s h ip s on w atersh ed s s m a lle r th a n
100 sq u are m ile s from lo n g -te rm c lim a to lo g ic a l d a ta a lr e a d y in e x is te n c e ;
and b ) t o make com prehensive h y d ro lo g ic s tu d ie s o f fo u r s m a ll w atersh ed s
i n e a s te r n Montana.
The w atersh ed s s e le c te d f o r stu d y a re Bacon Creek
i n W heatland C ounty, Duck Creek i n P r a i r i e and McCone C o u n tie s, Hump
Creek i n Sweet G rass C ounty, and lone Man Coulee in Pondera County.
Con­
tin u o u s re c o rd s o f c lim a tic f a c t o r s and stream flow a re b e in g o b ta in e d from
th e s e fo u r b a s in s .
A v a r i e t y o f p eak-flow p r e d ic tio n te c h n iq u e s , which
u t i l i z e d a ta such as t h a t b ein g c o lle c te d , a re b ein g exam ined.
Among th e te c h n iq u e s b e in g c o n sid e re d under th e second phase o f th e
D rainage C o r r e la tio n R esearch P r o je c t i s one which was developed by th e
S o i l C o n se rv a tio n S e rv ic e , U« S. Departm ent o f A g ric u ltu re (SCS).
The
SCS method p o s s e s s e s many d e s ir a b le f e a t u r e s , and seems t o have c o n sid ­
e r a b le p o t e n t i a l as a t o o l f o r p r e d ic tin g flo o d f r e q u e n c ie s .
The stu d y
r e p o rte d in t h i s t h e s i s a n a ly z e s th e method developed by th e SCS; d e s c rib e s
th e use o f a r e l a t e d com puter program ; t e s t s th e p ro g ram 's a b i l i t y t o re=produee a c t u a l hydrographs from a s e le c te d w a tersh ed ;, and e v a lu a te s th e
p o s s ib le u t i l i t y o f t h i s method on Montana w a te rsh e d s.
The. in v e s t i g a t i o n r e p o r te d h e r e in c o n s is te d o f th e a n a l y s i s , u sin g
th e SCS m ethod, o f a s in g le ra in -c a u s e d ru n o f f event which o ccu rred on
Duck C reek, th e l a r g e s t o f th e fo u r-w a te rs h e d s
bein g s tu d ie d by th e .
" 3 “
D rainage C o r r e la tio n R esearch P r o je c t.
Duck Creok i s an ephem eral stre a m
t y p i c a l o f most e a s te r n Montana stream s which d r a in s m a ll w a te rsh e d s.
Jt-
i s d ry most o f th e tim e , b u t o c c a s io n a lly has s u rfa c e flow a f t e r a r a i n caused r u n o f f ev en t o r d u rin g s p rin g snow m elt.
Jn th e f o u r y e a rs f o r
VJhich d a ta have been o b ta in e d a t Duck C reek, th e r e have been o n ly a few
ru n o f f e v e n ts o f consequence, and o n ly a n event- which o c c u rre d on June 16,
1965 le n d s i t s e l f t o a n a n a ly s is by th e SCS method,
A number o f e v e n ts would need t o be a n aly z e d b e fo re c o n c lu siv e s t a t e ­
ments as t o th e v a l i d i t y o f t h e ■SCS method co u ld be made.
N e v e rth e le s s,
i t i s b e lie v e d t h a t th e r e s u l t s o f th e a n a ly s is o f t h i s one storm w i l l be
a v a lu a b le c o n tr ib u tio n in e s tim a tin g th e a p p l i c a b i l i t y o f th e method to
Montana, w atersh ed s
C hapter I I
LITERATURE REVIEW
S c i e n t i f i c hydro lo g y is a r e l a t i v e l y new a r e a - o f s tu d y .
A p p li­
c a tio n o f th e s c i e n t i f i c approach t o h y d ro lo g ic problem s has had itsg r e a t e s t grow th in t h i s c e n tu r y , and e s p e c i a l l y in th e l a s t t h i r t y ■
y ears.
However, th e f i r s t h y d ro lo g ic m easurem ents p ro b a b ly were made
s e v e r a l c e n tu r ie s B. C„
IVhny i n t e r e s t i n g a r t i c l e s ab o u t th e b eg in n in g s
i n h y d ro lo g ic s tu d y have been w r itt e n and a few o f th e s e w i l l be d e s ­
c rib e d below , a f t e r which a d e s c r ip ti o n o f modern h y d ro lo g ic f i e l d s w i l l ,
be p re s e n te d .
H i s t o r i c a l Hydrology
Biswas ( 1966, 1967) and Hoyt (1942) have each a u th o re d h i s t o r i c a l
a c c o u n ts t e l l i n g o f e a r ly e f f o r t s t o cope w ith th e problem o f peak flo o d
d is c h a r g e .
'
■
Records of th e l e v e l o f th e N ile R iv e r i n Egypt can be tr a c e d back
t o about 3000-3500 B0 Co
N ilo m eters were used t o re c o rd th e maximum,
le v e l s re a ch e d d u rin g each flo o d se a so n .
There were th r e e g e n e r a l ty p e s o f n ilo m e te rs u se d .
The f i r s t was
s im ply a c l i f f on th e r i v e r 's edge upon which y e a r ly maximum flo o d s ta g e s
were re c o rd e d by c a r v in g s .
A second ty p e had s t a i r s on th e banks o f th e
r i v e r which gave e a s i e r a c c e ss t o th e flo o d s ta g e l e v e l .
The most a c ­
c u ra te ty p e was a r e s e r v o i r connected t o th e r i v e r by underground c o n d u its
S t a i r s gave a c c e ss t o a c e n t r a l column o r th e r e s e r v o i r w a lls where th e
le v e l s were re c o rd e d .
In a s e c tio n o f th e second c a ta r a c t a t Semna, no
few er th a n 179 d i s t i n c t e n g ra v in g s have been found, d a tin g back t o 1750-
■
1800 B„ Co o r e a r l i e r o
Heron o f A le x a n d ria s who liv e d in th e second c e n tu ry B. Cc f e s ­
ta b l i s h e d some f a i r l y c l e a r id e a s about w ater m easurem ent,
This is
shown by th e fo llo w in g q u o ta tio n from h is D iopfe r a . C h ap ter .13; w here,
a c c o rd in g t o Hoyt (1 9 4 2 ), Heron s t a t e s t h a t ,
"Observe alw ays t h a t i t does not s u f f i c e t o d eterm in e th e '
s e c tio n o f flo w , t o know th e q u a n tity o f ' w ater f u r n is h e d
by th e s p r in g . This we s a id was tw elv e sq u are d i g i t s » I t
i s -necessary t o f in d th e v e lo c i ty o f i t s c u r r e n t, because
th e more ra p id th e flo w , th e more w a ter th e s p rin g w i l l
f u r n i s h , and th e slo w er i t i s , th e le s s i t w i l l p ro d u c e »
For t h i s re a s o n , a f t e r having dug a r e s e r v o i r under th e
s tre a m , examine by means o f a s u n - d ia l how much w a tsi
flow s in to i t in an h o u r, and from t h a t deduce th e quan­
t i t y o f w a ter fu r n is h e d in a d a y ,"
A p p a re n tly , t h is , knowledge was not w e ll u n d e rsto o d f o r many y e a r s .
One
example o f t h i s comes from th e w ritin g s o f S ex tu s J u liu s F ro n tin n s ,
s u p e rin te n d e n t o f Home's w a te r su p p ly who w rote in h is Be Aquis around
97 A, D, about the- Homan sy stem ,
He had o n ly a h a z j id e a o f v e l o c i t i e s
o f ru n n in g w a te r and f a i l e d t o a p p r e c ia te th e tim e elem ent w ith re g a rd
•to flow r a t e s ,
■Leonardo de V inci (1452-1519 A, D .) a ls o a id ed th e developm ent of
hydrology c o n s id e ra b ly .
His w r itin g s d e s c rib in g th e re a so n s f o r v a r ­
i a t i o n o f d is c h a rg e from a c a n a l th ro u g h an o r i f i c e d em o n strate h is fu n ­
d am en tal knowledge o f h y d r a u lic s .
P ie r r e P e r r a u lf (1628-1703) made measurements on a p o r tio n o f th e
S ein e R iv er b a s in in France to compare r a i n f a l l and r u n o f f ,
His r e s u l t s
in d ic a te d t h a t th e t o t a l p r e c i p i t a t i o n in th e form o f r a in and snow was
- 6 "
n e a r ly s i x tim e s t h a t c a r r ie d by th e r i v e r .
For th e f i r s t tim e i t was
proved t h a t norm al p r e c i p i t a t i o n was more th a n ad eq u ate t o su p p ly w ater
t o th e r i v e r s and s p r in g s .
Edme M a rio tte (1620-1684) ex ten d ed P e r r a n l t 's
work t o in c lu d e th e e n t i r e S eine b a s in above P a ris and found s im ila r
re s u lts .
An E n g lish a stro n o m er Edmund H alley (1656=1742) c o n trib u te d t o thef i e l d o f hydro lo g y by h i s ex p erim en ts w ith e v a p o ra tio n .
He d em o n strated
t h a t th e w a te r e v a p o ra te d from th e ocean was more th a n s u f f i c i e n t t o
su p p ly a l l th e stream s and r i v e r s .
In 1768, a French e n g in e e r, M, Chezy:, developed th e w e ll known f o r ­
mula b e a rin g h is name, V « C l/BS) f o r c a lc u la tin g .flow v e l o c i t i e s where
R i s th e h y d ra u lic
r a d iu s and S i s th e f r i c t i o n s lo p e .
Ci s - a v a r ia b le
known as th e Chezy
C, and was p ro b a b ly c o n sid e re d t o be a measure of .
boundary ro u g h n e ss.
However,
o f c h an n e l sh ap e.
G a n q u ille t and K u tte r developed afo rm u la f o r e v a l­
i t has been shown t h a t C i s a ls o a f u n c tio n
u a tin g C in 1869 w hich, a lth o u g h c o m p lic a te d , found popular- u s e .
However,
H enderson ( 1966) r e p o r ts t h a t ind ep en d en t work by G auckler in 1868 and
Hagen i n l 88l d em o n strated t h a t th e s im p le r r e l a t i o n s h i p
* 0.167
C « £>--------11
(I)
f i t - th e s a m e 'd a ta used by G a n q u ille t and K u tte r ju s t a s w e ll as th e more
co m p lic ate d e x p re s s io n .
R i s -the h y d ra u lic ra d iu s and n i s a measure o f
th e boundary ro u g h n e ss,
"n" is -g e n e ra lly r e f e r r e d t o i n th e .U n ite d S ta te s
a s th e Manning roughness c o e f f i c i e n t , a f t e r R. Manning, an Irish m an , who
- 7 -
was w rongly g iv e n c r e d i t f o r th e G auckler and Bagen fo rm u la by a French™
man named Flamant.
T herefore, C hezy's equation f o r flow v e lo c i ty can-be
c o n v e rte d t o th e "Manning e q u a tio n " g iv in g
V = 1.1>9 b O-667 S0 -?
n
where I „49 =
■
3 .2 8 b ein g th e number of f e e t in a m eter.
(2 )
When th e .
m e tric system i s b e in g u se d , th e c o n s ta n t 1 .4 9 Is sim ply 1 «0 0 „
H ydrologic measurements were no t c o n sid e re d t o be o f much im portance
d u rin g th e e a r l y h i s t o r y o f th e U nited S t a t e s „
P o p u la tio n c e n te rs d e ­
velo p ed a lo n g th e r iv e r s and la k e s and so no s h o rta g e of w a ter was ex­
p e rie n c e d u n t i l , th e w estw ard exp an sio n in to th e a r id and s e m i-a rid r e g io n s.
The b e g in n in g o f s y s te m a tic c o l l e c t i o n o f h y d ro lo g ic d a ta i n t h i s c o u n try
can p ro b a b ly be ta k e n t o be in 1888, when th e U, S . G e o lo g ic a l Survey
under th e d i r e c t i o n o f F re d e ric k H0 K ewell s e t up i t s f i r s t - riv e r-m e a ­
surem ent s t a t i o n on th e Rio Grande R iv er a t Embudo, New Mexico„
. Modern Hydrology
S ince about 1930, th e in c re a s e in th e amount of p r in t e d in fo rm a tio n
made a v a il a b le in th e f i e l d o f h y d rology has in c re a s e d v e ry r a p id ly .
T his in d ic a te s som ething o f th e in c re a s e d need, th e r e has been in re c e n t
y e a rs t o o b ta in more d a ta and develop b e t t e r p r e d ic tio n m ethods,
The s tu d y o f hydrology can be su b d iv id e d in to th e two g e n e r a l a re a s
o f s to c h a s tic , and d e te r m in is tic , h y d ro lo g y „
D e te rm in is tic h y d rology can
' be " f u r th e r s e p a ra te d i n t o p h y s ic a l o r a n a l y t i c a l , dynamic and p a ra m e tr ic „
S to c h a s tic hydro lo g y a tte m p ts t o p r e d ic t fu tu r e e v e n ts o r r e c o n s tr u c t
- 8 -
p a s t e v e n ts based on th e s t a t i s t i c a l p r o p e r tie s o f th e known re c o rd .
White ( 1967) s t a t e s t h a t i f th e v a lu e t h a t a v a r ia b le has im p lie s an
e le m e n t■o f chance, th e n i t i s a s t o c h a s t i c v a r i a b l e „
Thus i f th e re c o rd
a v a il a b le f o r some v a r ia b le (th e v a lu e of which i s random in n a tu re o r
s t o c h a s t i c ) is r e s t r i c t e d in tim e , th e n th e p r e d ic te d f u tu r e p r o je c tio n
o f t h i s re c o rd is done by s t a t i s t i c a l means.
P h y s ic a l ( a n a l y t i c a l ) hydro lo g y a d d re s s e s i t s e l f t o p a r t i c u l a r
s p e c ia liz e d problem s o f th e h y d ro lo g ic p r o c e s s „
I t does no t t r y t o su p p ly
any answ ers t o peak d is c h a rg e , a n n u a l y i e l d , o r freq u e n cy s t u d i e s .
In
a sen se t h i s branch o f h y d ro lo g y i s p u re re s e a rc h i n t h a t i t seeks t o
e s t a b l i s h r e l a t i o n s h i p s betw een v a r ia b le s o p e ra tin g in th e h y d ro lo g ic
c y c le b u t does n o t a tte m p t t o s o lv e any r e l a t e d p r a c t i c a l ■p ro b lem s„
Dynamic hydro lo g y i s th e term f o r h y d ro lo g ic s tu d ie s in v o lv in g th e
dynamic wave th e o r ie s o f f l u i d flo w .
These wave th e o r ie s have been
a p p lie d t o o v e rla n d flow a s w e ll as open c h an n e l flow t o d e riv e syn­
t h e t i c ru n o f f h y d ro g ra p h s.
P a ra m e tric hydro lo g y a tte m p ts t o d is c o v e r th e r e la t i o n s h i p s among
p h y s ic a l p a ra m e te rs t h a t a re in v o lv e d in t h e - p a r t i c u l a r h y d ro lo g ic -events
t h a t a re o f i n t e r e s t and th e n t o use them t o sim u la te n o n -reco rd ed e v e n ts .
Amprocho and E a rt (1964) l i s t methods o f c o r r e l a t i o n a n a l y s i s , p a r t i a l
sy stem s y n th e s is w ith l i n e a r o r n o n lin e a r a n a ly s is , and g e n e r a l system
s y n th e s is a s. methods used in p a ra m e tric h y d ro lo g y .
In th e p r e d ic tio n o f peak ru n o ff from -a .sm all w atershed, by a method
such as' t h a t developed by th e SCS, b o th s to c h a s tic and d e te r m in is tic
“ 9>
hydro lo g y come in to p la y .
The s tre a m flow i t s e l f , b e in g th e r e s u l t
o f p r e c i p i t a t i o n , i s a s t o c h a s t i c p ro c e s s .
W atershed c h a r a c t e r i s t i c s ,
which m odify o r a f f e c t th e stream -flow , a r e , - by th e m se lv e s, p h y s ic a l
p a ra m e te rs .
Dynamic h y d ro lo g y must be c o n sid e re d in th e flo o d ro u tin g
p ro c e ss w h ile p a ra m e tric hydro lo g y i s u t i l i z e d t o f in d c o r r e la tio n s
among th e v a rio u s w a tersh e d p a ra m e te rs „
A d is c u s s io n of th e te c h n iq u e f o r p r e d ic tin g flo o d fre q u e n c ie s
which i s c u r r e n tly in use by th e S o il C o n se rv a tio n S e rv ic e , i s re s e rv e d
f o r C hapter I I I , because i t i s th e b a s is f o r t h i s t h e s i s „
C hapter I I I
SOIL CONSERVATION SERVICE RUNOFF PREDICTION METHOD
The S o il C o n se rv a tio n S e rv ic e method, o f p r e d ic tin g r u n o f f from ungag ed w a tersh e d s is c h a r a c te r iz e d by th e developm ent o f a s y n th e tic u n it
hydfographo
Under t h i s method th e sto rm c h a r a c t e r i s t i c s a r e tra n s fo rm e d
in to a s y n th e s iz e d f lo o d ru n o f f h y drograph by th e b a s in c h a r a c t e r i s t i c s ^
th e shape o f th e s y n th e t ic u n it hydrograph and th e h a s e f low h y d ro g rap h „
The g e n e r a l p ro ced u re which i s fo llo w e d in d ev elo p in g a flo o d ru n o ff
hydrograph i s shown by th e blo ck diagram i n F ig u re I .
As shown in F ig u re I , th e sto rm ru n o f f volume must f i r s t be d e r iv e d
from th e sto rm c h a r a c t e r i s t i c s and th e b a s in c h a r a c t e r i s t i c s c
This sto rm
ru n o f f volume i s th e n shaped in to a sto rm hydrograph by use o f a syn­
t h e t i c u n it hydrograph w hich in t u r n i s d e riv e d from th e b a s in and storm
c h a ra c te ris tic s «
A b aseflo w hydrograph th e n i s added t o th e sto rm h y ­
d ro g rap h a s in d ic a te d i n F ig u re I t o produce th e flo o d ru n o f f hydrograph.
T his sequence o f o p e ra tio n s in v o lv e d i n p ro d u cin g th e flo o d ru n o ff hy­
d ro g rap h com prises a m a th e m atica l w atersh ed model.
The g e n e r a l fram e­
work o f th e w atersh ed model has been in c o rp o ra te d in to a program f o r
s o lu tio n by a d i g i t a l com puter.
.
The b a s in c h a r a c t e r i s t i c s o f a p a r t i - ■
c u la r w a tersh e d must be s u p p lie d as in p u t t o th e com puter t o tra n s fo rm
th e g e n e r a l model in to a s p e c i f i c model f o r th e w atersh ed in .q u e s t io n .
P ro p o se d . Use o f SCS Method
The proposed way o f t e s t i n g th e SCS method* is. t o use i t on an a c t u a l
*TMs m eth o d -is o u tlin e d in th e Hydrology s e c tio n of th e SCS N a tio n a l
E n g in eerin g Handbook (1 9 6 4 ),
11
Storm
Char a c t s r i s t i c s
B asin
C h a r a c te r is tic s
S y n th e tic
U nit
Eydrograph
Storm
■R unoff
Volume
St orm
R unoff
Hydrograph
Flood
R unoff
Hydrograph
F igure I :
Block Diagram D e p ictin g S o il C o n serv atio n
S e rv ic e Runoff P r e d ic tio n Method
- 12
storm where th e input (storm ) and the output (ru n off hydrograph) are
known.
The procedure should be t o supply data c h a r a c te r iz in g the w ater­
shed and storm c h a r a c t e r is tic s as input t o th e computer program which th en
u ses th e w atershed model t o sim ulate a ru n off hydrograph.
The volume o f
th e sim ulated hydrograph i s compared w ith th a t o f th e a c tu a l ev en t.
If
th er e are major d isc re p a n cies in th e volum es, th e valu es c h a r a cter iz in g
th e b a sin parameters may be a lt e r e d , and th e computer program run a g a in .
When th e volumes are ad ju sted to be e s s e n t i a l l y the same, th e model is
con sid ered t o be a v a lid r e p r e se n ta tio n o f th e w atershed.
The v a lid it y
o f th e SCS method depends upon th e a b i l i t y o f the a d ju sted model to
a c c u r a te ly reproduce th e a c tu a l ru n off hydrograph, in clu d in g th e peak
d isc h a r g e.
A fte r th e model has been a d ju sted , i t i s then p o s s ib le t o route
d e sig n storms through th e model.and th ereb y sim ulate d e sig n hydrographs.
■U nit Hydrograph Theory
""
The u n it h ydrograph (UH) f o r . a g iv e n w atersh ed i s d e fin e d a s th e d i s ­
ch arg e - to - tim e r e l a t i o n s h i p t h a t y ie ld s one in ch o f ru n o f f from a sto rm
o f g iv e n d u r a tio n o v er th e e n t i r e w atersh ed a r e a .
U nit hydro g rap h s a re
g e n e r a lly d e riv e d from as many a c t u a l re c o rd e d storm s as p o s s ib le and
th e n g e n e r a lly a re assumed t o re p re se n t, th e
a l l storm s o f s im ila r d u r a tio n s .
u n it ru n o f f fu n c tio n s f o r
Sherman (1932) is g iv e n c r e d i t f o r f o r ­
m u la tio n o f th e u n it h ydrograph th e o ry w h ile Snyder (1938) f i r s t i n t r o ­
duced a method f o r c o n s tr u c tin g a s y n th e t ic UH which may be used f o r th e
s tu d y o f ungaged w a te rs h e d s .
S e v e ra l o th e r'm e th o d s f o r d e f in in g s y n th e tic
- 13 -
UH have been developed s in c e Snyder in c lu d in g th o s e by Commons (19^2
M itc h e ll (1 9 4 8 ), and Gray ( 1961) e
System S y n th e s is and A n a ly sis
Where no a c t u a l hydrographs a re a v a il a b le f o r a w a te rsh e d , th e SCS
method o f p r e d ic tin g ru n o ff can he c l a s s i f i e d as a method o f g e n e ra l
system s y n th e s is .
I f a n a c t u a l u n it hyd ro g rap h is a v a i l a b l e , on th e
o th e r hand, th e SCS method would be one o f p a r t i a l system s y n th e s is w ith
l i n e a r system a n a l y s i s .
System s y n th e s is a c c o rd in g t o Amorocho and B art (1964) i s a method
o f d e s c r ib in g th e o p e ra tio n of a p h y s ic a l system w ith a c o m b in atio n of
components t h a t e x i s t i n th e system and w hose. fu n c tio n s a re known and p r e ­
d ic ta b le .
System a n a l y s i s , on th e o th e r hand, i s a method by w hich th e r e ­
la t i o n s h i p betw een th e in p u t and o u tp u t t o th e system i s e s ta b lis h e d
m a th e m a tic a lly by m easuring o n ly th e p r o p e r tie s o f th e in p u t (sto rm d a t a )
and o u tp u t ( r u n o f f ) w ith o u t re g a rd in g th e n a tu re o f th e sy stem .
An e x p la n a tio n of th e l i n e a r and n o n lin e a r p r o p e r tie s o f ru n o ff
p r e d ic tio n methods w i l l fo llo w l a t e r i n t h i s c h a p te r.
On a gaged w atersh ed s in c e an a c t u a l UH i s a v a i l a b l e , i t is an
a n a l y t i c (as opposed t o s y n t h e t i c ) f u n c tio n s in c e th e i n t e r n a l c h a ra c ­
t e r i s t i c s o f th e system a re n o t known o r s y n th e s iz e d .
Even though th e
a c t u a l hydrograph i s a v a i l a b l e , how ever, s y n th e tic m o d ific a tio n s a re
1
n e c e s s a ry ,
I
in te r c e p t io n o f p r e c i p i t a t i o n by v e g e ta tio n and baseflow
c h a r a c t e r i s t i c s , f o r in s ta n c e , must be s y n th e s iz e d .
T h e re fo re , even on
" .14 "
a gaged w a te rsh e d , th e SCS method i s p a r t i a l l y s y n th e t ic , and may he
c l a s s i f i e d as one o f p a r t i a l system s y n th e s is w ith l i n e a r a n a l y s i s .
On an ungaged w a te rsh e d , where i t i s n e c e s sa ry t o use a s y n th e tic
UH th e e n t i r e system i s s y n th e t ic ; th u s th e c l a s s i f i c a t i o n o f g e n e ra l
s y n th e s is method a p p lie s t o th e p r e d ic tio n o f .r u n o f f hydrographs on u n -.
gaged w a te rsh e d s.
F u n c tio n in g o f a G eneral S y n th e s is Method•
• The system which tra n s fo rm s r a i n f a l l t o ru n o ff can be th o u g h t o f as '
made up o f th r e e s e p a r a te subsystem s when th e u n it h y drograph approach
i s b ein g c o n s id e re d .
I ) The f i r s t sub sy stem , which c r e a te s a " r a in fa ll
e x c e s s " f u n c tio n , m o d ifie s th e t o t a l r a i n f a l l in p u t t o acco u n t f o r i n ­
f i l t r a t i o n , i n te r c e p t io n , and d e p re s s io n s to r a g e .
The r a i n f a l l excess
th u s computed i s th e amount o f r a i n f a l l t h a t is a v a ila b le f o r runoff-.
2 ) The second subsystem c r e a te s a "storm ru n o f f" f u n c tio n by o p e ra tin g on
th e r a i n f a l l e x cess f u n c tio n .
to p o g ra p h ic c h a r a c t e r i s t i c s .
This su b sy stem makes use o f th e b a s i n 's
3 ) F in a lly , th e t h i r d su b sy stem , which, ere.-
a t e s th e " flo o d r u n o f f " f u n c tio n u ses b aseflo w in fo rm a tio n t o a l t e r th e
sto rm ru n o f f f u n c tio n .
The combined e f f e c t o f th e s e th r e e subsystem s is
assumed t o d u p lic a te th e n a t u r a l p ro c e ss e s which occur on th e a c tu a l
w a tersh e d b e in g s tu d ie d .
The p a ra g rap h s t h a t fo llo w d e s c rib e in d e t a i l
th e s e th r e e subsystem s a s s y n th e s iz e d by th e SCS method.
R a i n f a l l E x c e ssi
The r a i n f a l l e x cess f u n c tio n (produced by th e f i r s t
su bsystem ) i s g iv e n , a c c o rd in g t o th e SCS m ethod, by e q u a tio n ( 3) ,
=■ .15 ~
(3)'
where Q i s th e amount o f r a i n f a l l e x cess in in ch es over th e w atershed,
P i s th e sto rm r a i n f a l l in in c h e s , and S i s d e fin e d as th e maximum
p o t e n t i a l d if f e r e n c e betw een P and Q (hence th e maximum i n f i l t r a t i o n
c a p a c ity ) a t th e tim e o f th e s to rm 's b e g in n in g 0
E q uation (3 ) i s based on a h y p o th e s is .
I f th e e q u a tio n can be
shown t o be t r u e , th e n th e h y p o th e sis can be assumed t o be t r u e „
The
o r i g i n a l h y p o th e sis can be s t a t e d as s u c h :
— and S =4> I as P
S
P
co
(4 )
where G i s th e a c t u a l r e t e n t i o n d u rin g a sto rm , S i s th e p o t e n t i a l
maximum r e t e n t i o n , Q i s th e d i r e c t ru n o f f (o r th e a c t u a l r u n o f f ) , and P
i s th e t o t a l storm r a i n f a l l (o r th e p o t e n t i a l maximum r u n o f f )„
So when
flo o d p ro d u cin g storm s' a re c o n s id e re d , i t can be s a id t h a t :
H
(5)
E quation (5 ) cannot be. proven m a th e m a tic a lly , however, i t fo llo w s from
e q u a tio n (3 ) which e m p ir ic a lly has been found t o be v a l i d .
Since G - = P - ^ Q , e q u a tio n (5 ) can be r e w r itte n :
The SCS H ydrology Handbook b eg in s th e developm ent of e q u a tio n (3 ) w ith
“ 16 *•
th e sta te m e n t o f e q u a tio n (6 )„
As P goes t o i n f i n i t y , th e r a t i o (P
Q)/,S->1 and Q /P->1.
Keep­
in g in mind t h a t P, Q, and S a re t o t a l volumes f o r a sto rm , (P - Q)
f i n a l l y f i l l s th e e n t i r e s o i l p r o f i l e t o i t s maximum v a lu e S as de­
te rm in e d f o r th e c o n d itio n of th e w atersh ed a t th e b e g in n in g o f a sto rm .
Now, s o lv in g d i r e c t l y f o r ru n o f f volume from e q u a tio n (6 ):
Qs
P2
P-PS
(7 )
A f u r t h e r ad ju stm en t o f P can be made f o r th e i n i t i a l a b s tr a c tio n
Ia which red u ces P by th e amount of i n t e r c e p t i o n , d e p re s s io n s to r a g e ,
and i n f i l t r a t i o n a t th e s to r m 's b e g in n in g b e fo re ru n o ff o c c u rs .
S e v e ra l
r e la t i o n s h i p s can now be re v is e d t o allo w f o r th e i n i t i a l a b s tr a c tio n
( i n e f f e c t , t h i s amounts t o r e d e f in in g term s which now have s l i g h t l y
d i f f e r e n t meanings th a n .th e c o rre sp o n d in g term s in e q u a tio n s (4 ) th ro u g h
(7 ) ).
P = Q+ G f l a
(8)
8=2 Ia+ G = P - Q
(9)
G =. ( P - l a ) - Q
(10)
E q u atio n (7 ) can a ls o be r e s t a t e d :
•
■
Q s J Z j l J bJ L
P - Ta 4 S
( 11 )
E x istin g - d a ta from s e v e r a l w atersh ed s were s tu d ie d and i t was found t h a t
-17
Ia can be ta k e n to be e q u a l t o -.25=
-
By s u b s t i t u t i n g t h i s v alu e in
e q u a tio n ( 1 1 ), e q u a tio n (3 ) i s f i n a l l y d e riv e d .
The SCS has p re p a re d a g r a p h ic a l s o lu tio n (ru n o ff a s a f u n c tio n o f
p r e c i p i t a t i o n ) of e q u a tio n ( 3) , which is shown in Appendix A.
As is
e v id e n t in Appendix A, p r e c i p i t a t i o n i s r e l a t e d t o ru n o f f th ro u g h a
'fa m ily o f c u rv e s , each curve b ein g drawn f o r a p a r t i c u l a r curve number
(CN) 0
The curve numbers a re a f u n c tio n o f S and a re g iv e n by th e r e ­
la tio n s h ip ;
CM =
1000
S +10
( 12)
The p a ra m e te r CM i s used in s te a d o f S as in te g e r v a lu e s of S do
n o t produce curves t h a t le n d th em selv es t o e asy i n t e r p o l a t i o n .
The
curve num bers, how ever, make th e P v s , Q p lo t e a s i e r t o u s e .
The ru n o f f e q u a tio n , e q u a tio n ( 3) , used by th e SCS i s a r e l a tio n s h ip
betw een P and Q-in v o lv in g .only one p a ra m e te r, th e p a ra m ete r b ein g S,
S
can now be e m p ir ic a lly r e l a t e d t o as many c h a r a c t e r i s t i c s a s i s th o u g h t
t o be n e c e s s a ry .
The d e v e lo p e rs o f t h i s method found t h a t s o i l and cover-
c o n d itio n s had th e most e f f e c t on th e v a lu e of S (and th e r e f o r e on th e
CM),
The curve number. CM is th e r e f o r e term ed th e s o i l c o v er complex
number.
For v a rio u s com binations of s o i l ty p e and v e g e ta l c o v e r, s o i l co v er
complex numbers have been developed e m p ir ic a lly .
To. d e term in e such a
number, s m a ll w atersh ed s were found which had o n ly one ty p e of s o i l and
o nly one ty p e o f cover c o n d itio n ,
A number o f p o in ts were p l o t t e d , one
" 18 •“
p o in t p e r sto rm , on a g ra p h o f t o t a l p r e c i p i t a t i o n in in c h e s v e rsu s t o t a l
r u n o f f i n in c h e s .
The CM curve t h a t b e s t f i t s t h i s p lo t i s th e n ta k e n to
be th e r e p r e s e n ta tiv e curve number f o r t h a t s o i l co v er com plex.
s u l t s o f a l l such p lo t s made by
th e SCS a re summarized in
In u sin g th e SCS m ethod, curve
The r e ­
Appendix C.
numbers (CN) a re d eterm in ed by r e ­
f e r r i n g t o a t a b l e such a s t h a t shown in Appendix C, and s e l e c t i n g th e
CK t h a t co rre sp o n d s t o th e a p p ro p ria te s o i l ty p e and v e g e ta l cover con­
d itio n .
The s o i l c l a s s i f i c a t i o n used d iv id e s a l l s o i l s i n t o fo u r groups
(A, B, C, and D) a c c o rd in g t o t h e i r p e r m e a b i l i t i e s „
The p e rm e a b ility o f
group A s o i l s i s h ig h e s t and o f
th e D s o i l s , th e lo w e s t. The d e s c r ip ­
ti o n s o f th e v a rio u s s o i l ty p e s
a re g iv e n i n Appendix B. Musgrave and
H o ltan , a s - r e p o r te d by Chow (196 4 ), have q u a n tif ie d i n f i l t r a t i o n r a te s
f o r th e fo u r s o i l g ro u p s .
Minimum i n f i l t r a t i o n r a t e s f o r groups D, C,
B, and A a re g iv e n by th e ran g es 0 t o 0 .0 5 , 0 .0 5 t o 0 .1 5 , 0 .1 5 t o 0 .3 0 ,
and 0 .3 0 t o 0.45 in c h e s p e r h o u r, r e s p e c tiv e ly .
A v e g e ta l co v er c o n d itio n i s d e s c rib e d a s some n a tu r a l o r c u l t i ­
v a te d c o n d itio n .
For in s ta n c e th e co v er may be d e sc rib e d v a r io u s ly as
f a llo w , co n to u red sm all' g r a in in p o o r c o n d itio n , p a s tu r e i n f a i r con­
d i t i o n , o r woods in good c o n d itio n .
The e f f e c t o f th e a n te c e d e n t m o istu re c o n d itio n (AMC) i s accounted
f o r by a d ju s t in g th e s o i l co v er complex number p re v io u s ly c a lc u la te d .
The curve number was o r i g i n a l l y developed w ith average AMC b ein g assum ed,
However, f o r c o n d itio n s o f .very d ry and v e ry wet a n te c e d e n t s o i l m o istu re
c o n d itio n s , ty p e I and ty p e .I I I , r e s p e c t i v e l y , a re u sed .
Tlie ty p e I I
- 19 -
c o n d itio n i s con sid ered t o be th e average c o n d itio n .
Whether th e AMC-
c a l l s fo r typ e I o r .ty p e I I I treatm ent i s determined by th e guide lin e s
in Table I.
The lim it s on th e dormant sea so n apply t o unfrozen ground
and no snow co v er.
A fter th e c o rr e ct typ e o f AMC i s determ ined, th e r e are standard
curves showing th e adjustm ents t o be made on th e s o i l cover complex
numbers as shown in Figure 2 .
Values fo r th e a d ju sted CN can be tak en
a t p o in ts between lin e s shown fo r ty p es I , I I , and I I I i f i t i s f e l t th a t
th e AMC are s u f f i c i e n t l y w e ll known.
Storm R un off:
The second subsystem (th a t which produces th e storm
ru n off fu n c tio n ) i s assumed t o be a lin e a r co n v o lu tio n by u n it hydrograph th e o r y .
The purpose o f th e co n v o lu tio n p rocess i s e s s e n t i a l l y t o
convert a r a i n f a l l e x c e ss fu n c tio n o f a c e r ta in volume in t o a runoff
fu n c tio n having th e same volume.
The co n v o lu tio n in t e g r a l d e scr ib in g
t h i s r u n o ff fu n c tio n q ( t ) i s g iv e n by:
q(t) =
Pt
u (t - Y ) i ( r ) d'Z'
.
(13)
J q
The k e r n e l fu n c tio n u (t - T ) i s th e in sta n ta n eo u s u n it hydrograph (the
u n it hydrograph which t h e o r e t ic a lly r e s u lt s from a r a i n f a l l ex cess occu r­
r in g in sta n ta n e o u sly on a l l p a rts o f a w atersh ed ), i ( y ) i s th e r a i n f a l l
e x c e ss input fu n c tio n , and t ’ (th e lim it in g tim e fo r r ) i s a fu n c tio n o f
t Q, t Q b ein g th e d u ration tim e o f th e input fu n c tio n (sto r m ).
For t
t 1 = t and when t ^ t 0 , t 1 = t 0 .
The b a s ic c o n v o lu tio n p ro cess i s shown g r a p h ic a lly in Figure 3 .
20
Tablo I :
r
Types o f A n teced en t M oisture C o n d itio n s
Dormant Season
( in c h es )
AMC
i
T o ta l 5-day A n teced en t R a in f a ll
Growing Season
( in ch es )
I
LA
O
1.4
II
0.5 - 1.1
1.4 - 2.1
III
1.1
,1
____________________I
100
90
80
70
A d ju sted
Curve
50
Number
40
30
20
10
0
o
io
20
30
4o
50
6o
70
8o
90
Curve Number - Type I I
F ig u re 2 :
A djustm ent o f Curve Number Value f o r Types o f AVC
100
21 -
/.
7
SCS In s ta n ta n e o u s Unit
Hydrogra ph
S im p lifie d Ins Lantanaous
U nit Hydrograph
2 .6 7 t
u(t-Z ) i ( t )
dZ
------ 1 Q-d rC i" 5 t p —
F ig u re 3:
C on v o lu tio n of R a i n f a l l Excess i(? r) and I n s ta n ­
ta n eo u s U nit Hydrograph u (b - X )
~ 22 “
S t a r t i n g from tb s ex cess f u n c tio n i ( f ) v e rs u s Z , each in crem en talvolume o f r a i n f a l l is m u ltip lie d by th e in s ta n ta n e o u s UH (IUH) and i s
summed in th e r i g h t tim e sequence t o y ie ld th e storm- ru n o f f fu n c tio n
q ( t ) v e rs u s t 0
The in s ta n ta n e o u s u n it hydrograph shown i s t h a t used by
th e SCS when d e v elo p in g a s y n th e tic u n it hydrograph f o r a n ungaged w a te r­
sh e d .
This s y n th e tic UH- was developed f o r th e SCS by Victor'Mock-us as
r e p o r te d i n th e SCS N a tio n a l E n g in ee rin g Handbook (196k )„
The t r i a n g u l a r
IUH shown w ith a d o tte d l i n e i s n o rm ally u se d , b e c a u s e -o f i t s s im p lic ity
f o r ru n o f f c a lc u la tio n s made by Iaand0
However, when th e com puter i s
u t i l i z e d , th e more e x a c t c u r v i l i n e a r IUH i s e q u a lly e a sy t o a p p ly .
The r a i n f a l l excess- f u n c tio n i ( Y ) can he used d i r e c t l y w ith th e
IUH t o produce th e ru n o ff ..fu n c tio n q ( t ).
However, th e way i n which v a lu e s
o f i ( Z ) sh o u ld be c a lc u la te d i s no t obvious from th e e a r l i e r d ev elo p ­
ment o f .eq u atio n ( 3) ,
The volume o f r a i n f a l l excess i. (w hich i s e q u i­
v a le n t t o th e volum e. o f ru n o f f q) f o r th e tim e increm ent d r
is e q u a l t o
th e v alu e Q g iv e n by e q u a tio n (3 ) a t tim e Z t dY minus Q by e q u a tio n (3 )
a t tim e Z ,
Tne volume o f p r e c i p i t a t i o n P i s th e t o t a l p r e c i p i t a t i o n o f
th e sto rm u p .to tim e
Z-\ d Z
and X i r e s p e c tiv e ly ,
(dQ ), caused by th e sto rm o f d r
Q 's a t tim e s
Y t d X and % «
based, on th e e n t i r e sto rm
Tiie increm ent of. Q,
le n g th must be g iv e n as a d iffe re n c e - o f
This i s t r u e s in c e th e ru n o f f e q u a tio n i s
(th e i n i t i a l a b s t r a c t i o n must be accounted f o r
o n ly o n c e ),
The base tim e f o r th e c u r v i l i n e a r UH in F ig u re 3 i s ta k e n t o be 5,0 0
'tim e s th e tim e t o p e a k .
This v alu e o f b ase tim e i s a r b i t r a r y b u t does
.
“ 23 ~
n o t in c o rp o ra te .a p p re c ia b le e r r o r i n th e r e s u l t s as th e c o rre sp o n d in g
v a lu e s o f d is c h a rg e a re v e ry sm alls
The peak flow r a t e f o r th e c u r­
v i l i n e a r UH i s th e same a s t h a t f o r th e t r i a n g u l a r v e rs io n whose base
tim e (d eterm in ed m a th e m a tic a lly ) i s found t o be 2 .6 7 tim e s th e tim e t o
peak ( t p ) o
The t r i a n g u l a r h ydro g rap h b ase tim e o f 2 .6 7 t p i s used as
i t g iv e s th e same v a lu e o f ru n o f f volume as th e c u r v i l i n e a r v e r s io n , th e
volume b e in g re p re s e n te d by th e a re a u n d er th e c u rv e .
ra te
The peak flow
i s d e riv e d u sin g th e t r i a n g u l a r shaped UH and i s g iv e n by th e
g e n e r a l e q u a tio n
' P - j ^
wi t h
and
and
'
t p s D/2 + L s D/2 + 0 . 6 t c
.
t p - 2 .6 7 t p f o r t r i a n g u l a r u n it hydrographs
tp s $ .0 t_ f o r c u r v i l i n e a r u n it hydrographs
(14)
(15)
(16)
(17)
where K i s a c o n s ta n t whose v a lu e depends on th e u n its u se d , A i s th e
a r e a , Q i s t o t a l volume o f r u n o f f , tp i s tim e t o peak, t ^ i s th e base
tim e , D i s sto rm d u r a tio n tim e , t c i s th e tim e o f c o n c e n tr a tio n , and I
i s th e b a s in la g tim e .
IC i s e q u a l t o 484 when Q i s i n in c h e s , A in -
sq u are m ile s and t p , L and D a re in h o u r s .
f e e t p e r second. .
.
Peak flow i s th e n in cu b ic
1
For th e example shown i n F ig u re 3, w here. th e c o n v o lu tio n i n t e g r a l
g e n e r a lly cannot be so lv e d e x a c tly , a c t u a l p r a c tic e d i c t a t e s t h a t th e
™ 2h “
sto rm in p u t be broken up in to s m a ll in crem en ts a %.
D o f e q u a tio n (15) i s th e n e q u a l t o a r
„
The sto rm d u r a tio n ■
E q u atio n (14) to g e th e r w ith
e i t h e r ( l 6 ) o r (1 7 ) i s s u f f i c i e n t t o d e s c rib e th e ru n o f f hydrograph from
a subw atershed due t o a n in c re m e n ta l sto rm .
The hydrograph can be g iv e n
th e t r i a n g u l a r o r c u r v i l i n e a r shape a s d e s ir e d .
Flood R u n o ff:
The t h i r d subsystem ( th a t which p roduces th e flo o d
ru n o f f f u n c tio n ) i s th e sim ple p ro ced u re o f ad d in g th e bass-flow hy d ro g rap h t o o b ta in th e r e s u l t i n g flo o d h y d ro g rap h ,
The h aseflo w hydrograph
may be o b ta in e d by any o f th e s ta n d a rd te x tb o o k methods a s lo n g a s th e
same p ro c e d u re is used c o n s i s t e n t l y ,
C hannel Flood R outlug
When a w a tersh e d i s d iv id e d i n t o subw atersheds f o r th e purpose o f
p r e d ic tin g ru n o f f more a c c u r a te ly , i t i s n e c e s s a ry t o r o u te hydrographs
th ro u g h th e n a t u r a l c h a n n e ls .
The ro u te d hydrograph (o u tflo w h y dro-
grap h from a c h a n n e l) i s th e n i n a p ro p e r form t o be added t o a n o th e r
ro u te d h ydrograph o r t o a n o th e r subw atershed ru n o ff hydrography a f t e r
w hich i t may be ro u te d th ro u g h a second re a c h o f c h a n n e l.
The method chosen by th e SCS f o r c h an n e l flo o d r o u tin g i s term ed
th e "convex m ethod" a f t e r th e name a p p lie d t o th e m ath e m atica l p r in c ip le upon which i t i s b a se d .
The convex method i s based on th e p r in c ip le t h a t when a flo o d p a sse s
th ro u g h a re a c h o f n a t u r a l c h an n e l th e r e i s a tim e i n t e r v a l such t h a t
i f I^ ^
then I
Og A-
(l8a)
25
-
-
i f Ij_ — Oj, th en
whe Se
and
— Og —
( l8 b )
exte th e irate s o f in flow and outflow r e s p e c t iv e ly a t tim e
t s tj_, and Og i s the, r a te o f outflow a t tim e t * t^ 4- A .t = t g .
Note
th a t Ig ( inflow r a te a t t g ) does not e n ter in t o t h is method.
If A t is
0^, and Og form a "convex s e t " .
Erom con­
chosen as s p e c if ie d th en
vex s e t th eo ry we can th en w rite th e working equation
. O2 = (I -
c)
(1 9 )
O1+ CI1
where C i s a parameter w ith th e range O -C —I .
From th e d e f in it io n o f a convex s e t , i t can be s a id th a t whenever
any two p o in ts x and y are in a convex s e t L, th en ev ery p o in t on th e
lin e con n ectin g them i s a ls o in L.
A form al d e f in it io n from s e t th eo ry
g iv e n by Charnes and Cooper ( 1961) s t a t e s t h a t :
a s e t o f p o in ts L i s
convex i f , whenever x , y C L , th en ux-f- ( I - u)y-e L fo r a l l 0 —u - 1 .
The lim it s on th e valu e o f C in su re th a t eq uation ( 1 9 ) meets th e
c o n d itio n s o f th e eq u ation s ( l 8 a ) and ( l8 b ) .
C = ..
It fo llo w s t h a t :
H - O 1
(2 0 )
I t can a ls o be shown from Figure 4 t h a t :
O2 - Oi
__
=
I 1 - O1
“
( 21 )
where K i s a parameter w ith tim e u n its not y e t having any p h y s ic a l mean-
-
26
-
Inflow
Outflow
Flow
Eato
O-
Tiiue
F ig u re 4 :
R e la tio n s h ip betw een A t and K
- 27 -
lo g .
From e q u a tio n s (20) and (21) i t can be seen t h a t i
(2 2 )
A t = CK
I f use o f t h i s method i s t o be made on ungaged w atersheds, some
e m p iric a l r e la tio n s h ip s need t o be d eveloped f o r e v a lu a tio n o f C and
K«
This has been done by th e SCS from knowledge g ain ed from' stu d y of
gaged w a tersh e d s „
I t was found t h a t
C
S
e q u a tio n ■(23) e x p re ss e s th e v alu e
V
(23)
v + 1.7
f o r C v e ry w e ll ex cep t a t extrem e v a lu e s o f V(<0„5 and -1 0 * 0 ), where
V i s th e av erag e stre a m v e l o c i t y in f e e t p e r second.
be th e t r a v e l tim e f o r th e re a c h .
K was a ls o found t o
I f K is in hours and L is th e reach
le n g th i n f e e t , th e n :
3600 V
(24)
I t i s obvious from th e e m p iric a l r e la tio n s h ip s f o r C and K t h a t as
th e w a ter s u rfa c e e le v a tio n ch an g es, v a ry in g v e l o c i t i e s w i l l cause C and
K t o vary w ith tim e .
A p ro ced u re f o r d e te rm in in g V was sought so th a t
C and K could he assumed c o n s ta n t f o r any g iv e n ro u tin g problem .
I t was
found t h a t i f th e av erag e v e lo c i ty V was b ased on th e stre a m flow v e lo ­
c i t i e s f o r a l l d is c h a rg e s o f th e inflow hydrograph g r e a te r th a n o n e -h a lf
o f th e peak d is c h a rg e , th e r e s u l t i n g o u tflo w hydrograph was n e a rly th e
same as" i f i t were-, c a lc u la te d u sin g v a ry in g C and IC=
- 28 -
Tha v a lu e o f A t t o be used i s th e n a p ro d u ct o f C and K and r e ­
mains c o n s ta n t f o r th e e n t i r e r o u tin g .
The v alu e o f A t may tu r n out
t o be in c o n v e n ie n t f r a c t i o n s o f an hour and th e r e f o r e d i f f i c u l t t o u s e „
SCS p r a c tic e i s t o choose a co n v en ien t A t 1 and c a lc u la te a new C, c a lle d
C' , such t h a t ro u tin g by e q u a tio n (19) g iv e s i d e n t i c a l r e s u l t s „
a d ju stm e n t is
.
The
.
'
(25)
R outing is now accom plished by r e w r itin g e q u a tio n (19) t o g iv e th e r e s u l t ;
(26)
O2 a ( I - C ) O1 -^C1I i
R e s e rv o ir Flood R outing
"
Runoff hydrographs a re ro u te d th ro u g h r e s e r v o ir s by th e s to ra g e in ­
d ic a t io n m ethod,
This method i s based on th e c o n tin u ity e q u a tio n shown
h e re i n i t s d i f f e r e n t i a l form .
i(t)
S
q (t)
Ar
Cl G
(27)
where i ( t ) i s th e r a te o f th e inflow a t tim e t , q ( t ) is th e r a t e of o u t­
flow a t tim e t , and d S /d t is th e r a t e o f change in sto r a g e .
The b a s ic
w orking e q u a tio n is w r i t t e n :
(1]^ + I2 ) A t/2 - (O-^+ Og ) A t/2 s Sg -
(28)
where I is in flo w , 0 i s o u tflo w , S i s s to r a g e , t is a tim e in crem en t,
s u b s c r ip ts I and 2 a re f o r t s t j and t s t j + A t - tg r e s p e c tiv e ly .
R ed u ctio n o f t h i s g i v e s ;
(I j "t"I r ” O j )A t -r 2Sj . s Og A t »f* 2Sg
(29)
D e fin in g c o n s ta n ts Cif. and Cy a s ;
~ (ij+ Ig
” Oj ) At + 2 S j
(30)
Ce = Og A t + 2Sg
(31)
I t th e n fo llo w s t h a t from e q u a tio n (2 9 ) ;
is f i r s t e v a lu a te d from known v a lu e s ^ th e n s e t e q u a l t o Ce„
T his v a lu e o f
i s th e n s u b s t i t u t e d i n t o e q u a tio n (31)=
There is one
s e t o f v a lu e s (Og and Sg) on th e s to ra g e - d is c h a rg e curve f o r th e r e s e r ­
v o ir t h a t s a t i s f i e s t h i s l i n e a r e q u a tio n , - This p rocedure c o n s ti tu te s
one s te p in s o lv in g th e c o n tin u ity e q u a tio n by n u m erical ap p ro x im a tio n .
To ro u te a hydrograph th ro u g h a r e s e r v o i r t h i s p ro c e ss must be re p e a te d
u n t i l flo o d flow s have n e a r ly d im in ish e d t o th e o r i g i n a l b a s e f low ,
Systems C l a s s i f i c a t i o n of SCS Method
The runoff dynamics of an actual watershed might be described as a
distributed,, non-linear, time variant system.
Many of the models con­
structed to describe this system, however, are classified as lumped,
linear, and time invariant-.
Early models with these assumptions were
those.developed by Sherman (1932) and Bernard (1935)=
Sherman developed
the unit-graph.concepts often called unit hydrograph th eo r y .
Bernard is
= 30 ■"
given the credit for implementing use of the distribution graph (a bargraph comparable to a unit liydrograph except that runoff volumes are
expressed as percent of total runoff versus time).
A distributed system, in the field of hydrology, is defined as one
with time and space variation in-rainfall intensities<> A lumped system'
or model is one which allows only time variation but no space variation
in rainfall intensity.
This is to say that rainfall intensity is uniform
over the watershed area under consideration at any given time.
The SCS method in its basic form (as currently explained) would be
classified as a lumped system.
By using the SCS runoff prediction method
in conjunction with reservoir and channel flood routing techniques, the
resulting system, will in part be distributed.
Chow (1 9 6 7 ) describes this
■type of system as a "distributed system of lumped-system models".
On
each of several subwatersheds the rainfall intensity is uniform, or each
of the subsystems .is lumped.
However, at any given time, the intensity
can vary from subwatershed to subwatersbed and, is in this sense distri­
buted.
A system is linear if the unit responses of various input magnitudes
are identical.
The watershed runoff function is linear if one unit hydro-
graph is sufficient to accurately describe all storms of a given duration
occurring on a given watershed.
This is never the. case, however, as
Childs (1958) and others have shown.
Childs states that the -larger the
flood, the higher the peak and the shorter the time to peak on the unit
hydrogfaph.
He demonstrates this fact by showing four .unit, hydrographs.
-31 -
o f th r e e - h o u r storm s on Naugatuck R iv er a t Thoicaston, C o n n e c tic u t.
The peak o f a m ajor flo o d has more th a n double th e peak d e riv e d f o r a
m inor flo o d and ab o u t tw o - th ir d s o f th e tim e t o peak .
O bviously, th e
v a ria n c e o f th e storm p a t t e r n o r r a i n f a l l ex cess fu n c tio n a f f e c t s .t h e
u n it hydrograph sh a p e . •• N o n - lin e a r ity i s th e n th e case when th e d e riv e d
u n i t ■hydrograph v a r ie s w ith sto rm p a t t e r n and t o t a l r a i n f a l l excess am ount«
A system t h a t g iv e s th e same re sp o n se f o r a g iv e n in p u t r e g a r d le s s
o f tim e is a tim e in v a r ia n t sy stem .
The su b w atersh ed p o r ti o n o f th e SCS
model i s based on u n it h ydrograph th e o ry and i s th e r e f o r e tim e i n v a r i a n t ,
T his i s n o t to o r e s t r i c t i v e an- a ssu m p tio n as th e r a i n f a l l in p u t t o th e
subw atershed r u n o f f model i s p re a d ju s te d f o r s o i l and co v er c o n d itio n s ,
•antecedent m o is tu re , and tim e o f y e a r .
These a re th e main item s g iv in g
th e ru n o f f f u n c tio n (sy stem r e s p o n s e ) a tim e v a r ia n t n a tu r e .
S p a t i a l and. te m p o ra l v a r i a t i o n s in r a i n f a l l d i s t r i b u t i o n can be
acco u n ted f o r w ith th e SCS a p p ro a ch .
These v a r ia tio n s a re s im u la te d by
d iv id in g a w atersh ed in to s e v e r a l su b w atersh ed s and by making th e tim e
increm ent on th e p r e c i p i t a t i o n v e rs u s tim e in p u t graph s m a ll enough so
t h a t th e g rap h n e a r ly m atches th e a c t u a l curved r e l a t i o n s h i p .
amount of r a i n f a l l can be d i f f e r e n t f o r each subw atershed..
p a t t e r n can have an i n f i n i t e number o f shape v a r i a t i o n s .
The t o t a l
The sto rm
S p a tia l v a r­
i a t i o n i s n o t t o t a l l y acco u n ted f o r s in c e th e r e i s s t i l l no s p a t i a l v a r ­
i a t i o n allow ed w ith in th e su b w atersh ed j th u s s p a t i a l v a r ia tio n ' is only
p a r t i a l l y s im u la te d .
The subw atersh ed s c a n , how ever, be made a s sm all
a s i s p r a c t i c a l f o r th e tim e and expense t h a t can be s p e n t in th e a n a ly s is .
■* 3 2
-
Tib.e tim e o f sto rm b e g in n in g and d u r a tio n can a ls o be d e sig n a te d as
n e c e s s a ry t o .conform t o a n a c t u a l storm ,
i s a ls o p a r t i a l l y s im u la te d 0
T herefore, te m p o ra l v a r i a t i o n
Chapter JLV
SOIL CONSERVATION SERVICE PROJECT JQRMUIATION PROGRAM - HYDROLOGY
The S o il C o n s e rv a tio n -S e rv ic e , i n 1963, o b ta in e d (from a p r iv a te
c o n s u ltin g fir m known a s C» E, I 0 R„, I n c 0 ) a d i g i t a l computer program
d e sig n e d t o so lv e th e " ru n o ff hyd ro g rap h p r e d ic tio n " r e l a t i o n s h i p s d e s ­
c rib e d i n C hapter I I I 0
The com puter program, which was w r itt e n in th e
F o r tr a n language f o r th e IBM 7OgO-computer system , i s e n t i t l e d " P ro je c t
F o rm u la tio n Program - H ydrology" and i s a m a th e m atica l model o f a w ater
shed e x p e rie n c in g p r e c i p i t a t i o n , s u rfa c e r u n o f f , and c h a n n e l flo w .
The
program can ro u te a n u n lim ite d number o f h y p o th e tic a l o r a c t u a l storms
th ro u g h a w atersh ed having as many as 60 s t r u c tu r e s and '120 c r o s s - s e c ­
t io n s d e s c rib e d .
The program has gone th ro u g h s e v e r a l r e v is io n s , most r e c e n tly in
O ctober, 1967„
I t i s now w r i t t e n in F o r tr a n IV-G and u t i l i z e s th e IBM '
360/40 com puter system .
The most re c e n t in s tr u c tio n s , f o r u sin g th e
P r o je c t F o rm u la tio n Program (PFP) were p u b lis h e d by C«, E0 I v R0, Inc«
(1964) and th e SCS ( 1965)0
The PFP c o n s is ts e s s e n t i a l l y o f a s e r i e s o f s u b ro u tin e s which may
be so lv e d i n a v a r i e t y o f com bin atio n s and sequences,* a sch em atic o v e r­
view o f th e PFP i s shown i n F ig u re 5»
The p a r t i c u l a r sequence t o be
fo llo w e d in a g iv e n problem i s d eterm in ed by i n s tr u c tio n s t o a "S tan­
d ard C o n tro l" r o u ti n e , which c a l l s th e s u b ro u tin e s in th e p ro p e r o rd e r,
and p ro v id e s the a d d i t i o n a l in fo rm a tio n n e c e s sa ry t o p erfo rm th e work
o f th e s u b ro u tin e .
The e n t i r e program is monitored by a n "E xecutive
C o n tro l" , which d e s c rib e s th e p a r t i c u l a r sto rm under c o n s id e r a tio n .
E xecutive C o n tro l
P ro b .
P ro b . I
# I
TT 2
P ro b .
T a b u la r Eata
P ro b .
#3
S ta n d a rd C o n tro l
REACH
RHOFFX
SAVMOV
ADDHYD
IP P ro b lcn is.
actual sto rm
OUTPUT
F ig u re 5:
Schem atic o f P r o je c t
F o rm u latio n Program
O p eratio n
C ro s s -s e c tio n
- 35 -
To fo rm u la te a PFP problem , i t is f i r s t n e c e s sa ry t o re a d in
s e v e r a l t a b l e s , a s in d ic a te d on F ig u re
c i f i c f o r th e p a r t i c u l a r w a te rsh e d .
some g e n e ra l and some sp e ­
A fte r t h i s i s done, S ta n d a rd Con­
t r o l c a rd s a re re a d i n t o d e s c rib e th e l o g i c a l sequence in which flo o d
r o u tin g s th ro u g h th e s tre a m re a c h e s and ,s tr u c tu r e s sh o u ld bo perform ed.
T his sequence o f o p e ra tio n s i s , o f c o u rs e , i d e n t i c a l t o th e .sequence
t h a t th e h y d r o lo g is t fo llo w s i n s o lv in g th e problem m an u ally .
To r e f l e c t a f u tu r e change in a w a te rsh e d , any p o r tio n o f th e
S ta n d a rd C o n tro l can be m o d ified a t any tim e by a d d itio n , a l t e r a t i o n , o r
d e l e t i o n o f w a tersh e d d a ta ,.
E x ecu tiv e C o n tro l card s a re th e n read in to
th e com puter t o d e s c rib e each o f th e a l t e r n a t i v e sto rm s i t u a t i o n s t h a t
a re t o be a n a ly s e d .
An i n f i n i t e number o f problem s may be s e t up and ru n
by th e E xecutive C o n tro l f o r a g iv e n s e t o f w atersh ed c h a r a c t e r i s t i c s .
Each d i r e c t i v e o f th e E xecu tiv e C o n tro l s p e c i f i e s th e sto rm p r e c i p i ­
t a t i o n , i t s s t a r t i n g tim e , th e a n te c e d e n t m o istu re c o n d itio n under
which i t i s t o be a n a ly z e d , and t h e . p o r t i o n o f th e w atersh ed th ro u g h which
i t i s t o be ro u te d .
Each subw atershed d e s c rib e d may have d i f f e r e n t t o t a l r a i n f a l l am ounts,
d i f f e r e n t sto rm s t a r t i n g tim e s , d i f f e r e n t sto rm tim e d u ra tio n s and p a t ­
t e r n s , and v a ry in g a n te c e d e n t m o istu re c o n d itio n s ,
A g iv e n sto rm s i t ­
u a tio n ' i s then, a p p lie d t o th e S tan d ard C o n tro l to e f f e c t a s o lu tio n .
A d d itio n a l storm s may th e n be s e t up and s o lv e d ,
A.s has been see n , th e
S ta n d a rd C o n tro l can a t any tim e be changed t o r e f l e c t proposed changes
on th e w a te rsh e d .
A fte r a change, any h y p o th e tic a l o r a c t u a l sto rm can
~ 36 a g a in be a p p lie d t o th e m o d ified w atersh ed t o e v a lu a te th e 'changes made
i n th e outflow h y d ro g rap h .
PFP Subroutine. Arrangement
The SCS program has a t o t a l o f tw elv e s u b ro u tin e s (se v e n of which
a r e c o m p u ta tio n a l)'.. T h e ir r e l a t i o n s h i p s t o th e main program and t o
o th e r s u b ro u tin e s are, .shown in ..Figure 6 .
The seven c o m p u ta tio n a l s u b ro u tin e s ' a re c a lle d BNOFFX, HESVOR,
BEACH, ADDHZD', OUTPUT, INTERP, and PEAK. ' They, r e s p e c t i v e l y , c a lc u la te
a ru n o f f hydrograph f o r a su b w atersh ed ;, ro u te an in p u t hy d ro g rap h th ro u g h
a r e s e r v o i r by th e s to r a g e - i n d i c a t i o n method; ro u te an in p u t hydrograph
th ro u g h ' a c h a n n e l re a c h by th e convex method; add two h y d ro g rap h s; p r i n t
a n d /o r punch th e o u tp u t o p tio n s s p e c if ie d ; a d ju s t th e tim e increm ent f o r
BESVOB, BEACH, and ADDHYD; and c a lc u la te c o o rd in a te s o f th e h ig h e s t peaks
( to a maximum o f t e n ) o f a h y d ro g rap h .
.The o th e r f iv e s u b ro u tin e s a re c a ll e d SAVMOV, UPDATE, SETUP, READ-5,
and READINo
SAVMOV g iv e s th e w r i t e r o f S ta n d a rd C o n tro l th e a b i l i t y to
move an e n t i r e hydrograph from one s to ra g e lo c a t io n t o a n o th e r and to
save i t .th e re u n til- n e e d e d l a t e r .
UPDATE causes th e S ta n d a rd C o n tro l,
l i s t i n g c u r r e n tly in fo r c e t o b e .p r in te d o u t.
This would b e ,u se d a f t e r
some a l t e r a t i o n o f S ta n d a rd C o n tro l had b een made,
a l l c o n tr o l o f th e c o m p u ta tio n a l s u b r o u tin e s .
SETUP has. th e o v e r­
READ 5 and RSADlN. cause
th e program t o re a d in th e d a ta which d escrib e th e p h y s ic a l f e a tu r e s of
th e watershed and the p r o p e r tie s o f th e sto rm b ein g s im u la te d .
Tabular Data
Several types of data that are necessary for the operation of the
- 37 -
I1-Eiin Program
UPDATE
RNOFFX
RESVOR
REACH
ADDHYD
SAVMOV
OUTPUT
INTER?
F ig u re 6 :
S u b ro u tin e Schema f o r S o il C o n se rv a tio n S e rv ic e
P r o je c t F o rm u latio n Program - H ydrolcgy
PEAK
“■38 "
P r o je c t F o rm u latio n Program can be s u p p lie d t o th e com puter i n t a b u l a r
Porm0
These d a ta a re v a lu e s f o r th e r e l a t i o n s h i p betw een th e ro u tin g
c o e f f i c i e n t C and av erag e v e l o c i t y Vj th e c u r v i l i n e a r u n it hydrography
sto rm p a t t e r n s ; th e s ta g e - s to r a g e - d is c h a r g e r e l a t i o n f o r r e s e r v o i r s and
th e s ta g e - a r e a - d is c h a r g e r e l a t i o n f o r c h an n e l c r o s s - s e c t io n s .
The G - V g ra p h is ta b u la te d - f o r com puter use in v e l o c i t y ■incre­
ments o f 0 .2 f e e t p e r seco n d .
The u n it hydrograph i s s u p p lie d in dimen­
s io n le s s form as q/q_ v e rsu s t / t
ir
P
.
D esign sto rm p a tte r n s a re described
i n c u m u la tiv e ,, d im e n sio n le ss form w ith c o o rd in a te s o f P/l-jp and t / t p
where
IV i s th e s to rm 's t o t a l p r e c i p i t a t i o n .
A c tu al storm s can be
re a d i n e i t h e r dim ensioned o r d im e n sio n le ss form b u t alw ays a s a cumu­
l a t i v e g ra p h .
I f a c t u a l dim ensions are used, r a i n f a l l d e p th and d u r a tio n
i n E xecu tiv e C o n tro l a re t o be g iv e n a s 1 .0 .
I f , how ever, d im e n sio n less
c o o rd in a te s a re used f o r a c t u a l storm s in t a b u l a r d a ta , th e a c tu a l v a lu e s
o f d e p th and d u r a tio n must be s u p p lie d i n th e Executive C o n t r o l .' The
s t r u c t u r e and c r o s s - s e c ti o n d a ta can be g iv e n in any d e s ir a b le increm ent
o f e le v a tio n .
This sh o u ld be a sm a ll enough increm ent so t h a t th e assumed
s t r a i g h t l i n e betw een p o in ts i s n e a r ly c o in c id e n t w ith th e curved r e ­
la t i o n s h i p from which th e p o in ts were s e l e c t e d .
The e le v a tio n in c r e ­
ment' can be v a rie d a t w i l l th ro u g h o u t th e s e t a b l e s .
IChe way in which th e s e t a b u la r d a ta a re u t i l i z e d by th e E xecutive
and S ta n d a rd C o n tro l i s o u tlin e d by th e flow c h a r t in F ig u re 5.
The
,
problem s posed by th e E xecutive C o n tro l-a re in d iv id u a l, d i s t i n c t sto rm s ,
an i n f i n i t e number o f which can be p ro c e ss e d by th e PFP.
A f te r p ro b lem -.
- 39 -
No. I has been worked by th e S ta n d a rd C o n tro l th ro u g h i t s v a rio u s sub­
r o u t i n e s , problem No. 2 i s th e n d e s c rib e d by th e E x ecu tiv e C o n tro l and
s o lv e d .
T his c o n tin u e s u n t i l a l l s t a t e d problem s have been so lv e d .
.
These s u b ro u tin e s in t u r n use th e t a b u l a r d a ta (shown in sq u a re s on
F i g u r e '5 ) t o com plete t h e i r f u n c tio n .
REACH needs th e C - V and th e
c r o s s - s e c t i o n g rap h s t o com plete i t s t a s k .
T h e■c r o s s - s e c ti o n in fo rm a tio n
i s needed w hether OUTPUT is c a ll e d o r n o t .
RNOFFX u ses th e UH and e i t h e r
a d e s ig n o r a c t u a l sto rm P - -t g ra p h .
o f th e t a b u l a r d a ta .
r o u tin g problem .
SAVMOV an d -ADDHYD do n o t ■make use
RESVOR .must c a l l th e s tr u c tu r e d a ta t o perform i t s
All- f iv e o f th e w orking s u b ro u tin e s may have t o c a l l
OUTPUT ( i f s p e c if ie d by s ta n d a rd c o n tr o l) b e fo re r e tu r n in g t o S tan d ard
C o n tro l. S ta n d a rd C o n tro l '
S tan d ard C o n tro l is a n o rd e re d s e t o f in s tr u c t i o n s t o th e com puter
t h a t o u tlin e th e sequence o f o p e ra tio n s t h a t sim u la te ru n o f f from a w a te r­
shed a r ea .
These o p e r a tio n s , which have a lre a d y been o u tlin e d , a re done
by th e s u b ro u tin e s RNOFFX. REGVOR, REACH, ABDHYD, and SAVMOV. . F ig u re ?
shows a sample w a te rsh e d , w ith two r e s e r v o i r s and two main stre a m b ra n c h e s ,
which is su b d iv id e d in to f iv e su b w a te rsh ed s.
A ta b le o f th e c o rre sp o n d ­
in g S ta n d a rd C o n tro l l i s t i n g f o r t h i s sample w atershed i s a l s o g iv e n .
The s tr u c tu r e - a n d c r o s s - s e c t i o n lo c a tio n s a re numbered so t h a t th e re a d e r
can fo llo w th ro u g h th e S ta n d a rd C o n tro l t o see t h a t i t a d e q u a te ly d e s c rib e s
th e way i n which r a i n f a l l e x cess i s c o n v e rte d in to r u n o f f »
There a r e ,
how ever, some assu m p tio n s in t h i s c o n n e c tio n .which' make th e s im u la tio n .
— ij O “
2
Area
S u b ro u tin e
I
II
RNOFFX
RESVOR
REACH
RKOFFX
ADDHYD
III
IV
SAVMOV
RNOFFX
RESVOR
REACH
RNOFFX
ADDHYD
SAVMOV
SAVMOV
ADDHYD
REACH
RNOFFX
V
ADDIIYD
II
Subw atershed a re a
A
S tr u c tu r e lo c a t io n
3--- O
C r o s s - s e c tI on l o c a t i on
-->-
S tream co u rse
____
Subw atershed boundary
IV
C ro ssS e c tio n
S tr u c tu r e
01
01
001
001
001
001
6
7
5
6
7
5
7
02
02
002
002
002
002
002
003
004
004
004
Hydrograph S to rag e
L o catio n s
Input In p u t Output
#2
#1
6
6
7
5
7
I
5
7
6
5
6
6
7
I
6
7
5
6
7
5
6
7
5
6
7
O utput O ptions
Hyd Elev Peak Vol
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
F ig u re 7 •* Sample W atershed w ith C orresponding Standard C o n tro l f o r th e
S o il C o n se rv a tio n S e rv ic e P r o je c t F o rm u latio n Program
i
" 4l "
much e a s i e r w ith o u t-a d d in g s u b s t a n t i a l e r r o r to th e o p e r a tio n .
For
exam ple, th e outflow hydrograph from s t r u c t u r e I i s ro u te d th ro u g h
a re a I I a s i f no a d d i t i o n a l ru n o f f w e re .b e in g su p p lie d from a re a I I .
Now, th e r e e x i s t s an outflow hydrograph from th e ch an n el' re a c h in a re a
I I at- s e c tio n I 0
To t h i s hydrog rap h i s th e n added th e ru n o f f hydrograph
from a re a I I as i f i t h a d ■not a r r iv e d a t s e c tio n I by way o f th e ch an n el
sy stem .
T his assu m p tio n i s , o f c o u rs e , n o t p h y s ic a lly th e case bu t soon
a f t e r le a v in g th e u p stream subw atersh ed s th e c h an n el h y drograph i s very
la r g e compared t o th e l o c a l a re a ru n o f f so t h a t th e e r r o r r e s u l t i n g from
t h i s a ss u m p tio n -is c o n sid e re d s m a ll.
Computer lo c a tio n s f o r hydrograph s to ra g e a re shown on th e ta b le
in c lu d e d in F ig u re 7=
There a re sev en d i f f e r e n t lo c a tio n s su p p lie d where
a l l th e c o o rd in a te s o f p o in ts from a hydrograph can be s bored (up t o 300
p o in ts ).
These p o in ts a re a l l d e s c rib e d by a tim e and d is c h a rg e v a lu e „
A ll s u b ro u tin e s , have an in p u t and an o u tp u t hydrograph .except ADDHYD- which
h as two in p u t and one o u tp u t hydrographs'.
The numbering o f s to ra g e l o ­
c a tio n s- as shown i s s e t and c o n s i s t e n t l y used ex cep t f o r th e SAVMOV sub­
r o u tin e which can th e n be used t o p la c e a hydrograph i n th e c o r r e c t lo c a ­
t i o n f o r .th e su bsequent o p e r a tio n .
This r i g i d numbering system is .u s e d
so t h a t f e w e r 'e r r o r s w i l l be made by a te c h n ic ia n p re p a rin g th e S tan d ard
C o n tro l.
A ll th e p o s s ib le o u tp u t o p tio n s a re a ls o shown in F ig u re 7»
These
in c lu d e p r i n t i n g out a l l th e v a lu e s o f th e hy d ro g rap h , th e co rre sp o n d in g
w a te r s u rfa c e e le v a tio n s , up t o th e t e n h ig h e s t peak d is c h a rg e v a lu e s and
" 42 ”
their times of occurrence, and.the total Volume under the hydrograph
given in three sets of units, cfs-hrs, acre-feet, and. inches of runoff
over the watershed.
O ther in fo rm a tio n th a n t h a t shown must a ls o he s u p p lie d .
Area
i n sq u are m ile s , ru n o f f curve number CN, and tim e o f c o n c e n tra tio n in
hours' must a ls o be g iv e n w ith th e RNOFFX'command.
RESVOR must a ls o know,
th e s u rfa c e e le v a tio n o f th e r e s e r v o i r a t tim e t s 0.
le n g th o f a re a ch
i n f e e t and a r o u tin g c o e f f i c i e n t ' ( i f one is t o he s u p p lie d in stea d of
b e in g c a lc u la te d by th e program ) a re needed t o com plete th e REACH sub­
ro u tin e ,
ADDHYD and SAVMOV a re com plete as shown i n F ig u re 7=
With re g a rd t o th e num bering o f stre a m c h an n el c r o s s -s e c tio n s and
c o n tr o l s t r u c t u r e s , n u m e ric al v a lu e s may be g iv e n in any o rd e r, a lth o u g h
a l o g i c a l s e q u e n tia l o rd e r i s e a s i e r f o r o th e rs t o fo llo w .
However, th e
way in which th e s e numbers a re used i n S ta n d a rd C o n tro l i s v e ry im p o rtan t
as w i l l be se e n when th e use o f th e E xecutive C o n tro l i s e x p la in e d .
The
im p o rta n t th in g t o remember i s t h a t any number used more th a n once must
a p p ea r c o n s e c u tiv e ly in th e S tan d ard C o n tro l l i s t i n g .
s e c tio n 001 i s used a s i t i s in Figure
T hat i s , i f c r o s s -
th e fo u r tim e s t h a t i t appears
must fo llo w one another w ith o u t i n t e r r u p t i o n by o th e r num bers.
E xecutive C o n tro l'
E xecu tiv e C o n tro l i s a s e t o f commands t h a t have th e o v e r - a l l con­
t r o l o f the. com puter s o lu tio n t o s t a t e d h y d ro lo g ic p ro b lem s.
As i n ­
d ic a te d e a r l i e r , each E xecutive C o n tro l d i r e c t i v e s p e c i f i e s th e p ro p e r­
t i e s of th e h y p o th e tic a l o r a c t u a l sto rm t h a t i s t o be ro u te d .
Storm
- 43 ~
p r o p e r tie s accounted f o r in t h i s model in clu d e storm p a tte r n , t o t a l r a in ­
f a l l amount, storm le n g th , and s t a r t in g tim e .
The p r o p e r tie s may vary
f^Ora subw&tdrehod t o eubwaterehsd but are a s e Umadl unifdym over edch in ­
d iv id u a l subw atershed.
The storm p a tte r n i s g e n e r a lly read in to th e computer w ith a dimen­
s io n le s s cum ulative r a i n f a l l amount o rd in ate and a dim ensioned tim e co­
o r d in a te .
However, i t i s p o s s ib le t o read in both co o rd in a tes w ith e it h e r
dim ensioned or d im en sio n less s c a l e s .
The d im en sio n less v a lu e s are th en
transform ed t o dim ensioned v a lu es by s p e c ify in g th e t o t a l r a i n f a l l amount,
th e t o t a l storm le n g th th a t a p p lie s t o th e p a r tic u la r c a s e , or b oth .
This
f l e x i b l e arrangement i s u s e fu l f o r ap p ly in g h y p o th e tic a l storms t o th e
system .
In th e case o f a c tu a l storm s, cum ulative graphs w ith th e c o r r e c t
tim e and p r e c ip it a t io n dim ensions can be read in d i r e c t l y .
INCREM, COMPUT, EEDCMP are a d d itio n a l statem ents used in E xecutive
C ontrol which sim ply are shorthand fo r increm ent, compute, and end o f
com putations, r e s p e c t iv e ly .
They are not su b rou tin es but sim ply cqmmands
th a t are used by th e main program t o carry out th e d e sir e d c o n tr o l s e ­
quences.
Examples o f E xecutive C o n tro l :
tr a te d in Table
tr o l.
II
S e v e r a l example problems are i l l u s ­
t o dem onstrate th e f l e x i b i l i t y o f th e E xecutive Con­
Problem No. I breaks th e w atershed in t o th ree subwatersheds each
r e c e iv in g d if fe r e n t amounts o f r a i n f a l l .
R a in fa ll Table No. I would be
g iv e n in d im en sio n less depth u n its and tim e in hours s in c e th e amount o f
r a i n f a l l i s s p e c if ie d and 1 .0 0 i s g iv e n under r a i n f a l l d u ra tio n .
The
Table I I :
Example o f E xecutive C ontrol on Sample Watershed
R a in f a ll
S ta r tin g
Through
AMC
Prom
Prob Command Hyd
Depth Duration Table
Time
t Sec# S tr . S ee. S t r .
h rs.
( in . ) (h o u r s) (n o . )
h r s.
I
2
HCREM 1 .0
COMPUT
COMPUT
002
COMPUT
ENDCMP
COMPUT
COMPUT
COMPUT
ENDCMP
01
02
0 .0
0 .0
0 .0
4.1 5
3 .5 0
4 .2 9
1 .0 0
1 .0 0
1 .0 0
I
I
I
2
2
2
0.9
004
0 .0
1 .7
4.1 5
3 .5 0
4 .2 9
1 .0 0
1 .0 0
1 .0 0
3
3
3
I
I
I
001
02
004
01
02
002
001
02
3
HCREM 0 .5
COMPUT
COMPUT
ENDCMP
01
02
001
004
0 .0
o .5
1 .0 0
1 .0 0
1 .0 0
1 .0 0
2
2
3
3 .
k
HCREM 1 .0
COMPUT
ENDCMP
01
004
0 .0
4 .5 0
1 .0 0
4
2
01
004
0 .0
3 .0 0
1 .0 0
5
2
5
COMPUT
ENDCMP
,
-
"
a n te c e d e n t m o istu re c o n d itio n ( AW) i s type I I o r norma I „
S ta r t in g tim e
i s g iv e n a s z e ro on a l l subw atersheds,,
Problem No. 2 i s s im ila r .to No. I e x ce p t t h a t sto rm movement is
acco u n ted f o r by v a ry in g th e s t a r t i n g tim e on th e v a rio u s su b w a te rsh ed s. ■
A lso th e storm p a t t e r n i s c o n sid e re d t o be d i f f e r e n t i n shape o r le n g th
a s r a i n f a l l Table No. 3 i s u se d .
The AMC i s ty p e I o r v e ry d ry .
Problem No. 3 i s a n a c t u a l sto rm t h a t i s ta k e n as u n ifo rm in amount
o v er th e e n t i r e w a te rsh e d .
I t s s t a r t i n g tim e .v a rie s f o r two su b areas and
a .new Table (No. 2 ) d e s c rib e s th e sto rm p a tte r n s which i s g iv e n in tr u e
u n its o f in c h es and ho u rs s in c e th e f a c t o r s used f o r r a i n f a l l d ep th and
d u r a tio n a re b o th g iv e n a s u n ity .
Problem s 4 and 5 a re d e s ig n storm s and.
a re uniform ov er th e e n t i r e a re a in r a i n f a l l amount and s t a r t i n g tim e .
The r a i n f a l l d e p th s g iv e n would, co rresp o n d t o some c a lc u la te d d e sig n ■sto rm
amount f o r a g iv e n fre q u e n c y sto rm f o r th e a re a in q u e s tio n .
R a in f a ll
T ables 4 and 5 might be storm p a tte r n s f o r 12 hours and 24 h o u r sto rm s.
A normal AMC would alw ays be assumed fo r- d e s ig n s to rm s .
IH CREM states th e tim e increm en t i n h o u rs t h a t th e com puter should
use in d e v elo p in g th e h y d ro g ra p h s..
COMPUT i n s t r u c t s th e com puter to
compute what i s c a lle d f o r i n S tan d ard C o n tro l betw een th e str u c tu r e ( s ) .
a n d /o r c r o s s - s e c t i o n { s ) in d ic a te d in th e command.
EHBCMP in d ic a te s th e
end of a COMPUT s e r i e s and sends c o n tr o l back to th e b e g in n in g of S tan d ard
C o n tro l t o s t a r t a new ru n o f f problem , b ased on a n o th e r sto rm d e sc rib e d
i n th e E xecutive C o n tro l
C hapter V
PREPARATION OF WATERSHED DATA
The p r e p a r a tio n o f w atersh ed and sto rm d a ta f o r use w ith th e S o il
C o n se rv a tio n S e rv ic e P r o je c t F o rm u la tio n Program (PFP) w i l l now be
d e m o n stra te d .
The example used w i l l be th e Duck Creek W atershed n e a r
Brockway, Montana and th e sto rm o f June 16, 196 $.
F ig u re 8 i s a map
o f th e Duck Creek drainage" showing th e lo c a t io n of r a i n gages and w ater
s ta g e re c o rd e rs c
The stre a m netw ork i s a l s o c l e a r l y s e e n , as is th e su b ­
d iv is io n ^ o f th e w atersh ed i n t o su b w atersh ed s =
The l a r g e s t o f th e f o u r w atersh ed s u n d er stu d y by th e D rainage
'C o r r e la tio n R esearch P r o je c t, Duck Creek (54 square m ile s ) , lo c a te d so u th
of Brockway, Montana, was s e le c te d f o r th e in v e s t ig a ti o n r e p o rte d h e r e in .
I t was chosen f o r s e v e r a l r e a s o n s :
l ) i t s s i z e ; 2 ) th e o ccu rren ce in
1965 o f a ra in -c a u s e d ru n o ff event which ap p eared to be s u i t a b l e f o r
a n a ly s is ; and 3) p a r t i c u l a r i n t e r e s t in t h i s w atersh ed by th e Montana
State- o f f ic e o f th e SCS,
In stru m e n ts i n s t a l l e d a t Duck- Creek by th e
D rainage C o r r e la tio n R esearch P r o je c t in c lu d e th r e e w e ath e r s ta t io n s
which m easure wind v e l o c i t y , a i r and s o i l te m p e ra tu re , and s o i l m o istu re ;
fo u r n o n -re c o rd in g and th r e e c o n tin u o u s -re c o rd in g r a i n g a g es; and two
c o n tin u o u s -re c o rd in g w a te r l e v e l r e c o r d e r s .
One- w a ter l e v e l re c o rd e r is
lo c a te d on th e E ast Fork o f Duck Creek where i t i s c ro s se d by State- High­
way 2 5 3 ,
The o th e r i s lo c a te d on Duck Creek 330 f e e t n o rth o f th e c e n te r
l in e of th e county road betw een s e c tio n s . 11 and 1.4, T17N, R46e .
The PFP i s a g e n e r a liz e d program d e sig n e d t o be used on a wide .
v a r i e t y o f w a te rsh e d s, and is- capable o f p ro c e ss in g many ty p e s o f d a ta .
TVV
Figure 8 :
Duck Creek Watershed
A n a ly sis o f th e Duch Creek w atersh ed d id no t r e q u ir e u t i l i s a t i o n o f a l l
th e program c a p a b i l i t i e s «, • The d a ta s u p p lie d t o th e com puter f o r Duek
Creek r e l a t e t o I ) subw atershed a re a s and ch an n el le n g th s , 2 ) .stagera re a and s ta g e -d is c h a r g e r e l a t i o n s h i p s , 3 ) curve numbers and a n te c e d e n t
m o istu re c o n d itio n s , 4 ) tim e o f c o n c e n tr a tio n , and 5) sto rm d a t a „
These
axe d is c u s s e d in d e t a i l below „■
Subw atershed A reas and Channel Langths
■ For p u rp o ses o f c o n s tr u c tin g a model o f th e Duck Creek ch an n el n e t ­
w ork, th e Duck Creek w atersh ed was su b d iv id e d in to tw e n ty -fo u r su b w ater­
sheds »
The p r o je c te d a r e a , c h an n e l meander le n g th , and th e flo o d p la in •
le n g th were m easured f o r each of th e su b w a te rsh e d s„ ' A reas were d eterm in ed
by p la n im e te rin g a e r i a l photographs' ( s c a l e ;
SCSo
4" a I m i.) su p p lie d by th e
Both meander and flo o d p l a i n le n g th s were measured on th e same
p h o tographs w ith a map and p la n m easure.
S tag e-A rea and S ta g e -D is charge R e la tio n s h ip s
For th e outflow s e c tio n o f each o f th e su b w a te rsh ed s, s ta g e - a r e a a n d ■
s ta g e -d is c h a r g e curves must be s u p p lie d t o th e PFP.
To g e t t h i s i n f o r ­
m ation i t was n e c e s s a ry t o o b ta in c h an n e l c r o s s -s e c tio n s in th e f i e l d a t
tw e n ty -s ix lo c a t io n s .
Frqm th e c r o s s - s e c ti o n su rv ey n o te s , s ta g e - a r e a cu rv es were o b ta in e d
by assum ing t h a t th e w a te r s u rfa c e i s alw ays l a t e r a l l y h o r iz o n ta l.
The s ta g e -d is c h a r g e curve f o r each s e c tio n was c a lc u la te d by th e
.Manning e q u a tio n ;
«31
Q=
lj-C)
<"
ARO'6 6 7 S°"5
(33)
where n is the Fanning roughness coefficient, R the hydraulic radius, and
S the friction slope at that section.
Friction Slope ; Friction slope is taken to be equal to the channel
slope on. Fuck -Creek for several reasons.
First of all, Henderson (1966) states that because of th e steep
slopes usually present in the .upper catchment regions where the runoff
problem exists, bed slope will be the only significant slope term and •
the discharge will be a function of depth alone.
Bed slope can be con­
sidered the significant slope factor for slopes greater than 10 feet per
mile.
.. "
Furthermore, the cross-sections on Duck Creek are taken at an average
of two miles apart. .Also, there are many variations in cross-section
shape between any two measured cross-sections.
Therefore,-the actual
friction slops could be expected to deviate from the average bed slope
throughout the channel reach.
The difference between the average friction
slope and the average "bed slope, however, would be expected to be very
small.
Zone of Transit ion:
The stage-discharge curves used are a combina­
tion of curves based on different assumptions„
The channel slope used for
lower flows, where the flow is confined to the main channel, is the slope
of the channel bed.
For very large.flows covering the flood plain and
•flowing at depths greater'than the vegetation height, the effective slope
" 50 ^
i s t h a t o f th e flo o d p l a i n .
The im portance o f t h i s c o n sid e ra tio n o f
slo p e i s a p p a re n t when th e r a t i o o f meander le n g th t o flo o d p l a i n le n g th
i s h ig h ; as i t i s on low er p o rtio n s o f Duck Creek where i t re a c h e s a
v a lu e of tw o.
A t r a n s i t i o n zone e x i s t s in which th e e f f e c t iv e slo p e v a r ie s b e­
tw een th e ch an n el' bed and' flo o d ' p l a i n s lo p e s (shown in F ig u re 9)«
This ■
t r a n s i t i o n would be d i f f i c u l t t o s im u la te w ith o u t e x te n s iv e knowledge of
th e w a te rsh e d .
T h e re fo re , in t h i s s tu d y th e s ta g e -d is c h a rg e , curve i s a
f u n c tio n o f th e c h an n e l b e d 's lo p e u n t i l a p p ro x im a te ly one f o o t o f w a ter
i s flo w in g on th e flo o d p la i n ; above t h i s d e p th th e f lo o d p l a i n slo p e is
c o n sid e re d e f f e c t i v e .
pfenning1s Rough n ess C o e f f i c i e n t :
The v a lu e s of M anning's roughness
c o e f f i c i e n t "n" were s e le c te d u sin g a number o f photo g rap h s o f ch an n el
s e c tio n s f o r which "n" had been c a lc u la te d by V. Tt Chow (1 9 5 0 ).
These
were compared w ith photographs- o f Duck Creek t o d eterm in e th e "n" v alu e
-used f o r th e v a rio u s c h a n n e l re a c h e s o f Duck C reek.
An a tte m p t was made t o check t h i s d e te rm in a tio n w ith a s e t o f U. S.
G e o lo g ic a l Survey (USGS) s te r e o s c o p ic c o lo r s lid e s t h a t have been used
f o r roughness c o e f f i c i e n t d e te rm in a tio n s f o r t h a t o r g a n iz a tio n .
U nfor­
t u n a t e l y , th e s e t o f s l i d e s viewed d id no t in c lu d e exam ples -sim ila r t o
th o s e found on Duck C reek.
One f u r t h e r com parison was made■in an a tte m p t t o e v a lu a te th e
e f f e c t i v e roughness o f Duck C reek.
T his method was d ev elo p ed by Cowan
(1956). and can be summarized w ith th e fo llo w in g r e l a t i o n s h i p :
-
5.1
-
Above t h i s d e p th flo o d p l a i n le n g th e f f e c t i v e
:
T r a n s itio n Zone
—.'
/
Belov? t h i s d e p th c h an n e l meander le n g th e f f e c t i v e
T y p ic a l Stream Channel C ro s s -s e c tio n
Flood. P la in le n g th
T y p ic a l P lan View o f M eandering Stream
F ig u re 9 :
T y p ic a l P la n View and C ro s s -s e c tio n of a M eandering Stream
T
52
-
n r (D0 -Kii1 + ng >
n3 + n^)n^
(34)
where n i s th e d e s ir e d roughness c o e f f i c i e n t t o be used in i n n i n g 's
fo rn m la c
n0 , H1 , rig,
and n^ a re the f r a c t i o n a l v a lu e s o f n d e t e r ­
mined r e s p e c tiv e ly by ty p e o f c h an n el bed and s id e s lo p e m a te r ia l, e f f e c t
of s u rfa c e i r r e g u l a r i t i e s , v a r i a t i o n i n shape and s iz e of c r o s s - s e c t! o n ,
e f f e c t o f o b s tr u c tio n , and v e g e ta tio n c o n d itio n s „
n r i s a m u ltip ly in g
c o r r e c t io n f a c t o r and i s a f u n c tio n o f th e r a t i o of meander le n g th to .
f l o o d .p l a i n le n g th f o r any g iv e n re a c h of c h a n n e l,
Tlie roughness c o e f­
f i c i e n t . g iv e n by t h i s method i s l a r g e r th a n th o se d eterm in ed by phot,O^
g rap h co m p ariso n s„
The-, problem connected w ith ph o to g rap h view ing f o r "n" d e te rm in a tio n s
i s t h a t e f f e c t of m eandering cannot g e n e r a lly be d e term in e d .
I f one is
u sin g th e ch an n el meander le n g th on s lo p e d e te rm in a tio n s th e n th e "n"
v a lu e found i s p ro b a b ly c o r r e c t .
However, i f th e flo o d , p l a i n le n g th 'is
b e in g used (w hich i s th e case f o r overbank flo o d flo w s ) "n" must be a d ­
ju s te d f o r th e degree o f m eandering0
' For th e in -c h a n n e l flow c o n d itio n , "n" was d eterm in ed a s d is c u s s e d
a b o v e»
The,m eander c h an n e l slo p e was used f o r t h i s c o n d itio n .
Hqwsyer,
f o r th e overbank flow c o n d itio n , "n" on th e flo o d p l a i n was determined by
p re v io u s ly e x p la in e d methods and was h ig h e r th a n th e c h an n e l ”n" used f o r
th e in -c h a n n e l c o n d itio n .
a s te e p e r o n e.'
The slo p e f o r th e overbank flow i s , of c o u rs e ,
"n" was ta k e n t o be 0.005 h ig h e r f o r th e main ch an n el
p o r ti o n o f th e c r o s s - s e c t i o n th a n f o r th e overbank flow c a s e .
This is
- 53 -
done t o a cco u n t f o r th e f a c t t h a t much o f th e flow in th e a re a of th e
c h an n e l i s a c t u a l l y fo llo w in g th e chann el.
This is more c o n v en ien t th a n
assum ing t h a t th e c h a n n e l p o r ti o n o f th e flow is a c tin g on a m ild e r s lo p e .
H y d ra u lic E a d iu s ?
O ften th e c r o s s - s e c ti o n of a n a t u r a l stre a m i s so
i r r e g u l a r t h a t th e Manning e q u a tio n cannot be c o n v e n ie n tly a p p lie d t o th e
c r o s s - s e c t i o n a s a w hole.
For th e w a te r s u rfa c e e le v a tio n s where th e flow
i s i n t r a n s i t i o n betw een c h a n n e l and flo o d p l a i n flo w , n e ith e r th e w e tted
p e rim e te r P n o r th e h y d ra u lic r a d iu s B a c c u r a te ly r e p r e s e n ts the- a c tu a l
c o n d itio n .
An a l t e r n a t e way t o express- t h i s id ea is t o say t h a t th e ex­
ponent on R does n o t ' e q u a l O.667 i n th e t r a n s i t i o n zo n e.
T nis i s e s ­
p e c i a l l y tr u e i f th e main c h an n e l i s deep and th e flo o d p l a i n is q u ite
fla t.
To a l l e v i a t e t h i s problem , th e c r o s s - s e c t i o n a l a re a can be broken
up in to s e v e r a l p o r tio n s making th e p o r tio n d iv is io n s a t th e sh arp b reak s
i n th e s e c tio n .
Computer S o lu tio n of M anning1s E q u a tio n ;
A com puter program was
w r i t t e n by th e a u th o r in th e F o r tra n I I language f o r th e IBM 1620 com­
p u te r (Appendix D) t o so lv e M anning's .E q u atio n f o r Q a t a g iv e n c ro s s s e c tio n f o r a l l d ep th s (by o n e -fo o t in c re m e n ts ) betw een s p e c if ie d l i m i t s ,
■ Where th e c r o s s - s e c t i o n i s ir r e g u la r - , th e program f i r s t - computes
a re a and w e tte d p e rim e te r 'fo r each p o r tio n of th e c r o s s - s e c t i o n .
s
.
s t a g e “d is c h a rg e in form ation i s th e n p r in t e d out f o r t h a t p o r tio n .
The
Tne
same c a lc u la tio n s a re made -and p r in t e d ou t f o r a l l th e p o r tio n s of a
p a r tic u la r c ro s s -s e c tio n .
F i n a l l y , th e s ta g e -d is c h a rg e v a lu e s f o r a l l
p o r tio n s a re summed up and p r in t e d out a s th e s ta g e -d is c h a r g e r e l a t i o n s h i p
” 54 - .
valid for the whole cross-section.
This summary information is then
used as input to the PFP0
T e s tin g th e R e l i a b i l i t y o f Manning1s E q u atio n ;
The r e l i a b i l i t y o f
M anning1s e q u a tio n and o f th e com puter program was t e s t e d by comparing
th e s ta g e -d is c h a r g e r a t i n g cu rv es w i t h .th o s e which have been developed
by th e USGS f o r th e E ast Fork (F ig u re 1 0 ) o f Duck Creek and f o r Duck
Creek (F ig u re .1 1 ) .
The r a t i n g curve f o r th e E ast Fork was developed f o r
th e same lo c a t io n ( p r e v io u s ly d e s c rib e d ) used in t h i s s tu d y . ■The r a tin g curve f o r Duck Creek as developed by th e .USGS i s b a se d .o n t h e i r s t a f f
gage lo c a te d a t th e b rid g e where Duck Creek flow s under th e county road
betw een s e c tio n s 11 and 14, T17N, R46e .
The Montana S ta te U n iv e rs ity
s ta g e re c o r d e r was o r i g i n a l l y p la c e d a t t h i s same lo c a tio n b u t was moved
i n Ju n e, 1964 to a p o in t 330 f e e t n o rth (downstream ) of. th e county road
c e n te rlin e .
Ttie o ld r a t i n g curve does no t now a p p ly t o th e new lo c a tio n
o f th e MSU s ta g e re c o r d e r and s in c e t h i s p a p er in c lu d e s a s tu d y o f th e
ru n o f f ev en t o f June l 6 , 1965 a new r a t i n g curve had t o be d ev elo p ed .
Flow has been, measured on three occasions by the USGS since the re­
corder on'Duck Creek was moved.
Two of these measurements were made in
the spring when the flow was over an iced channel.
Therefore, an accurate
rating curve cannot be drawn based on actual measurements.
Tb was 'de­
termined that t h e .Manning equation gave a sufficiently accurate rating
curve. ■ This was done by comparing the actual and calculated rating curves
at the recorder on the East Fork,
At -this location, the rating curve
given by M nnin g 's equation fell n ea rly .on top of the best visually fitted
Based on
Itenning's Equation
3/ 10/66
3/ 26/ 59^
1
^
USGS Bating Curve
° \ ^ 6/ 6/64
10
100
D isc h a rg e ( c f s )
1000
I d e n o tes flow
o v er ic e
C o rre c ted USGS valu<
6/ l 6/ 65x
/
Duck Creek R atin g Curve
O utside Gage R eading ( f e e t )
F ig u re 11:
NBU - p re v io u s r a t i n g curve
(new gage lo c a t io n )
6/ 16/65
O rig in a l USGS v a lu e
USGS r a t i n g curve
( s t a f f gage lo c a t io n )
3 /1 3 /6 6
u p re n t r a t i n g curve b ased on Nfenning1s E quation
I
10
100
D isch arg e ( c f s )
1000
- 57 -
lin e through p o in ts measured by the USGS.
Since t h is i s tr u e , i t may
be assumed th a t th e r a tin g curve fo r Duck Creek c a lc u la te d by th e Manning
v a l e t iofcehig should be adequate fbV purposes o f t h is stu d y .
As a lrea d y s t a t e d , two d if f e r e n t slo p e s have bean u t i l i z e d fo r
d evelop in g r a tin g curves u sin g Manning's eq u a tio n , depending on whether
th e flow i s m ainly in -ch a n n el or on th e flo o d p la in .
In th e former c a s e ,
th e le n g th o f th e main channel c e n te r lin e or th e meander le n g th was used
t o determ ine th e bed s lo p e .
th e flo o d p la in was u sed .
In the l a t t e r c a s e , however, th e le n g th o f
This le n g th is o f course sh o r te r than th e meander
le n g th g iv in g th e flo o d p la in a g r e a te r slo p e than th e main ch an n el.
In
th e case o f Duck Creek, th e average r a t io o f meander t o flo o d p la in le n g th
i s about I . 8 9 .
Curve Numbers and A ntecedent Mfoisture C ondition
As shown in Chapter I I I , th e s o il- c o v e r complex number (CN) p lays a
v i t a l r o le in th e SCS method o f determ ining r u n o ff.
A com posite CN must
be c a lc u la te d fo r a w atershed i f more th an one s o i l typ e or cover con­
d it io n e x i s t s .
The curve numbers used by th e SCS f o r v a rio u s com binations
o f s o i l and cover c o n d itio n s are g iv e n in Appendix C.
■ A com posite CN was c a lc u la te d f o r each o f th e 2 k subwatersheds on th e
Duck Creek w atershed.
The method used t o compute t h i s com posite i s shown
below and i s summarized in Table I I I . ' F ir s t i t was determ ined what th e CN
would be i f th e whole subwatershed c o n s is te d o f one s o i l ty p e .
This was
done on a w eighted b a s is accordin g t o th e p ercen tages o f a cres f a l l i n g in
th e vario u s cover c l a s s e s .
This was done fo r each s o i l typ e (types B and
-
Table I I I :
(I)
(S)
58
-
C a lc u la tio n o f Composite Curve Number
on a Sample Subwatershed
(3)
(4)
(5).
(6)
(7)
$ Of
Column
$ o f area
S o il
Cover
Curve Number
Type C ondition from Appendix C t o t a l area (3) % (4) o f s o i l , type (5) x (6)
B
S tr ip
' farming
Range
80.5*
69
21.4
78.6 .
17.2
54.2
CN i f a l l type B s o i l . . . .
C
S tr ip
farming
Range
87*
21.4
78.6
79
CN i f a l l type C s o i l . . . .
29.3
20.9
70.7
57.0
18.6
62.0
Composite CN (rounded t o n ea rest whole number)
=
78
*An average o f CN's fo r fa llo w and sm a ll g r a in (s tr a ig h t row in good
h y d ro lo g ic c o n d itio n ) cover c o n d itio n c l a s s e s .
“ 59 ”
C were th e o nly ty p e s o c c u rrin g on Duck C reek ),
The w eighted CH's o b ta in e d f o r each s o i l ty p e in d iv id u a lly a re
th e n a g a in w eighted w ith re g a rd t o th e p e rc e n ta g e s o f a re a w ith in each
su bw atershed t h a t f a l l in to th e v a rio u s s o i l g ro u p s,
Tiris method of
f ig u r in g a com posite CN is b ased on th e assu m p tio n t h a t th e v a rio u s s o i l
ty p e p e rc e n ta g e s used occur i n th o s e same p e rc e n ta g e s on each o f v a rio u s
c o v er c o n d itio n groups u se d .
I f t h i s i s n o t tr u e , s i g n i f i c a n t e r r o r s i n
CN c a l c u l a t i o n co u ld o c c u r.
I t i s f e l t t h a t such an e r r o r would not be
N
im p o rtan t i n th e case o f Duck Creek s in c e i n n e a r ly a l l su b w atersh ed s,
one s o i l ty p e o r co v er c o n d itio n was p re d o m in a n t„
When t h i s i s not t r u e ,
i t i s n e c e s sa ry t o c a lc u la te th e w eighted CN f o r each su b area o f each
su b w a te rsh ed , whereupon th e breakdown o f s o i l ty p e s f o r each .'subarea would
have t o be d e te rm in e d .
C reek,
T his d e t a i l was no t c o n sid e re d n e c e s sa ry on Duck
.-
The d e te rm in a tio n of CN from Appendix C, which i s b ased on an av erag e
a n te c e d e n t m o istu re c o n d itio n (AMC)> i s in p u t t o th e PFP,
A lso , th e
a c t u a l AMC i s d e te rm in e d , as d e s c rib e d in C hapter I I I , and re a d in to th e
PFP,
The a d ju stm en t of CN is i n t e r n a l t o th e PFP.
For th e storm o f June
,16, 1965 on Duck C reek, th e AMC was d eterm in ed t o be d ry (Type I ) ,
Time of Concentration
The tim e o f c o n c e n tra tio n f o r any g iv e n ch an n el re a c h i s ta k e n to
be. th e tim e o f t r a v e l f o r f u l l bank flow c o n d itio n s ,
The v e lo c i ty f o r
f u l l bank flow i s d eterm in ed by Manning’s e q u a tio n a t b o th ends of th e
c h an n e l re a c h , ' T ra v e l tim e is th e n g iv e n by .the f o l l o w i n g 'r e l a t i o n s h i p :
t = __
V1 + V2
(35 )
L i s th e re a c h le n g th in f e e t , V1 and V2 a re th e v e l o c i t i e s a t th e i n ­
flow and outflo w s e c tio n s o f th e c h an n e l re a c h and t is th e t r a v e l tim e
th ro u g h th e re a c h .
In th e case where th e re a c h in q u e s tio n i s betw een
a stre a m c ro s s s e c tio n and th e boundary o f th e w a tersh e d , v e lo c i ty i s
ta k e n t o be z e ro a t th e boundary.
These tim e s a re th e n added down th ro u g h
th e w atersh ed t o f in d th e w atersh ed la g tim e (tim e betw een c e n te rs o f TJiass
o f th e ra in s to rm and th e outflo w h y d ro g ra p h ) f o r th e w a te rsh e d .
When t h i s
c a l c u l a t i o n does not m atch th e a c t u a l la g tim e as observ ed from outflow
h y d ro g ra p h s, each re a c h t r a v e l tim e must be a d ju s te d by p r o p o r tio n a l
m u l t i p l i c a t i o n so t h a t th e a c t u a l la g tim e i s o b ta in e d .
The tim e o f con­
c e n t r a t i o n f o r each in d iv id u a l sub w atersh ed i s th e n ta k e n t o be a p o r tio n
o f th e stre a m f u ll- b a n k flow tim e p lu s o v e rla n d and t r i b u t a r y ch an n el
flow tim e s .
The co m b in atio n o f main stre a m and s id e c h an n e l t r a v e l tim es'
t h a t i s lo n g e s t, i s ta k e n t o be th e tim e o f c o n c e n tra tio n f o r th e sub­
w a te rsh e d .
The t r i b u t a r y c h a n n e l t r a v e l tim e s were based on th e v e lo c ity of
two o r th r e e f e e t p e r second a t th e mouth and zero a t th e h ead .
These
two v e l o c i t i e s and. th e le n g th o f th e t r i b u t a r y ch an n el a re th e n s u f f i c i e n t
t o g iv e th e tim e o f t r a v e l as g iv en by e q u a tio n (3 5 ),
This i s an a p p ro x i­
mate method b u t s u f f i c i e n t l y a c c u ra te on the. Buck Creek subw atersheds b e ­
cause th e y a re c h a r a c t e r i s t i c a l l y lo n g and narrow.
The t r i b u t a r y ch an n el
" 6l .tim es o f t r a v e l were s h o r t compared t o th e mala c h an n e l t r a v e l tim e s .
For s h o r t e r , w id er subw atersheds th e d e te rm in a tio n o f tim e o f t r a v e l
and tim e o f c o n c e n tr a tio n would need more s c r u t i n y , ■f o r th e s id e ch an n el
tim e s would c o n s t i t u t e l a r g e r p e rc e n ta g e s o f th e t o t a l tim e s .
Storm E ata
1
Both a c t u a l and d e s ig n storm s can be handled by th e PFP=,
The -ra in ­
f a l l amount is alw ays re a d in as e i t h e r th e a c t u a l amount from some storm
o r th e d e sig n r a i n f a l l amount a s d i c t a t e d by some d e s ig n c r i t e r i a .
p a t t e r n o f an a c t u a l sto rm can be ta k e n i n t o a c c o u n t„
The
For in s ta n c e , when
th e w a te r s h e d 'is broken down in to s e v e r a l su b w atersh ed s a d i f f e r e n t r a i n ­
f a l l amount can be d e s ig n a te d f o r each w a te rsh e d .
a ls o be acco u n ted f o r i n a c t u a l s to rm s.
Temporal v a r ia tio n s ' can
The s t a r t i n g tim e o f th e r a i n ­
f a l l can be d i f f e r e n t f o r each su b w atersh ed .
'
Rainfall patterns can be read into the program as cumulative dimen­
sionless graphs or graphs with the actual time and rainfall amounts as
abscissa and ordinate, respectively.
As many as nine different patterns
can be used in any one run of the computer program.
The amount o f r a i n f a l l f a l l i n g on each of th e 24 subw atersheds on
Duck Creek was d eterm in ed by th e T h ie sse n Method..
The T h ie sse n polygon
was drawn f o r the seven r a i n gages on o r n e a r th e w atershed.
With t h i s
method th e r a i n f a l l over the e n t i r e T h ie sse n su b area i s c o n sid e re d t o be
u n iform and e q u a l.i n v a lu e t o th e amount re c o rd ed a t th e gage which gen­
e r a l l y f a l l s i n th e c e n te r o f th e polygon i f th e gages a re e q u a lly sp aced .
As would be e x p e c te d , some o f th e su b w atersh ed s f a l l i n two o r th re e ' of
•" 62 ™
th e T h ie sse n p o ly g o n s, i n which case th e r a i n f a l l amount i s a w eighted
amount b ased on th e p e rc e n ta g e s o f a re a f a l l i n g in each o f th e p o ly g o n s„
F o r tu n a te ly , th e edges o f th e polygons f a l l c lo s e t o th e rid g e b e ­
tw een th e East and West Forks o f Duck C reekj t h i s e lim in a te s th e l a r g e s t
c r i t i c i s m o f th e T h ie sse n method which says t h a t th e method does no t ta k e
i n t o acco u n t g e o g ra p h ic f e a t u r e s „
Storm movement was ta k e n in to acco u n t by v a ry in g th e s t a r t i n g tim e
f o r each o f th e su b w a te rsh e d s.
The speed o f th e sto rm was determ ined by
e x am in atio n o f th e re c o rd s o f th e th r e e co n tin u o u s re c o rd in g r a i n gages.
The tim e f o r movement of. th e storm a c r o s s th e w atersh ed was found t o be
about 3 .5 hours f o r th e sto rm of June 16, 1965.
The s t a r t i n g tim es f o r
th e v a rio u s subw atersheds w e re 'th e n d eterm in ed t o th e n e a r e s t 0 .1 hour by
v i s u a l l y d e te rm in in g th e r e l a t i v e p o s itio n s o f t h e i r c e n tr o id s .
Summary
The amount o f and k in d s o f d a ta s u p p lie d t o th e PFP v a ry from w a te r­
shed t o w a te rsh e d .
Not a l l ty p e s o f d a ta t h a t could be p ro c e sse d by th e
program need be - used in e v ery w atersh ed model developed f o r th e computer
s o lu t i o n .
For exam ple, a lth o u g h th e r e a re a number o f s m a ll sto c k pond
r e s e r v o i r s on Duck Creek w a te rsh e d , t h e i r e f f e c t is f e l t t o be m inor, and
th e r e f o r e th e model does not in c lu d e any r e s e r v o i r in fo rm a tio n .
s u p p lie d t o PFP has been d is c u s s e d i n t h i s c h a p te r.
The d a ta
-With t h i s in fo rm a tio n ,
th e PFP is cap ab le o f c a lc u la tin g th e ru n o f f hydrograph from Duck Creek
based on th e u s u a l SCS h y d ro lo g ic fo rm u las and p ro c e d u re s .
C h ap ter VI
ACTUAL AUD HYPOTHETICAL STOHtS
The a c t u a l storm, o f June l 6 , 1965 on Duck Creek was used to
a d ju s t a r a i n f a l l - r u n o f f model o f th e w atershed.
Then h y p o th e tic a l
storms based on U0 S. W eather B ureau fre q u e n c y d a ta were ro u te d th ro u g h
th e modal t o p r e d ic t peak d is c h a r g e s ,■
A c tu al-S to rm o f June 16, 1965
The a c t u a l sto rm used f o r model a d ju stm e n t on Duck Creek has
h e r e to f o r e been c a ll e d th e sto rm o f June 16, 1965.
The r e s u l t i n g peak
d is c h a rg e a c t u a l l y o c c u rre d on t h i s d a te , a lth o u g h th e sto rm i n q u e stio n
s t a r t e d a t about 6 a.m . on June 13 and l a s t e d u n t i l ab o u t 4_a , m .,..June 16
f o r a t o t a l d u r a tio n o f rJO hours = These tim e s a re av erag e tim es as th e
sto rm ' had s l i g h t l y v a ry in g d u ra tio n s as i t moved a c ro s s th e w a tersh e d .
The m a jo rity o f r a i n f a l l o c cu rred d u rin g th r e e main b u r s ts a p p ro x i­
m ately a day a p a r t .
The d u r a tio n of th e b u r s ts were a p p ro x im a te ly 3 , I ,
and 6 h o u rs ,
F ig u re 12 shows th e a r e a l d i s t r i b u t i o n o f th e t o t a l amount o f r a i n ­
f a l l in th e form o f a n is o h y e t a l map„
This i s based on th e re c o rd s from
a t o t a l o f sev en r a i n gages on o r n e a r th e w a te rsh e d .
The sto rm moved g e n e r a lly in a n o rth w e s te r ly d i r e c t i o n down th e
w a te rs h e d ’s main c h a n n e l.
An i n d ic a tio n o f th e storm movement was ob­
ta in e d by s tu d y in g re c o rd s o f tim e v e rs u s cum ulative r a i n f a l l amount byp e rc e n ta g e f o r two o f th e th r e e co n tin u o u s re c o rd in g r a i n g a g e s.
These
in d ic a te d t h a t th e d if f e r e n c e i n tim e a t th e two re c o rd e r p o in ts a t which
th e same p e rc e n ta g e s o f t o t a l sto rm amount had o c c u rre d was ab o u t two
— 64 —
F ig u re 12: I s o h y e ta l M p of Juna l 6 , 1965 Storm on Buck Creek M te rs h s d
“ 65 "
h o u rs„
This was approxim ately tr u e f o r a l l th r e e b u r s ts so t h a t one
sto rm p a t t e r n was assumed t o be ad eq u ate f o r a l l o f th e subw atersheds.
Assuming t h a t th e sto rm tr a v e le d a t a c o n s ta n t r a t e o f sp e e d , th e 2»0
h o u r d if f e r e n c e in tim e o f sto rm b e g in n in g betw een th e c o n tin u o u s r e ­
c o rd in g .p o in ts becomes -3°5 hours from th e a r e a l c e n tr o id s o f th e two
most w id ely s e p a ra te d su b w a te rsh e d s.
Hyppthetleal Storms
Storm d u ra tio n s o f .12 and 24 h o u rs were chosen a r b i t r a r i l y f o r
th e purpose o f u sin g th e SGS method t o p r e d ic t peak d is c h a r g e s .
R ain­
f a l l am ounts ro u te d f o r b o th d u ra tio n s were i n 0 .5 in c h in crem en ts and
over a range such t h a t 5? 10, 2 5 , 50, and 1 0 0 -y ear fre q u e n c y storm s would,
be in c lu d e d .
These amounts a re th o s e p r e d ic te d by th e W eather Bureau in
t h e i r T e c h n ic a l Paper Ho. 40 a s p re p a re d by David H e r s h f ie ld ' (196.1).
T h e re fo re , f o r .12-h o u r s to rm s, p r e c i p i t a t i o n P o f 2 .0 , 2 .5 , 3,„0, 3 .5 ,
and 4 .0 in c h e s j and 24-h o u r storm s w ith a P o f 2 .0 , 2 .5 , 3 .0 , 3 .5 , 4 .0 ,
and 4 .5 in c h es were ro u te d . The tim e o f storm b e g in n in g was ta k e n t o be c o n s ta n t on a l l sub­
w a tersh e d s s in c e th e r e i s l i t t l e
in fo rm a tio n on th e d i r e c t i o n of p ro - .
dom inant sto rm movement on Duck C reek.
I f a c o n s is te n t p a t t e r n o f sto rm
movement was known i n th e case o f a p a r tic u la r .w a te r s h e d , than.som e v a rie d
tim e o f sto rm b e g in n in g could be assum ed, even f o r h y p o t h e t i c a l ' sto rm s ».
A lso , th e t o t a l amount, o f . r a i n f a l l must be assumed t o be c o n sta n t
on a l l subw atersheds u n le s s th e r e i s in fo rm a tio n in d ic a tin g t h a t th e _
sto rm c e n te r f o r most known a c t u a l storm s i s c o n s is te n tly lo c a te d i n one
-
66
-
p o r tio n o f th e w a te rsh e d „■ Such in fo rm a tio n is not known f o r Duck Creek.
T h e re fo re ^ r a i n f a l l amounts were c o n sid e re d t o be s p a t i a l l y in v a r i a n t . •
The e f f e c t o f th e lo c a t io n o f sto rm c e n te r s co u ld be s tu d ie d > however,
by c e n te r in g storm s i n v a rio u s p a r ts o f th e w atersh ed and com paring th e
c a lc u la te d outflow h ydrograph r e s u l t s .
A c tu a l R unoff Hydrograph
The a c t u a l ru n o f f hydrograp h f o r th e sto rm of June 16, 1965 is
shown in F ig u re 13.
T his hydrograph had been developed by p re v io u s i n ­
v e s t i g a t o r s based on th e b e s t d e te rm in a tio n o f th e r a t i n g curve in e f f e c t
at- the- new s tre a m s ta g e re c o rd e r- lo c a t i o n .
The volume o f r u n o f f -a sso c i­
a te d w ith t h i s curve i s 0 ,4 3 in ch es f o r th e 54 square m ile Duck Creek
w a te rsh e d .
A f te r t h i s s tu d y was w e ll under way i t was d is c o v e r e d ,th a t two
e r r o r s had been com m itted in th e r e d u c tio n o f th e c o n tin u o u s s ta g s r e ­
c o rd e r d a ta .
The f i r s t , made by s tu d e n ts w orking on th e D rainage C o rre­
l a t i o n Research. P r o je c t, was t h a t th e volume p re v io u s ly c a lc u la te d was
- in e r r o r .
in c h e s ,
The r e s u l t i n g y ie ld sh o u ld have been 0 ,28 in s te a d of th e 0,43
The second e r r o r was made by th e U, S. G e o lo g ic a l Survey in
t h e i r p u b lic a tio n s .
The peak s ta g e p r in t e d f o r th e June l6., 1965 storm--
was 4,74 f e e t which g iv e s a peak o f 870 c fs based on t h e i r r a t i n g cu rv e
f o r Duck C reek ,
The s ta g e v a lu e should h a v e 'b e e n 2 ,8 8 fe e t.w h ic h g iv e s a
peak o f 340 c fs in s te a d .
Since th e o r i g i n a l r a t i n g curve f o r th e new
lo c a t io n was based p r im a r ily on t h i s one storm , it, i s now in v a lid .
:1000
Bassd on p re v io u s r a t i n g curve
Based on c u rre n t r a t i n g curve
- .6 8
-
The author has developed* another r a tin g curve based on th e Manning
Equation, t h is being j u s t i f i e d fo r reasons d escrib ed in Chapter V.
two p o in ts are Known on th e r a tin g cu rv e.
Only-
One i s the stortii being t e s t e d
and th e o th er i s th e e le v a t io n or sta g e a t which th e flow i s a ero ,
A
r a tin g curve was drawn through th e se two p o in ts based on th e lfenning
Equation.
The ru n off hydrograph was ag a in drawn based on th e new r a tin g
cu rve, and i s a ls o shown in Figure 13.
The o rd in a tes o f t h i s p lo t were
read in to a computer program w r itte n by Gary Lewis t o determ ine the y i e l d .
The y ie ld now b e lie v e d c o rr e ct fo r th e June l 6 , 19&5 storm on Duck C reek.
i s 0 .3 5 in c h e s.
Computer Runs Completed
A number o f runs or storm ro u tin g s were made on two d if f e r e n t occa­
s io n s .
These runs are summarized in Table IV.
Runs I-A through I-M and 2 -A through 2-M are id e n t ic a l except fo r
th e curve numbers (CN) u sed .
The number I runs make use o f a s e t of
CN1s o r ig in a lly thought t o be th o se in e f f e c t on Duck Creek.
For the
number 2 runs, each CN o f the s e t was reduced by th e value o f th r e e .
The A and B runs (both numbers I and 2 ) caused th e June 16, 1965
storm t o be routed through th e Duck Creek m odel.
The o n ly d iffe r e n c e
between A and B i s th e assum ption made about th e tim e o f th e storm 's
b eg in n in g .
Runs C through M are f o r h y p o th e tic a l storm s.
Runs C t o H are
*With a s s is ta n c e from Gary le w is , graduate stud en t a t Montana S ta te .
U n iv e r sity working towards an M. S. Degree in C iv il E ngineering.
-
Table IV:
69
-
Summary o f Computer Runs Completed
Antecedent
Run Date Type o f Amount D uration Time o f
Moisture
( i n . ) (h o u r s) Storm 's
Storm
of
B eginning C ondition
run
I-A 10/
B 25/
. C 6?
D
E
F
G
H
I
J
K
L
M
A ctual Varied
A ctual Varied
Hypo4 .5
4 .0
th e tical
3 .5
3 .0
2 .5
2 .0
• 4 .0
3 .5
3 .0
2 .5
2 .0
70
70
24
2 -A l l /
B 27/
C 67
D
E
F
G
H
I
J
K
L
M
A ctu al Varied
A ctual Varied
Hypo4 .5
4 .0
th e tical
3 .5
3 .0
2 .5
2 .0
4 .0
3 .5
3 .0
2 .5
2 .0
70
70
24
Curve
MTumtier
CN
Varied
Constant
Constant
Dry
Dry
Average
O r ig in a lly
determined
from Appendix
C f o r each
subwatershed
Varied
Constant
Constant
Dry
Dry
Average
CN now th ree
l e s s than
th o se fo r runs
I-A t o I-M
12
12
i
*“ 7 0 "
2 4 -h o u r d u r a tio n storm s w ith v a r ia b le r a i n f a l l am ounts, w h ile I t o M
a re 12-hou r d u r a tio n storm s w ith v a r ia b le r a i n f a l l am ounts»
C h a p te r V II
RESULTS
The d a ta a v a il a b le on th e sto rm o f June l 6 , 1965 on the' Duck
Creek w atersh ed was used t o s e t up th e com puter model f o r a n a ly s is by
th e S o il C o n se rv a tio n S e rv ic e - P r o je c t F o rm u latio n Program (SCS-PFP)0 '
Two s e t s o f com puter ru n s were made by th e SCS in B y a t t s v i l l e } Maryland
on an. IBM 360/40 e l e c t r o n i c com puter.
A c tu a l Storm E v a lu a tio n
' The i n i t i a l ru n gave a ' t o t a l w a tersh e d y ie ld o f 0,5 7 in c h e s .
This
was h ig h e r th a n th e a c t u a l y ie ld m easured a t th e stre a m gage which was
0 ,3 5 in c h e s .
However, a t th e tim e th e com puter ru n s were made th e a c t u a l
y ie ld was th o u g h t t o be 0.43 in ch es (due t o p re v io u s ly e x p la in e d e r r o r ) .
The model w a s ■i n i t i a l l y s e t up by e v a lu a tin g th e s o il- c o v e r com­
p le x numbers (CU) th o u g h t t o be th o s e in e f f e c t on Duck C reek.
These
a re b ased on th e c h a r t used by th e SCS (se e Appendix C o f t h i s p a p e r ).
The p ro ced u re used by th e SCS i s t o c h e c k . th e y ie ld f o r th e o r i g i n a l l y
d eterm in ed s e t o f CN 's.
The CNt S a re th e n a d ju s te d u n t i l th e c a lc u la te d
y ie ld e q u a ls th e a c t u a l y i e l d .
This i s c o n sid e re d t o be th e c a lc u la te d
ru n o f f hydrograph which can now be compared t o an a c t u a l ru n o ff hy d ro graph i f i t i s a v a i l a b l e .
In a n e f f o r t t o c o r r e c t th e y ie ld t o 0.4 3 in c h es (th o u g h t a t th e
tim e t o have been th e a c t u a l y i e l d ) th e a u th o r red u ced th e CN's fora l l su b w a te rsh e d s'b y a v a lu e o f th r e e and th e second s e t o f computer
ru n s was made.
Ttie r e s u l t i n g output, was hydrographs h av in g y ie ld s e x ­
a c t l y e q u a l t o 0,43 in c h e s .
■
-7 2 Computer Ees n I t s ;
F ig u re 14 shows th e a c t u a l ru n o f f hydrograph
f o r th e June l 6 , 1965 sto rm , p o in ts in d ic a tin g th e computed hydrograph
p e a k s , and two hydrographs which have been p o s tu la te d on th e b a s is -o f
th e b e s t evidence a v a i l a b l e .
Hie a c t u a l hydrograph a s measured has
a lo w e r, lo n g e r p r o f i l e th a n th e c a lc u la te d h y d ro g rap h s.
The c a l - ■
c u la te d hydrographs have h ig h peaks and s te e p e r r e c e s s io n lim b s ,
The f o u r i s o l a t e d p o in ts shown on F ig u re 14 a re th e. h ig h e s t peak
d is c h a rg e s c a lc u la te d by th e com puter ru n s I-A , 1-B, 2 -A, and 2 -B .., The
f i r s t runs,- each w ith a y i e l d o f 0.57 in c h e s , a re in d ic a te d by th e two
h ig h e s t p o in ts (l-A a-nd 1 -B ).
The h ig h e r o f th e s e (I-A ) i s f o r th e case
where the- tim e o f sto rm b e g in n in g was assumed t o vary from one subw a tersh e d t o th e n e x t.
c.fso
This hydrograph has a peak d is c h a rg e o f l4 l6
The lower, o f th e two (l- B ) w ith a d is c h a rg e of 1245 c fs i s based
on th e a ssu m p tio n t h a t th e s t a r t i n g tim e was th e same f o r a l l subwater-.sheds«
The l a t e r com puter ru n s w ith re d u c e d -c u rv e number v a lu e s r e ­
duced th e y i e l d t o 0.43 in c h e s , and th e peaks (2-A and 2-B ) t o 1144 and
.1006 c fs r e s p e c t i v e l y .
A gain th e h ig h e r peak was fo r th e case of th e
v a r ia b le sto rm b e g in n in g .
.The two hydrographs shown in t h e i r com plete form on F ig u re 14 have
b e en p o s tu la te d by th e a u th o r , and are b ased on th e r e s u l t s o f th e l a s t
com puter r u n s .
Each of th e s e hydrographs has a y ie ld of 0.35' in c h e s ,
m atching th e . y i e l d o f th e a c t u a l h y d ro g rap h .
t o th o s e o f th e l a t e r com puter ru n s .
T h e ir shapes a re i d e n t i c a l
I f f u r t h e r com puter ru n s should be
made w ith low er CN v a lu e s , • i t i s e x p ec te d t h a t th e shapes o f -th e .h y d ro -
5
I
Peak d is c h a rg e v a lu e s from
i
-5T-
1500
I-A
i>
:a
1400
I-B
I
:1300
2—
A
1:200
2 -B
S
Y ield = 0.5 7 V arious
Equal
Y ield = 0.43 V arious
Equal
■l
11
:5
I^
I
I
IE
.
graphs might change slightly.
Comparison of, the complete hydrographs
of the four computer runs which were made indicates that the change in
shape would, not be great, however,
As can be seen, there is a large discrepancy between the calculated
and actual hydrographs with regard to peak.
The SCS states-that the
method was not designed to match the hydrograph in shape but only in
peak value.
However, in this case, the calculated peak is either 2,41
■or 2,74 times as great as the actual peak depending on which assumption
is used for the time of storm beginning on each subwatershed,' The rami"'
fications of these results will be discussed in Chapter 7111,
Hypothetical Storm Evaluation
One purpose of this study was to predict flood peaks for various'
frequencies.
This was accomplished by routing a number of hypothetical
storms through the watershed model to determine the peak discharge pre­
The final results of this portion' o f the work
dicted by the SCS method.
is summarized in Figure
1
5
,
Of course no actual storms have occurred: by
.which these discharges can be compared.
Figure
'
1 5
is tentative and should not be used for design purposes.
I t i s shown h e re o n ly a s a d e m o n stra tio n o f how th e SCS--PFP r e s u l t s of
r o u tin g o f h y p o th e tic a l' storm s can be used in c o n ju n ctio n , w ith th e 'U, S , '
W eather B ureau fre q u e n c y d a ta t o p r e d ic t peak d is c h a rg e s from sm all w afer
sheds.
The two cu rv es marked WB ( f o r W eather B ureau) a re p lo ts of ex­
p e c te d p r e c i p i t a t i o n P v e rs u s th e r e t u r n p e rio d in y e a rs (a b s c is s a .scale
a t th e bottom o f th e g ra p h ) f o r th e sto rm o f m agnitude P f o r b o th 24-
- 75 -
Peak D ischarge qp
O
1000
2000
3000
4000
WB - 2k hour
WB - 12 h our -x „
^
DC - 12 hour
-DC - P.k hour
R etu rn P e rio d (Y e a rs)
F ig u re 15:
Exanple o f Peak D ischarge D esign C hart
Y(5 w>
and 12-h o u r storm s a s i n d i c a t e d 0
The o th e r two curves marked DC (f o r
Duck C reek) show th e p l o t s o f P v e rs u s peak d is c h a rg e qp (a b s c is s a
s c a le a t th e to p o f th e g ra p h ) f o r th e Duck Creek w a tersh e d a s d e t e r ­
mined by th e com puter model u sin g SCS hydro.logic d e sig n c r i t e r i a f o r
th e same two sto rm d u r a tio n s.
These two cu rv es re p re s e n t th e model as
s e t up f o r th e l a t e r com puter ru n s (n o t a s y e t ad ju sted as e a r l i e r ex ­
p la in e d and th u s n o t s u i t a b l e f o r d e s ig n u s e ) .
I f a d d i t i o n a l adjustm ent,
o f th e model co u ld be made, th e same p ro ced u re a s d e s c rib e d h e re would
be a p p lic a b le i n s e t t i n g up a s im ila r s e t o f curves f o r use i n d e s ig n .
I f F ig u re I 5 were t o be used f o r d e s ig n , th e fo llo w in g pro ced u re
sh o u ld he fo llo w e d t o p r o p e r ly p r e d ic t th e peak d is c h a rg e f o r a sto rm .
G e n e ra lly , s t r u c t u r e s on a w atersh ed a re h y d r a u lic a l ly d e sig n e d t o fu n c ­
t i o n p ro p e r ly f o r some peak d is c h a rg e caused by a s to rm -o f a p a r t i c u l a r
fre q u e n c y o r r e t u r n p e r io d .
Suppose f o r an exam ple, as shown on F ig u re-
15, we p la n t o d e s ig n a c u lv e r t t h a t w i l l h an d le a 50-y e a r freq u en cy
sto rm o f a d u r a tio n o f 2b h o u rs .
The p ro ced u re is t o s t a r t a t th e ' bottom
o f F ig u re 15 w ith th e 50-y e a r sto rm and p ro ceed v e r t i c a l l y a lo n g th e l in e
shown u n t i l th e VJB-24 h our curve i s m et,
Then i f th e o r d in a te P i s re a d ,
we f i n d t h a t th e W eather B ureau p r e d ic ts t h a t .th e p r e c i p i t a t i o n i s 3=715
in c h e s f o r a 50-y e a r - 24-h o u r d u r a tio n storm , . I f however, w.e. fo llo w a ■'
h o r i z o n t a l l i n e ( to th e r i g h t i n t h i s exam ple) u n t i l we meet th e d i s ­
charge f o r a 24-hour sto rm fo r . Duck C reek, and th e n p ro ceed v e r t i c a l l y ,
we f i n d t h a t qp - 3200 c f s ,
On th e o th e r h and, i f th e peak d is c h a rg e f o r a ru n o f f ev en t had been
- 77 -
m easured on Buck C reek, th e e x a c t o p p o s ite pro ced u re t o t h a t d e s ­
c rib e d in th e p re v io u s p a ra g ra p h , co u ld be fo llo w e d t o d eterm in e th e
fre q u e n c y o r r e t u r n p e rio d o f t h a t storm=
Chapter V III
D isc u ssio n
The in v e s t ig a ti o n d e s c rib e d in th e p re c e d in g c h a p te rs has been
o f two ty p e s .
F i r s t , a model o f Duck Creek w atersh ed was developed
and th e n t e s t e d by u s in g , as in p u t d a ta t o th e com puter program , i n ­
fo rm a tio n d e s c rib in g an a c t u a l sto rm which o ccu rred on th e w atershed
on June 16, 1965.
The r e s u l t i n g s y n th e tic hydrograph g e n e ra te d by th e
program was compared w ith th e a c t u a l hydrograph re c o rd ed a t th e mouth o f
th e w a te rsh e d .
program r e - r u n .
The model was a d ju s te d , a f t e r i n i t i a l com parison, and th e
Second, th e Duck Creek model was used t o p r e d ic t th e
hydrograph from c e r t a i n d e s ig n -ty p e storm s based on W eather Bureau sto rm
fre q u e n c y d a ta .
The Storm o f June l 6, 1965
The r e s u l t s from th e com puter ru n s f o r th e June 16, 1965 storm do
n o t compare v e ry c lo s e ly w ith th e a c t u a l h y drograph re c o rd e d f o r th e
e v e n t.
The d is c re p a n c y i s th o u g h t t o be m ainly th e r e s u l t o f im per­
f e c t i o n s i n th e m odel, b u t th e r e i s , how ever, a p o s s i b i l i t y t h a t th e
a c tu a l- hydrograph i s not e n t i r e l y c o r r e c t .
The peak d is c h a rg e t h a t
a c t u a l l y o c c u rre d i s f e l t t o be a c c u r a te ly known, because i t was d e­
te rm in e d from th e USGS r a t i n g curve f o r t h e i r c r e s t - s t a g e g a g e.
This
r a t i n g curve i s based on t e n c u rre n t m eter measurements o v e r a p e rio d
o f a t l e a s t t e n y e a r s . ' Except f o r th e peak d is c h a rg e , th e r e s t of th e
a c t u a l hydrograph was d eterm in ed by r e l a t i n g depths re c o rd e d a t th e
w a te r l e v e l re c o rd e r t o d is c h a rg e s .
As has been m entioned e a r l i e r , th e
w a te r l e v e l re c o rd e r i s lo c a te d s e v e r a l hundred f e e t dow nstream on Duck
- 79 -
Creek from th e c r e s t - s t a g e g ag e, and th e s ta g e -d is c h a r g e r e la tio n s h ip s
f o r th e two s t a t i o n s a re q u ite d i f f e r e n t .
The b e s t r a t i n g curve a v a i l ­
a b le a t th e w a te r l e v e l re c o r d e r u ses M anning's e q u a tio n and is drawn
th ro u g h o n ly two known p o i n t s .
P o s s ib le im p e rfe c tio n s i n th e model seem to f a l l i n one o f th e
fo llo w in g c a te g o r ie s :
I ) p r e p a r a tio n o f th e in p u t d a ta and 2 ) th e SCS
m ethod.
P r e p a ra tio n o f th e In p u t D r ta :
When one i s d e a lin g w ith hy­
d ro lo g ic problem s th e s i t u a t i o n n ev er o ccu rs t h a t th e r e i s a n over
s u f f ic ie n c y o f d a ta a v a i l a b l e .
There i s alw ays a l i m i t a t i o n on th e
tim e -d e p e n d en t d a ta a v a i l a b l e , and an economic l i m i t a t i o n on th e t h o r ­
oughness w ith which th e w a tersh e d p a ra m e te rs can be o b ta in e d .- A r a t h e r
s i g n i f i c a n t amount o f w a tersh e d d a ta were o b ta in e d f o r th e s tu d y r e ­
p o rte d h e r e in , in c lu d in g th e r e s u l t s o f a medium i n t e n s i t y s o i l su rv e y ,
numerous i n f i l t r a t i o n t e s t s , a com plete s t a d i a - l e v e l su rv e y o f th e
p r i n c i p a l s tre a m s , and more th a n 20 c h a n n e l c r o s s - s e c ti o n s u rv e y s.
It
would seem t h a t th e w a tersh e d p a ra m ete rs were d e lin e a te d , th e r e f o r e ,
more c o m p le te ly th a n co u ld be ex p ected in th e t y p i c a l s m a ll w atersh ed
d e s ig n i n v e s t i g a t i o n .
R e s u lts - o f th e s tu d y show t h a t even t h i s p r e ­
c i s i o n may n o t be ad eq u ate t o in s u re g r e a t acc u ra cy in d u p lic a tio n o f
a n a c t u a l h y d ro g rap h .
The way i n which v a rio u s w atersh ed c h a r a c t e r i s t i c s were u t i l i z e d
w i l l be d is c u s s e d below .
" 8o —
The curve num bers.(CE) which, a re used in th e SCS program t o c h a ra c ­
t e r i z e s o i l ty p e and lan d use tre a tm e n t were developed from la rg e quan­
t i t i e s o f d a ta which were o b ta in e d from a l l p a r t s o f th e U nited S t a t e s „
S in ce th e y r e p r e s e n t av erag e c o n d itio n s , and were no t developed s p e c i­
f i c a l l y f o r Montana, i t seems l i k e l y t h a t use o f th e CN t a b l e in Appendix
C may be re s p o n s ib le f o r some o f th e d is c re p a n c y in th e r e s u l t s .
In
p a r t i c u l a r , i t seems t h a t th e a d ju stm en t which is made f o r d ry a n te c e d e n t
m o istu re c o n d itio n s (ty p e I ) may not be la r g e enough.
I t may be t h a t
f o r Montana w a te rsh e d s, th e a d ju stm en t betw een av erag e and d ry c o n d itio n s
sh o u ld be l a r g e r th a n t h a t used n a tio n w id e »
Tbe CN's used in th e f i r s t s e t o f com puter ru n s were a d ju s te d f o r
th e second s e t o f runs, by re d u c in g each number by a v alu e o f t h r e e .
This
r e d u c tio n t h e o r e t i c a l l y sh o u ld have been p r o p o r tio n a l t o th e o r ig i n a l v a lu e
o f each CN f o r each su b w atersh ed .
I t i s u n c e r ta in what th e e f f e c t o f r e ­
d ucing i n e q u a l in s te a d o f p r o p o r tio n a l amounts might b e .
There are- in d ic a tio n s t h a t th e tim in g o f th e ru n o f f in th e model
was in e r r o r .
T his seems t o be e s p e c ia ll y tr u e in th e case of th e h ig h ­
e s t peak shown on F ig u re I h 0 As can be seen from th e main p o r tio n of th e
a c t u a l h y d ro g rap h , l e s s e r peaks o c cu rred b o th b e fo re and a f t e r th e m axi­
mum d is c h a r g e .
The c a lc u la te d hydrographs seem to have grouped a l l th r e e
peaks in to one.and c o n se q u e n tly gave to o h ig h an e s tim a te f o r th e maxi­
mum. d is c h a r g e , . The f a c t o r t h a t c o n tr o ls th e tim in g on th e model i s th e .
tim e o f c o n c e n tra tio n w hich i s ' d eterm in ed f o r each su b w a te rsh ed .
As -
'm en tio n ed e a r l i e r , on ly one time, of c o n c e n tra tio n can be s u p p lie d f o r
-
8 .1
-
each su b w a te rsh ed ; and th e r e f o r e no v a r i a t i o n can be assumed i n t h i s
tim e f o r d i f f e r e n t d is c h a r g e s „
The tim e o f c o n c e n tra tio n can be shown
t o v a ry w ith r a te o f d is c h a rg e so t h a t th is.b e c o m e s a li m i t i n g f a c t o r
i n th e c o n s tr u c tio n o f th e m odel.
The tim e s of. c o n c e n tra tio n f o r t h i s
s tu d y were based on v e l o c i t i e s as c a lc u la te d by th e Manning r e l a t i o n s h i p
f o r f u l l bank flo w .
The a c t u a l ev en t in 1965, produced l i t t l e
o r no
flo o d in g ;- i t seems p ro b a b le th e r e f o r e t h a t th e ch an n els were le s s th a n
b a n k f u ll most o f th e tim e .
'The t r u e v e l o c i t i e s were p ro b a b ly le s s th a n
th o s e c a lc u la te d , and th e tim e s o f c o n c e n tr a tio n la r g e r th a n t h o s e ' c a l ­
c u la t e d .
This seems - li k e ly t o acco u n t f o r th e f a c t t h a t th e c a lc u la te d
•peaks o ccu r a t tim e s e a r l i e r th a n th e o b serv ed p e a k s.
The SCS M ethod:
The SCS method was developed b e fo re e le c tr o n i c com­
p u te r s cou ld be u t i l i z e d t o so lv e such problem s and th e r e f o r e had to -b e
sim p ly c o n s tr u c te d so t h a t i t co u ld be so lv ed by h an d . . And as i s tr u e of
a l l methods developed f o r p r e d ic tin g peak d is c h a rg e s , th e SCS method is
based on many a ss u m p tio n s .
Assum ptions a re made e i t h e r because i t i s
th o u g h t t h a t th e y w i l l n o t g r e a t l y a f f e c t th e s o lu tio n o r because th e y
must be made t o make th e s o l u tio n e co n o m ica lly p o s s ib le .
Many tim es in
s o lv in g -h y d ro lo g ic p ro b lem s, assu m p tio n s must be made because: th e re , i s a
s c a r c i t y of in fo rm a tio n a v a i l a b l e , even though i t i s re c o g n iz e d t h a t th e s e
assu m p tio n s may s i g n i f i c a n t l y a f f e c t th e s o lu tio n .
The SCS m ethod. can be th o u g h t o f ,a s a m a th e m a tic a l.g ra p h ic model
which c o n s is ts o f a number o f fo rm u lae and g ra p h s.
A lthough some f l e x i ­
b i l i t y has been b u i l t in to th e o p e r a tio n - o f th e FFP, i t a p p e a rs t h a t th e
"
82
“
SCS method has not been b a s i c a l l y a l t e r e d in th e c o n v e rsio n in to a com­
p u te r m odel.
The q u e s tio n t h a t th e n a r i s e s i s w hether th e b a s ic method
i t s e l f co u ld now be ma.de more f l e x i b l e f o r com puter s o l u t i o n s ,
P oint's i n th e model t h a t seem t o be to o r i g i d a r e :
l) in itia l
a b s t r a c t i o n , 2 ) la g tim e , 3 ) s y n th e t ic u n it hydrograph sh a p e , 4 ) sto rm
p a t t e r n , and 5) th e r e s e r v o i r and flo o d r o u tin g m ethods,
Tlie i n i t i a l a b s t r a c t i o n I a i s assumed t o be e q u a l t o 0*2 S and th e
la g tim e t o be e q u a l t o 0 ,6 o f th e tim e of c o n c e n tr a tio n .
The c o e f f i ­
c ie n t s o f 0 ,2 and 0 ,6 a r e c e r t a i n l y f o r th e average c o n d itio n s f o r a
.number of w a tersh e d s t h a t were s tu d ie d by th e SOS,
The. raw d a ta from
which th e s e c o e f f i c i e n t s were d eterm in ed a re no t g iv en in th e SOS's
N a tio n a l E n g in ee rin g Handbook (MEH),
I f th e s e d a ta had b een s u p p lie d , i t
m ight be p o s s ib le t o choose more n e a r ly c o r r e c t f a c to r s f o r a s p e c if ic
a re a .
A lso , th e NEH d e fin e s o n ly one s y n th e tic hydrograph sh a p e , which i s
in te n d e d t o be used i n a l l c a s e s .
The PFP, however, i s cap ab le of a b so rb ­
in g any u n it h y drograph t h a t th e u s e r w ishes t o su p p ly .
From t h i s , i t
would s e e m .th a t t h e ' SCS method as o u tlin e d i n th e NEH is more r e s t r i c t i v e
th a n i s n e c e s s a ry now t h a t th e more f l e x i b l e computer program s a re a v a i l ­
ab le..
Only' two p o s s ib le storm ' p a tte r n s a re g iv e n by th e SCS f o r use in
t e s t i n g h y p o th e tic a l sto rm s .
The p a t t e r n most commonly used (shown in
F ig u re 5) is one i n which th e m i n b u r s t o f .th e storm comes a t about th e
m idpoint o f th e sto rm i n tim e ,
Tiie o th e r has th e main sto rm b u r s t come
“ 83 ~
e a r l i e r i n th e sto rm .
Again, th e PFP, b e in g .a b le t o accommodate any
sto rm p a t t e r n sh a p e , i s more f l e x i b l e th a n th e method d e s c rib e d by th e
scs.
The KSH s u g g e s ts s e v e r a l methods o f flo o d ro u tin g which 'may be u sed .
Only two o f t h e s e , how ever, have been in c o rp o ra te d in to th e computer p ro ­
gram,
The convex method i s th e o n ly p ro ced u re f o r c h an n e l flo o d ro u tin g
a v a i l a b l e , and th e s t o r a g e - i n d i c a t i o n method i s th e o n ly p ro ced u re f o r
r e s e r v o i r flo o d r o u tin g a v a i l a b l e ,
rI h ase a re methods which a re e a s i l y
a d a p ta b le t o manual s o lu tio n and p erh ap s -were chosen f o r t h i s re a s o n .
P o s s ib ly , o th e r methods would be more r e a l i s t i c and as e a s i l y handled by
th e com puter.
By s im ply ad d in g o th e r r o u tin g s u b r o u tin e s , th e o v e r a ll
com puter model could be made more f l e x i b l e .
D esign- Type Storms
'
An example o f d e s ig n p e a k .d is c h a rg e .d e te rm in a tio n b ased on freq u e n cy .
of storm .w as g iv e n in C hapter V II and needs no f u r t h e r a m p lif ic a tio n h e r e .
I t m ight be p o in te d o u t, how ever, t h a t th e .accuracy w ith which th e peak
d is c h a rg e o f a h y p o th e tic a l storm can be p r e d ic te d c an , be no b e t t e r th a n
th e a c c u ra c y of th e d e te r m in a tio n o f th e amount of r a i n f a l l t o be ex ­
p e c te d in any g iv e n lo c a t io n f o r th e sto rm freq u en cy ch o sen .
The hydrographs which were d eterm in ed f o r d e sig n storms, should b.o
c o n sid e re d only, f o r t h e i r q u a l i t a t i v e meaning and not t h e i r q u a n tita tiv e
re s u lts .
The re a so n f o r t h i s , , o f c o u rs e , i s t h a t th e model o f th e w a te r­
shed w a s.n o t th o ro u g h ly a d ju s te d i n th e sen se d e s c rib e d i n C hapter I I I , F u r th e r a d ju stm e n ts in th e model o r w atersh ed p a ram eters co u ld now be
- 84 ~
made q u ite r e a d i l y .
With a s a t i s f a c t o r i l y a d ju s te d model a v a i l a b l e , th e
h y p o th e tic a l storm s could be ro u te d th ro u g h ,th e model' once more, and d e ­
s ig n hydrographs would be th e re b y o b ta in ed ,
As f u r t h e r ru n o f f ev en ts
o ccu r on Duck C reek, i t may become p o s s ib le t o d eterm in e how th e ru n o ff
p a t t e r n changes w ith s iz e o f sto rm ; t h i s would p erm it m o d ific a tio n s to
be made t o th e w a tersh e d m odel, which co u ld th e n a g a in be s u b je c te d t o
th e h y p o th e tic a l s to rm s , and s t i l l more d e f i n i t i v e r e s u l t s o b ta in e d .
Program Use by Monta n a S ta te Highway Departm ent
The r e s u l t s o f th e s tu d y in d ic a te t h a t b e fo re t h e ' Montana S ta te
Highway Departm ent co u ld r e l i a b l y use th e SCS method o f p r e d ic tin g p ro ­
b a b le peak d is c h a rg e from Montana w atersheds-, a long ran g e stu d y and
c o l l e c t i o n of d a ta would, f i r s t be n e c e s s a ry .
B efore th e SCS method co u ld
be a p p lie d , maps lo c a tin g s o i l ty p e s and la n d use on th e w a te rsh e d , or
a s in g le map d e lin e a tin g th e s o il- c o v e r complex numbers (CM) on th e w a te r­
sh ed , would have t o be made a v a i l a b l e „
lan d use maps co u ld be drawn
l a r g e l y w ith th e use o f a e r i a l p h o to g rap h s and a m inim al f ir s th a n d know­
ledge o f th e lo c a t io n in v o lv e d .
H ydrologic s o i l ty p e s can p r e s e n tly be
d eterm in ed i n many a re a s i n Montana from e x is t in g d a ta from SCS s o i l
su rv e y s.-
However, la rg e s e c tio n s o f Montana have no t y e t been su rv ey ed .'
T herefore,,, a com plete s o i l ty p e map f o r th e s t a t e , co u ld n o t now be com­
p ile d .
For p r e d ic tio n o f a design" peak d is c h a rg e from a p a r t i c u l a r w a te rsh e d ,
a d d i t i o n a l d a ta would have t o "be c o l l e c t e d .
Areas of subw atersheds and
c h a n n e l re a c h le n g th s co u ld be measured from a e r i a l p h o to g rap h s i f th e y
" 85 “
were a v a il a b le f o r th e w atersh ed in q u e stio n ,,
n e c e s s a ry t o d eterm in e c h an n e l c r o s s - s e c t i o n s „
F ie ld su rv ey s would be
Channel be.d s lo p e s would
a l s o have t o be d eterm in ed in th e f i e l d u n le s s s u ita b le to p o g ra p h ic maps
were a v a i l a b l e „
The jy&nning rou g h n ess c o e f f i c i e n t co u ld be d eterm in ed by
in s p e c tin g th e a re a o r by view ing p h o to g rap h s o f th e channel*
Fbntana S ta te U n iv e rs ity i s p r e s e n tly i n s t a l l i n g a t h ir d - g e n e r a tio n
com puter, th e SIB Sigma. Y, which w i l l be .capable of ru n n in g th e c u rre n t
(1967) v e r s io n of th e SCS-PFP w ith a few m o d ific a tio n s *
U n fo rtu n a te ly ,
th e Sigma 7 was not a v a il a b le d u rin g th e .tim e of t h i s s tu d y , and i t was
n o t f e a s i b l e t o make -more th a n th e two s e ts o f ru n s p re v io u s ly .described*
To e f f e c t i v e l y make use o f such a program , th e h y d ro lo g is t sh o u ld have
e asy a c c e ss t o th e computer- because o f th e s e v e r a l t r i a l s which seem t o
be n e c e s s a ry in a d ju stm e n t and use o f a m odel.
In summary, th e SCS method r e q u ir e s c o l l e c t i o n o f a re a so n a b ly la r g e
amount o f d a ta .
I t has n o t been p o s s ib le , w ith th e d a ta -which, were a v a i l ­
a b le f o r t h i s s tu d y , t o e v a lu a te th e SCS method t o d eterm in e w hether such ■
amounts o f d a ta c o l l e c t i o n a re j u s t i f i e d .
Chapter IX
CONCLUSIONS
The i n v e s t ig a ti o n r e p o rte d h e r e in has been a stu d y o f th e SCS
method
o f p r e d ic tin g peak d is c h a rg e flow r a t e s from ra in -c a u s e d storm s
on- s m a ll w atersheds*
Data f o r one a c t u a l sto rm which o c c u rre d on Duck
Creek in P r a i r i e and MeCone C o u n tie s, Montana, to g e th e r w ith s e v e r a l
h y p o th e tic a l storm s f o r th e same w a te rsh e d , were p ro c e sse d by a com­
p u te r iz e d s o lu tio n o f th e SCS m ethod„
The r e s u l t i n g s y n th e tic hydro-
g rap h f o r th e a c t u a l sto rm was compared w ith th e a c t u a l hydrograph which
was re c o rd ed f o r th e event*
F in d in g s from th e s tu d y le a d t o th e fo llo w in g c o n c lu s io n s ;
1 - The SCS method i s a s y s te m a tic , lo g i c a l l y o rg a n iz ed p rocedure
w hich g e n e ra te s a s y n th e tic hydrograph .fo r a sm all w atershed*'
Tb
u t i l i z e s d a ta c h a r a c te r iz in g th e c a u s a tiv e ra in s to rm , w atersh ed p a ra ­
m eters , and a c c e p te d flo o d ro u tin g te c h n iq u e s «
The method has been
e f f e c t i v e l y programmed by th e SCS f o r com puter s o lu tio n .
2 - Comparison o f th e s y n th e tic hydrograph g e n e ra te d by th e com puter,
program f o r th e storm on June 16, 1965 on Duck Creek w ith th e a c tu a l
hydrograph w hich was re c o rd e d f o r th e same e v e n t, shows c o n s id e ra b le d i s ­
crepancy*
This i s th o u g h t t o be p r im a r ily caused by u sin g im proper v a lu e s
f o r w atersh ed p a ra m e te rs and f lo o d .r o u tin g c o e f f ic ie n ts , a s in p u t t o th e
com puter program*
A lte r n a tiv e f a c t o r s which may e x p la in p a r t o f th e d i s ­
c re p an c y in c lu d e th e p o s s i b i l i t y t h a t th e a c t u a l hydrograph f o r th e ev en t
may not be e n t i r e l y a c c u r a te , and th e p o s s i b i l i t y t h a t c e r t a i n ta b le s and
g raphs u t i l i z e d by th e SCS method may not r e f l e c t th e p ro p e r v a lu e s which
»" 87 “
sh ould be used i n Montana. •
3
■-
- S u c c e s s fu l use o f th e SCS method r e q u ir e s c a r e f u l d e f i n i t i o n of
w atersh ed p a ra m ete rs and flo o d ro u tin g c o e f f i c i e n t s .
VJhen a s a t i s f a c t o r y
model is f i n a l l y o b ta in e d , th e method r e p r e s e n ts a v e ry e f f e c t i v e , ra p id
method f o r d e te rm in in g peak flow r a t e s t o be ex p ected from an a c tu a l or
h y p o th e tic a l sto rm .
'
C h a p te r X
RECOMMENDATIONS AND .SUMMARY
S ince th e mode3. o f Dnck Creek w atersh ed has now been c o n s tru c te d
and p a r t i a l l y a d j u s t e d . f u r t h e r a d ju stm en t should be made as more, ru n ­
o f f e v e n ts occur on Duck Creek.
A lso , when a d d itio n a l d is c h a rg e m easure­
ments a re made by th e USGS, th e r e l i a b i l i t y o f th e p re s e n t r a t i n g curve
a t th e Montana S ta te U n iv e r s ity r e c o r d e r on Duck Creek sh o u ld be ch eck ed •
Mode.ls of o th e r Montana, w atersh ed s should be c o n s tru c te d t o a s c e r ­
t a i n th e v a r i a b i l i t y i n ru n o ff c h a r a c t e r i s t i c s among them .
Duck Creek
may not be r e p r e s e n ta tiv e o f e a s te r n Montana w atersh ed s f o r some u n fo re ­
se e n re a s o n s .
Thus, w ith o th e r models a v a i l a b l e , th e e r r o r s in d e sig n
sto rm peak d is c h a rg e p r e d ic tio n s would be d im in ish e d .
■ A nother a re a o f p o t e n t i a l stu d y would be th e t e s t i n g o f th e v a rio u s
f a c e t s o f th e SCS m ethod.
Since th e p re s e n t program i s b ased la r g e ly on
th e method used b e fo re th e adven t o f th e d i g i t a l com puter program , th e r e
a re components of th e method t h a t co u ld be more s o p h is tic a te d w ith o u t,
making -the problem s o lu tio n more d i f f i c u l t .
I t would a p p e a r th a t th e syn
t h e t i c hydrograph shape could be made more f l e x i b l e t o acco u n t f o r d i f ­
fe re n c e s i n a r e a , shape of w a te rsh e d , c lim a tic c o n d itio n and lo c a tio n .
C a lc u la tio n of th e t h e o r e t i c a l tim e o f c o n c e n tra tio n and la g tim e needs
f u r t h e r study.,
The im portance o f s y n th e s iz in g th e tim in g of ru n o ff has.
been shown by th e example used h e r e in .
In o rd e r t o make f u r t h e r s tu d y b o th e a s i e r and more p r o f i t a b l e , th e
SCS-PFP sh ould be a l t e r e d s l i g h t l y f o r use on th e new d i g i t a l computer
p r e s e n tly bein g i n s t a l l e d a t Montana S ta te U n iv e rs ity .
Summary
P r e d ic t io n o f th e peak d isch a rg e o f a r a in -c a u se d r u n o f f . event from
a w atershed by th e method d ev elo p ed by th e SCS has been d is c u s s e d .
The
developm ent o f t h i s method was o u t lin e d t-n Chapter I I I ,
More r e c e n t ly th e method has been programmed f o r use w ith an e l e c ­
t r o n ic com puter,
A d e s c r ip t io n o f t h i s program and an e x p la n a tio n o f i t s
o p e r a tio n i s found in Chapter IV,
The a b i l i t y o f th e SCS method t o a c c u r a te ly p r e d ic t peak d isch a rg e
was p a r t i a l l y t e s t e d w ith use o f th e com puter.
The model o f th e Duck-
Creek w atershed was c o n str u c te d and was su b je c te d t o th e storm o f June 1 6 ,
1965,
A lthough th e t e s t run i s not s u f f i c i e n t t o e v a lu a te th e p r e d ic tin g
a b i l i t y o f th e program, th e model i s now a v a ila b le f o r Duck Creek and can
be fu r th e r a d ju ste d by t e s t i n g o th er sto rm s.
APPENDIX
S o lu tio n o f Runoff Equation
D ir e c t R unoff (Q) in Inches
R a in fa ll (P) in Inches
- 92 APPENDIX B
H yd rologic S o i l Types
A.
(low r u n o ff p o t e n t i a l ) . S o i l s h avin g h ig h i n f i l t r a t i o n r a te s
even when th o ro u g h ly w etted and c o n s is t in g c h i e f l y o f d eep , w e ll
t o e x c e s s iv e ly d ra in ed sands or g r a v e ls . These s o i l s have a h igh
r a te o f w ater tr a n s m is s io n .
B.
S o i l s h avin g moderate i n f i l t r a t i o n r a t e s when th o ro u g h ly w etted and
c o n s is t in g c h i e f l y o f m od erately deep t o deep, m od erately w e ll t o
w e ll d rain ed s o i l s w ith m od erately f in e t o m oderately co a rse t e x ­
tu r e s . These s o i l s have a moderate r a te o f w ater tr a n s m is s io n .
C.
S o i l s h avin g slow i n f i l t r a t i o n r a t e s when th o ro u g h ly w etted and con ­
s i s t i n g c h i e f l y o f s o i l s w ith a la y e r th a t impedes downward move­
ment o f w a te r , or s o i l s w ith m o d era tely f in e t o f in e t e x t u r e . These
s o i l s have a slow r a te o f w ater tr a n s m is s io n .
D.
(High r u n o ff p o t e n t i a l ) . S o i l s h avin g v ery slow i n f i l t r a t i o n r a te s
when th o ro u g h ly w etted and c o n s is t in g c h i e f l y o f c la y s o i l s w ith a
h ig h s w e llin g p o t e n t i a l , s o i l s , w ith a permanent h ig h w ater t a b l e ,
s o i l s w ith a cla y p a n or c la y la y e r a t or near th e s u r f a c e , and
sh a llo w s o i l s over n e a r ly im pervious m a te r ia l. These s o i l s have a
v e r y slow r a te o f w ater tr a n s m is s io n .
-
93
-
APPENDIX C
Runoff curve numbers fo r hyd rologic s o i l - cover complexes
(Antecedent m oisture co n d itio n I I , and Ia = 0 .2 S )
Cover
land Use
Treatm ent
or p r a c t ic e
S tr a ig h t row
Fallow
Row crops
M
Tl
Contoured
If
Contoured & Terraced
Il
It
S tr a ig h t row
S m all
g r a in
Contoured
'
Contoured & Terraced
*•
C lo se -se e d e d S tr a ig h t row
legum es l /
Contoured
or
r o t a t io n
Ifeadow Contoured & Terraced
I!
It
It
11
It
P astu re
or range
Contoured
ft
11
Meadow
Woods
H yd rologic s o i l group
A
B
C
D
H yd rologic
c o n d itio n
»
W ■
Poor
Good
Poor ■
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
Good
Poor
F a ir
Good
Poor
F a ir
Good
Good
Poor
F a ir
Good
Farm steads
Roads ( d i r t ) 2 /
(hard s u r f a c e ) 2 /
l / C lo s e -d r ille d or b road cast.
2 / In cluding r ig h t-o f-w a y . ■
77
■
72
67
70
65
66
62
65
63
63
61
61
•
-
5%
66"
58
64
55
63
51
68
49
39
47
25
6
30
86
81
78
79
75
74
71
76
75
74
73
72
70
77
72
75
69
73
67
79
69
61
67
59
35
58
45
65
36
25
59
72
74
60
55
74
82
84
91
88
85
84
82
■ 80
• 78
84
83
82
81
94
91
89
88
86 .
82
81
88
87
85
84
82
78 • 81
' 79
85
81
83
78
80
89
85
85
83
83
76
86
79
74
80
81
88
83
79
78
75
70
71
77
■73
70
82
87
90
89
84
80
. 83
79
77
86
89
92.
-
9h -
APPENDIX D
MANNING Q CALCULATION FROM X-SECTION NOTES
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
.
C
C ■
C
C
C
C
C
'
A
AXSEC
ATOTL
COEFN
DELWS
IHWSEL
LOWSEL
NOWSEL =
NOXSA
=
NOXSP
NSUBXS =
P
PTOTL
PXSEC
SAVXL
Z=
SAVXR
SLOPE
Q
QXSEC
VXSEC
WSELEV =
=
X(I)
=
Y(I)
AREA BETWEEN TWO X-SECTION POINTS
' .
TOTAL AREA OF- ENTIRE X-SECTION
TOTAL AREA OF PORTION OF X-SECTION
FOR EXAMPLE,
AREA OF LEFT FLOOD, CHANNEL,
OR RIGHT FLOOD PLAIN
MANNING N COEFFICIENT
DISTANCE Y TO WATER SURFACE FROM NEXT POINT
(X,Y) ABOVE WATER SURFACE
HIGHEST WATER SURFACE TO BE INVESTIGATED
LOWEST WATER SURFACE TO BE INVESTIGATED
NO. OF WATER SURFACE ELEVATIONS TESTED
NO, OF X-SECTION AREAS
NO. OF X-SECTIOM POINTS, 10 IS THE MAXIMUM
NEW SUB X-SECTION
IF = O NEW SUB-SECTION TO BE READ
IF = I NEW X-SECT ION TO BE READ
PERIMETER
.
.
TOTAL PERIMETER IN SUB X-SECT ION
PERIMETER OF WHOLE X-SECTION
LOCATION TO SAVE VALUE OF X ON LEFT SIDE OF WS
INTERSECTION TO BE USED WITH NEW WS ELEVATIONS
SAME AS SAVXL EXCEPT FOR RIGHT SIDE
CHANNEL SLOPE
TOTAL DISCHARGE- IN SUB X-SECT ION DISCHARGE FROM WHOLE X-SECTION
AVERAGE VELOCITY FOR WHOLE X-SECT ION
WATER SURFACE ELEVATION
DISTANCE FROM HORZ -CONTROL
ELEV. ABOVE DATUM'
- 95 -
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
C
C
C
C
DISCHARGE Q CAN BE CALCULATED FROM MANNINGS EQUATION FOR
IRREGULAR NATURAL STREAM CROSS-SECTIONS.
THE WHOLE X-SEC
MAY BE SUBDIVIDED INTO SUB-SECTIONS AT SHARP GEOMETRICAL
THERE ARE FOUR DATA CARDS NECESSARY FOR EACH SUBBREAKS.
THERE FORMAT IS AS FOLLOWS.
SECTION •
CARD
I
-
2
3
‘4
COLUMNS
I - SG
I
6
11
16
21
31
I
- 5
- 10
- 15
- 20
- 30
- 40
-
S
9 — 16
17 - 24
ETC.
I - 8
ETC.
PRINT ANY TITLE SHOWING WATERSHED NAME,
LOCATION, SECTION NUMBER, ETC.
NOXSP
RIGHT JUSTIFIED
LOWSEL
RIGHT JUSTIFIED
IHWSEL
RIGHT JUSTIFIED
NSUBXS
RIGHT JUSTIFIED
COEFN
IN FORMAT XXXX.XXXXX
SLOPE IN FORMAT XXXX.XXXXX
X DIST TO 1ST POINT FROM REFERENCE
WITH FORMAT XXXXX.XX
X DIST TO 2ND PT FROM REFERENCE PT
•3RD .
ELEVATION Y CORRESPONDING TO,X OF CARD 3
-
"
AFTER ALL SUB-SECTIONS HAVE RUN FOR A GIVEN X-SECTION
ANOTHER CARD MUST BE READ TO IN IT IAL IXE THE SUMMARY PRINT
OPERATION.
THE CARD MUST HAVE THE LOWEST VALUE OF LOWSEL
FOR THE X-SECTIOM 'IN COLUMN 1-5",' RIGHT JUSTIFIED.
— 96
C
C
C
C
C
-
DIMENSION TITLE(40),X(IO) ,Y (10) .,DXD Y (9) ,A(9),P(9),D(IO),
IVXSEC(600),AX5EC(600),PXSEC(600),QXSEC(600)
PRINT 104
■
104 FORMAT(60H0
MANNING Q CALCULATION FROM
I X-SECT ION NOTES
NOTE THAT THE FOLLOWING DO LOOP IS GOOD ONLY FOR ELEVATIONS FROM 2500 TO 3100 FEET ' CHANGE ELEV• IN STATEMENT
19 TO FIT WATERSHED,DIMENSION STATEMENT MUST ALSO BE
CHANGED FOR VXSEC, AXSEC, PXSEC , AND QXSFC.
CONSTANTS
IN STATEMENTS 24, 106, AND 107 MUST CONFORM
19 DO 23 KK=2501,3100
24 K=KX-2500
AXSEC(K)=O.O
PXSEC(K)=0.0
23 QXSEC(K)=0.0
1 READ 89,(TITLE(I) ,1 = 1,40)
89 FORMAT(4CA2)
PRINT 90,(TITLEt I),1= 1,40)
90 FORMAT(IH l ,40A2///) ■
READ 9 1 ,NOXSP,LOWSEL,IHWSEL,NSUBXS,COEFN,SLOPE
91 FORMAT(415,2F10.5)
IF(NOXSP) 16,16,2
2 READ 92 , (X( I ).,I=I ,NOXS P )
READ 92, (Y(I),I=I ,NOXSP)
"
92 FORMAT(10F8.2)
PRINT 93, (X(I), I= I ,NOXSP)
93 FORMAT (4H X= 10 FS'. 2/)
PRINT 103, (Y(I), 1=1,NOXSP)
103 FORMAT(4H Y= 10F8.2//)
" ■
NO XSA = NOXSP-1
PRINT 95, COEFN
95 FORMAT(9H0
N =FlO.5/)
PRINT 97,SLOPE
97 FORMAT( 9H SLOPE =FlO.5///)
PRINT 101
101 FORMAT(62H WATER SURFACE
DISCHARGE Q END AREA
I VELOCITY
PERIMETER
/61H
ELEVATION
(CFS)
.2 (SC- FT)
(FPS)
(FT)
//)
DO 15 J =LOWSEL,IHWSEL
ATOTL=O.O
PTOTL=O.O
DO 3.1=1,NOXSP
AJ-J
D(I)=AJ-Yt I)
IF (D(D) 4,3,3
4 D(I)=O
3 CONTINUE
- 97 -
n n
n n n n
DO 18 1=1,NOXSA
11=1+1 ■
I F ( Y d I ) - Y ( D ) 5,17,5
17 DXDYl15=0
GO TO 18
5 DXDY(I) = IX(II)-X(I) !/(Y(II)-Y(I) I
18 CONTINUE
CALCULATE X AND Y COORDINATES WHERE W.5. INTERSECTS
X-SECTIOM ON LEFT SIDE FACING DOWNSTREAM.
THE IF(DXDY)
BYPASSES THIS SIDE IF X-SECTION IS OF RIGHT FLOOD SEC­
TION ONLY
K=I
IF(DXDYtK)) 6,81,81
■81 SAVXL = X(K)
KK=K
GO TO 9
6 K=K+I
IF (D(K) I 6,6,7
7 KK=K-I
SAVXL=X(KK)
DELWS=Y(KK)-AJ
. IF (DELWS) 9,9,8
8 X(KK)=XtKK)-DELWS*DXDY(KK)
CALCULATE X AND Y COORDINATES WHERE W.S. INTERESTS
X-SECTICM ON RIGHT SIDE FACING DOWNSTREAM
9 L=NOXSP
LLL=L-I
^
IFtDXDY(LLL)) 32,82,10
82 SAVXR=X(L)
LL=L
L = LLL
GO TO 13
10 L=L-I
. IF (D(L)) 10,10,11
11 L L = L + 1
SAVXR = Xt L D
DELW s =Y(LL)-AJ
IF (DELWS) 13,13,12
12 X(LL)=X(LL)-DELWSX-DXDY(L)
C.
CALCULATE AREA,PERM IMETER, AND MANNING Q
. 13 DO 14 I=KK, L
'11 = 1 + 1 ' '
At I )= (-ABS F (X-( I I )- X ( I )) )x-( {D ( I I )+ D ( I ) )/ 2 . )
• '•
P(I) =SQRTFt ( (ABSFtXf ID-X(I))) *#2 • )+ ( (ABSF (.D(I)-D(II)))
I tt-x-2-. ) )
ATOTL=ATOTL + A( I)
14 PTOTL=PTOTL+P(I) .
'
-
- $8 -
Q = (1.49/C0EFN)*((ATOTL**!. 6 6 7 ) / (PTOTL**0.667))*(SLOPE
1 ** 0 . 5 )
100
106
15
20
105
22
107
21
C
16
AVEVEL=QZATOTL
X(LL)=SAVXR
X(KK)=SAVXL
PRINT 100,
JsQs A TOTLjAVEV7EL ?PTOTL
FORMAT(3XsI5 s 8 X s F10.0,3X j F8.1»3X j F6.2»6X s F6.1)
L = J-2 500
PXSEC (L) =PXSEC ( D + P T O T L
AXSEC (L) =AXSECt D + A T O T L
QXSEC(L)=QXSEC(L)+Q
VXSEC(L)=QXSEO(L) /AXSEC(L)
IF(NSUBXS)20,1,20
PRINT 105
FORMAT(38H1
SUMMARY FOR ENTIRE CROSS SECTION
PRINT 101
READ 22 , LOWSEL _
FORMAT(15)
DO 21 J =LOWSEL,IHWSEL
L=J-2500
PRINT 100,J ,QXSEC(L) ,AXSEC(L) ,VXSEC(L) ,PXSEC(L)
GO TO 19
PLACE TWO BLANK DATA CARDS AT END OF DATA
CALL EXIT
'
.
END
///!
-
99
-
LITERATURE CITED
Amorocho, J . and H a rt, W. E ., "A C ritiq u e o f C u rren t Methods in
H ydrologic Systems I n v e s t i g a t i o n ," T ran s. Amer. Geo. Union,
V ol. 4 5 , 1964, p p . 307-321.
B e rn a rd , M s r r ill M., "An Approach t o D eterm inate Stream F lo w ,"
ASCE Transactions, V ol. 100, 1935, P» 34?.
B isw as, A s it K ., "H ydrologic E n g in eerin g P r io r t o 600 B. C .,"
J o u rn a l o f th e H y d rau lics D iv is io n , ASCE, V ol. 93, No. HY5,
P ro c . Paper 5^31, Septem ber, 1967, pp. 115-135•
B isw as, A s it K ., "The N ile : I t s O rig in and R is e ," W ater and Sewage
Works, V ol. 113, No, 8 , A ugust, 1966, p p . 282-292.
C. E. I , R ., I n c . , "Computer Program f o r P r o je c t F o rm u la tio n H ydrology, " J a n u a ry , 1964.
C harnes, A, and W. W. C ooper, Ifenagement Medels and I n d u s t r i a l
A p p lic a tio n s o f L in ear Programming, N. Y ., John W iley & Sons,
. I n c . , 1961.
C h ild s , E. F ., " N o rth e a s te rn Floods o f 1 9 5 5 z Flood C o n tro l H ydrology^”
J o u rn a l o f th e H y draulics D iv is io n , ASCE, V ol. 8 4 , No. HY3, P ro c /
P aper 1663, June 1958.
Chow, Ven Te, "H ydrologic D esign o f C u l v e r t s ," J o u rn a l o f th e H y d ra u lic ^
D iv is io n , ASCE, V ol. 88, No. HY2, P a r t . I ," Iferch, 1962.
Chow, Ven Te, Open Channel H y d ra u lic s , New York, John W iley & Sons,
I n c . , 1950. ■
Chow, Ven Te, "General R eport, ” P r o c e e d in g s, The I n te r n a t io n a l Hydrology
Symposium, V o l. 2 , Septem ber, 1967, pp. 50- 65 .
Chow, Ven Te, Handbook o f Hydrology, New York, McGraw-Hill Book Company,
1964.
Cowan, Woody L ., "E stim a tin g H y d rau lic Roughness C o e f f ic ie n ts ," A gr.
E ngr. , Vol.. 37, No. 7 , J u ly , 1956, p p . 473-75.
Henderson, F. M-., Open . ChanneI Flow, The Macmillan Company, New York, .
1966.
- 100
■ K e rsh fi e l d , David M., " B a in f a ll Frequency A tla s o f th e U. S.
C o o p erativ e S tu d ie s S e c tio n , T e c h n ic a l Paper Fo. 40, U* S. B. K .,
W ashington, D. C ., th y , 1961.
Hoyt, J , C ., "Development o f th e S cien ce o f R iv er Measurement H y d ro lo g y ,"
C i v i l E n g in e e rin g , V ol. 12, 1942, p p . 3 2 4 -6 .
,Sherman, L. K .,." S tre a m flo w from R a i n f a l l by th e U n it-g ra p h M ethod,"
Engr. News R ecord, V ol. 108, 1932, pp. $01-5*
S in g h , K rish an P i a r a , "N o n lin ear In s ta n ta n e o u s U nit-H ydrograph T h eo ry ,"
J o u rn a l o f H y d ra u lic s D iv is ion-,- AS CE, V ol. 9°# No. HY2, P ro c .
P a p e r3 5 $ 2 7 ~ M irch, 1964, p p . 313-347.
S n y d er, F. F ., " S y n th e tic U n it-G ra p h s, " T r a n s .,Am er. G eo p h y sical Union,
R ep o rts and P a p e rs , H ydrology, 195^*
S o i l C o n se rv a tio n Service-, "Computer Program f o r P r o je c t F o rm u latio n H y d ro lo g y ," 'U. S. D epartm ent o f A g r ic u ltu r e , E n g in ee rin g D iv is io n ,
T e c h n ic a l R elease No. 2 0, th y , 196$.
S o i l C o n se rv a tio n S e rv ic e , " S o il C o n se rv a tio n S e rv ic e N a tio n a l E n g in eer­
in g 'Handbook," 1964.
W hite, J . B ., " S to c h a s tic A spects o f R e s e rv o ir S to r a g e ," P ro ce e d in g s,
The I n t e r n a t i o n a l Hydrology. Symposium, V ol. I , Septem ber^ 19677
PP* 354-60. •
.
I STATE UNIVERSITY UBRARIK
3 1762 10013695 9
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F417
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A n a ly s is o f th e
S o i l C on servation
S e r v ic e P r o je c t Form ulation
Program - Hydrology__________
N A M C A N O A O O H tS S
FEB I S *70
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