Estimation of economic and hydrologic impacts of water management policies in the Yellowstone
River Basin
by Derrell Sylvester Peel
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Applied Economics
Montana State University
© Copyright by Derrell Sylvester Peel (1982)
Abstract:
A partitioned linear programming model of the Yellowstone River Basin is developed. The model
maximizes returns over variable costs to a vector of alternative irrigated agricultural crops. Demands
for water in municipal use, energy production and minimum instream flows are included in the model
as model constraints.
With the basic model as a benchmark, a number of scenarios reflecting alternative water management
policies and changes in important variables are evaluated. Specific scenarios include increased levels of
irrigation efficiency, increased irrigated acreage in the basin, below average levels of river flow which
would be associated with dry years and increased, levels of prices for agricultural products.
The results of the basic model indicate the presence of time and site specific water scarcities which are
exaggerated in the scenarios of increased agricultural prices or below average flows. The results also
indicate that water management policies designed to increase the level of irrigation water use efficiency
will, within some range, result in increases in returns over variable costs to irrigated agricultural
production. However, the costs of increasing irrigation efficiency are not calculated in the model.
Model results indicate that increasing irrigation efficiency may result in significant income
redistribution, between sectors within the basin. ESTIMATION OF ECONOMIC AND HYDROLOGIC IMPACTS OF WATER
MANAGEMENT POLICIES IN THE YELLOWSTONE RIVER BASIN
by
D e rre ll S y lv e ster Peel
A t h e s i s subm itted in p a r t i a l f u l f il l m e n t
of th e re q u ir e m e n ts f o r th e degree
of
Master of S cien ce
in
A p p l i e d Economics
MONTANA STATE UNIVERSITY
Bozeman, Montana
December 1982
MAIN U 8.
hi [SYS
ii
Cbp-
APPROVAL
o f a t h e s i s s u b m i t t e d by
D e rre ll S y lv e ste r Peel
T h i s t h e s i s h a s b e e n r e a d by e a c h member o f t h e t h e s i s
c o m m i t t e e and h a s b e en f o u n d t o be s a t i s f a c t o r y r e g a r d i n g
c o n te n t, E n g lish usage, fo rm at, c i t a t i o n s , b ib lio g r a p h ic
s t y l e , and c o n s i s t e n c y , and i s r e a d y f o r s u b m i s s i o n t o t h e
C ollege of G raduate S tu d ie s .
,,/
D ate
C h a i r p e r s o n , G r a d u a t e Committe e
Z7
Approved
t h e Major D e p a r t m e n t
, 19 8 Head, Major D e p a r t m e n t
D ate
A p proved f o r
/ L- D ate
Z—
G r a d u a t e Dean
iii
STATEMENT OF PERMISSION TO USE
In p r e s e n tin g t h i s t h e s i s in p a r t i a l f u l f i l l m e n t of th e
r e q u i r e m e n t s f o r a m a s t e r ' s d e g r e e a t Montana S t a t e U n i v e r ­
sity ,
I a g r e e t h a t t h e L i b r a r y s h a l l make i t a v a i l a b l e t o
borrow ers under r u l e s of th e L ib ra ry .
B r i e f q u o t a t i o n s fro m
t h i s t h e s is are allow able w ith o u t s p e c ia l perm issio n , pro ­
v i d e d t h a t a c c u r a t e acknowledgement o f s o u rc e i s made.
P e r m i s s i o n f o r e x t e n s i v e q u o t a t i o n fro m o r r e p r o d u c t i o n
o f t h i s t h e s i s may b e g r a n t e d by my m a j o r p r o f e s s o r , o r i n
h i s / h e r a b s e n c e , by t h e D i r e c t o r o f L i b r a r i e s , when, i n t h e
opinion of e i t h e r , th e proposed use of th e m a te r ia l i s fo r
sch o larly purposes.
Any c o p y i n g o r u s e o f t h e m a t e r i a l i n
t h i s t h e s i s f o r f i n a n c i a l g a in s h a l l n o t be allo w ed w ith o u t
my w r i t t e n p e r m i s s i o n .
S ignature
D a t e ____ ^ \
sZJLX
__________________
iv
V ita
D e r r e l l S y l v e s t e r P e e l was b o r n J u l y 3 0 , 1959 i n
Mul eshoe^ T e x a s , He i s t h e f o u r t h c h i l d o f M, A, raJ a c k ra
and D e a l i a P e e l , D e r r e l l and h i s f a m i l y moved t o P a b l o ,
Montana i n 1964, He g r a d u a t e d f r o m Ronan High S c h o o l i n
1977 and e n t e r e d Montana S t a t e U n i v e r s i t y t h a t f a l l .
A fter
he g r a d u a t e d w i t h a B,S, i n Farm and Ranch Management i n
t h e s p r i n g , he b e g an w o rk on an M.S, d e g r e e i n A p p l i e d
E c o n o m ic s i n t h e f a l l o f 1981,
V
Acknowledgm ents
I w o u l d l i k e t o e x p r e s s my s i n c e r e t h a n k s a n d
a p p r e c i a t i o n t o my g r a d u a t e c o m m i t t e e :
D r e R o b e r t. T a y l o r ,
Dre B r u c e B e a t t i e ,
and D r e R i c h a r d B r u s t k e r n f o r t h e i r
g u i d a n c e and a d v i c e .
. I e s p c e c i a l l y w i s h t o t h a n k my
g r a d u a t e c h a i r m a n ^ Dre R i c h a r d McConnen f o r h i s w i s e
c o u n s e l and n e v e r - e n d i n g f l o w o f i d e a s .
In a d d it i o n ,
I
w o u l d l i k e t o t h a n k Mike N i c k l i n and Ted W i l l i a m s i n t h e
C i v i l E n g i n e e r i n g d e p a r t m e n t and P h i l F a m e s o f t h e Montana
s t a t e o f f i c e o f SCS-USDA f o r t h e i r a d v i c e w i t h t e c h n i c a l
hydrologic m atters.
S i n c e r e a p p r e c i a t i o n i s e x t e n d e d t o my m o t h e r and my
f a m i l y f o r t h e i r c o n t i n u e d s u p p o r t t h r o u g h o u t my a c a d e m i c
career.
L astly,
t o my w i f e , P a t ,
I w a n t t o e x p r e s s my
d e e p e st g r a t i t u d e f o r both her d e d ic a te d a s s i s t a n c e w ith
t h e p r e p a r a t i o n o f t h i s t h e s i s and h e r c o n t i n u e d s u p p o r t
and p a t i e n c e t h r o u g h many l o n g d a y s and n i g h t s .
vi
TABLE OF CONTENTS
Page
Chapter
L i s t o f T a b l e s * o******************************
i
L l S t Of FiyUiTOS o o e e e e o e o e e e e c e o e e o e e e o e o o e e o o e
AbSt ITS Ct
e e e e e e e e f f e e e e e o e e e o o o o e o e e o e e e e e o e e o e e
INTRODUCTION
xx
Xl
Xll
9-e> e e o o e e e e o e o o e e e e e e e e e e e o o e o e e e e e e
S c l C l C Q ST O U n C l e e o e e e e o o e e e o e o e o e o o e o e o o e e o e o o e e o e
2
L O C fclI
6
I S S U 0 S © o © o o e o © o o o © ® © o o o o 9 o o o © © o o 6 o o © o o ©
S t 0 t 0
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IC
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o e © o e e e o o » e o © e » o e o © © ® ® e © 9 » o
Fo cl ©ifo I I y R o s o r v o d Watosr o © © * ® © ® ® © ® ® ® ® © © © ® ®
The Y e l l o w s t o n e R i v e r Compact©®®©®©®©®©®®®
The W ater Problem®o©©®®®©®®©®©®©®©©©©®©©®©©©©
P o s s i b l e S o l u t i o n s ®a©®©©©®©*©©*®®©©®©©©©©©* ©©
^ i r r i g a t i o n and R e t u r n Flows® ee®©©®®©©®©®®©®©©
W ater Quality©©oo©©©®®®©©©©©®©©©©©©®©©®®©©©©©
O b ^ e c t i v e s 0 0 ©©©©©©©©©©®®®®©©©©®©®®©®®®®°®®°°®
-ECONOMIC AND HYDROLOGIC THEORY0 o
o e e e e e o o o o o o e a o o
H y d r o l o g i c Theorye®©©©®©®©©®®©®©®©®©©©©®®®®©®
RunOffoo©®©©©©®©©©©©©©®©®®©®©©©®®®®®®©©0®®
Hydrographs© ©o©©©©©©®©.©©©*©®®©*®®®®®*®®®®®
S t r e a m f l o w and I r r i g a t i o n © * ©©©©®©o®©©©©©©®®®©
Economic Theorye©©©©©©©©©©©©©®®©©©©©©©®©®®®®®
H e n e f i t / C o s t Fr a mewor le©®©©©©©©©©©®©©©©©©©®
An A l t e r n a t i v e M e t h o d o l o g i c a l A p p r o a c h ,
THE MODEL® ©e
6
8
9
10
12
14
15
17
19
19
22
25
25
32
32
41
o o e ® e o © e © e o o e © o ® ® o ® ® o © ® ® ® © ® ® © ® ® ° ®
The S t a n d a r d L i n e a r Programming P r o b l e m ,
S p a t x a l Dxmensxon 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * 0 0 0 @0 0 0
Time Di me n s i o n * o*****************************
The Hydro l o g x o Model * * * * * * * * * * * * * * * * * * * * * * * @ 0
The I r r i g a t e d A g r i c u l t u r e Mo d e l «*«*. **»**»***
The O b ] e c t x v e Functxon* e*********************
The B a s x n wWxde Model ******** * **************oo
R e s e r v o x r s *e *********************************
l e e e e o e
47
52
53
56
59
60
63
v ii
TABLE OF CONTENTS--Continued
C hapter
Page
DATA SOURCES AND PREPARATION e
66
o o e o o e o e e o o o o o o e o e o
Th© BaSlC Mod ©I eooooooooeooooooooooooooooooe
H y d r o l o g i c D a t al e o o o e o o Q o e e o e e o e o e e o e o e o o o e o e e
Conve yanc e and F i e l d E f f i c i e n c i e s
R e tU rn Flows »ooe ooe e ooe QO- - ' ~~" ~~
Minimum Flow R e q u i r e m e n t s ' o o o e o o o o o o o o o o e o o o e e
M u n i c i p a l and E n e r g y R e l a t e d W ater Use
I r r i g a t e d Acres® oo@ooo@oe*®o*@*@o@oo0 o@o*@o®
I r r i g a t e d Crops® ®®e®oo®@@®®®®®®® ®o®®®®®®®®®®
R e t u r n s Over V a r i a b l e C o s t (ROVC)®®®®» ®. ®®. ®
S u g a r B e e t and Bean A c r e a g e R e s t r i c t i o n s ® ®®®
Net I r r i g a t i o n R e q u i r e m e n t s ® .......... .........................
A l t e r n a t i v e Scenarios®®®®®®*®®®®®*®®®®®®®®®®®
^ In creased I r r i g a t i o n E ffic ie n cy Scenarios
Dry Year S c e n a r i o s ® o ® ® ® ® * ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ®
I n c r e a s e d L e v e l o f A g r i c u l t u r a l P r i c e s ® ®®
I n c r e a s e d I r r i g a t e d Acreage S c e n a r io s
^
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R e s u l t s o f t h e B a s i c Model.®
,R e su lts of In c re a s e d I r r i g a t i o n E f f i c ie n c y
Scenarios®
H y d ro lo g ic Im pacts
Economic I m p a c t s
R e s u l t s o f t h e Dry Year S c e n a r i o s ®
R e s u l t s of th e I n c r e a s e d I r r i g a t e d Acreage
S c e n a r i o s ® o®®®®®®®®®®®®®®®®*®®®®®*®®®®®®®®
R e su lts of the In creased A g ric u ltu ra l P ric e s
Scenarios®.e®®®®®®®®*®®®®*®®®®®®®*®®®®®®®®
C a v e a t s and L i m i t a t i o n s o f t h i s Study®.®*®®®
S u g g e s t e d R e f i n e m e n t s o f t h e Mode l ®. . ®. ®.
0 0 0 0 0 0
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66
67
68
70
72
73
73
74
77
77
78
78
78
79
81
82
83
85
88
96
96
97
98
99
100
100
102
CONCLUSIONS, POLICY IMPLICATIONS AND SUGGESTIONS
FOR FURTHER RESEARCH® * ® ® o * ® ® ® e ® @ o ® o ® ® ® ® ® ® * ® ® ® ®
104
C o n c l u s i o n s and P o l i c y I mpl i cat i ons . ®®®®®. ®®.
S u g g e s t i o n s f o r F u r t h e r Research®. ®®. ®. ®®®®®.
104
112
v iii
TABLE OF CONTENTS--Continued
Page
Chapter
APPENDICESe
e e e o e e e e o e e o e e e o
A p p e n d l X
A®
e o o e o o e o o e o
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e o o o e e o e o o a a o o o a o o o o o o
116
125
127
o o o e e o o o o o o a o o o o o o o e o o o
136
o o © o © o o o o © e o o o o © o a © o o © o
A p p e n d ix Bo®®®®®®®®®®*
A p p e n d ix C®e®®*®*®®®®® o
0 » 9 O e O 0 O © © O O O O O © G O 9 O © O O
REFERENCES CITED.......................
ix
LIST OF TABLES
Table
1.
Page
The N in e S u b - b a s i n s o f t h e Y e l l o w s t o n e R i v e r and
A sso c ia ted H ydrologic D r a i n a g e s . , o . , ,
49
C u r r e n t and F u t u r e L e v e l s o f Conveyance and
F i e l d E f f i c i e n c i e s ®. . © . ©. o o o c o o o o e o o o o o o . o o . o o .
69
3.
R e t u r n Flow P a t t e r n Used i n t h e LP M o d e l . . . . . . . .
. 71
4.
Minimum I n s t r earn F l o ws o . . . . . . . . . . . . . . . . . . . . . . . . .
72
5.
I r r i g a t e d A c r e a g e s o f t h e N in e S u b - b a s i n s u s e d
i n t h e LP Model . o©. ©. ©©©. ©©. ©©©. . . . ©. ©. . ©. ©©©®
75
6.
A l t e r n a t i v e C r o p s f o r t h e N in e S u b - b a s i n s . . . . . . .
76
7.
B a s i n - w i d e Summary o f t h e B a s i c Model ( B I ) . . . . . .
89
8.
T o t a l D i v e r s i o n s and R e t u r n F l o w s . . © . © . . . . . . . . . ©
90
9.
D i v e r s i o n s by Sub—b a s i n . © © . . . © © © . . . . . . . © o © . © . . . .
90
10•
R e t u r n Flows by Sub—b a s i n .
. . . . . a . © © . © . © © . © . . . © . ©
91
11.
B asin -w id e Cropping P
t
.
92
12.
Ret u r n s t o Ag r i c u l t u r e©. . ©. . . . ©. ©. ©©©. ©. ©. ©. ©©©©
93
13.
Shadow P r i c e s o f Wat er©©©. ©o©. . ©©. . . -. . ©©©. . ©. ©©©
94
14.
Shadow P r i c e s o f I r r i g a t e d A c r e a g e . © . . . . . . . . . . . .
95
15.
Irrig a te d A lfalfa
for
Sub-basins I , 2,
16 .
Irrig a te d A lfalfa
for
S u b - b a s i n s 5 and 7 . . . . . . . .
118
17.
Irrig a te d A lfalfa
for
S u b -b a sin s 6, 8 ,
and 9 . . . .
119
18.
I r r i g a t e d Corn f o r G r a i n f o r A l l
S u b -b asin s.....
120
19.
I r r i g a t e d Feed B a r l e y f o r A l l S u b - b a s i n s . . . . . . . .
121
20 .
I r r i g a t e d B e an s f o r A l l Sub—b a s i n s . . . . . . . . . . . . . .
122
2.
a
t
e
r
n
s
.
3 , and 4© 117
X
LIST OF TABLES— C o n t i n u e d
Table
Page
21«
I r r i g a t e d Sugar B e e ts f o r A ll S u b - b a s i n s . .
0
22.
I r r i g a t e d Corn S i l a g e f o r A l l S u b - b a s i n s
0
0
0
9
0
0
124
23.
C l i m a t i c Zones f o r t h e Nine S u b - b a s i n s
0
0
0
0
0
0
126
24.
Ne t I r r i g a t i o n R e q u i r e m e n t s . . . . . . . . . . . . . . . . . . . . .
126
25.
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e B a s i c
Model (BI) and t h e P l and P2 S c e n a r i o s . . . . . . . .
128
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e El
Scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
129
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e E2 and E3
Scenarios.
. . . . @. . . .
130
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e Dl
S c e n ario *. . . . . . . . . . . . . o . . . . . . . . . . . . . . . o . . . . . . . .
131
26.
27.
28.
29.
30.
31.
32.
9
0
0
0
0
0
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e D2
S c e n a r i o . . . . . . . .
0
9
0
0
0
.
.
123
132
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e Al
Scenario.. . . . . . . o . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
133
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e A2
Scenario.. . . . . . . . . . O . . . . . . . . . . . . . . . . . . . . . . . . . .
134
C r o p p i n g P a t t e r n s by S u b - b a s i n f o r t h e A3
Scenario.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
135
xi
LIST OF FIGURES
Figure
Page
1.
S i m p l i f i e d Diagram o f t h e H y d r o l o g i c a l C y c l e . . , .
21
2.
D iagram m atic R e p r e s e n t a t i o n of th e Runoff
P
r
o
c
e
s
s
.
. . . =. . . . . < . » » 0 . . . . . .
23
A v e r a g e M o n th ly Flow o f t h e Y e l l o w s t o n e R i v e r
a t S i d n e y , M ontana, f o r W ater Y e a r s 1 9 3 4 - 1 9 8 0 .
26
4.
Components o f W ater L o s s fro m I r r i g a t i o n S y s t e m s
29
5.
C o n c e p t u a l D iagra m o f t h e I r r i g a t i o n R e t u r n
Flow S y s t e m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
M a r g i n a l B e n e f i t s (MBw) and M a r g i n a l C o s t s (MCw)
o f W ater U s e . . . . . . . . . . . . . . . . . . . . . . . . . ®• ®. . . . . ®
34
M a r g i n a l B e n e f i t s and M a r g i n a l C o s t s o f
I r r i g a t i o n E f f i c i e n c y (E1 ) . . . . . . . . . . . . . . . . . . . . .
38
P u b l i c and P r i v a t e M a r g i n a l B e n e f i t s and
M a r g i n a l C o s t s o f I r r i g a t i o n E f f i c i e n c y (E1 ) . . .
40
The Nine P l a n n i n g S u b - b a s i n s of t h e Y e l l o w s t o n e
R i v e r B a s i n . . . . .......... ..
48
10 .
The N in e S u b - b a s i n s a s a Ne t wo r k . . . . . . . . . . . . . . . .
50
11.
The Nine S u b - b a s i n s S u b m a t r i c e s i n t h e
P a r t i t i o n e d L i n e a r Programming Fram ew o rk . . . . . . .
51
Flow C h a r t o f t h e P r i n c i p a l Components o f t h e
LP Mo d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
"Movement63 o f W ater f ro m t h e R i v e r t o C r o p s i n
t h e LP Mo d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
"Movement" o f I n s t r e a m Flow from an U p s t r e a m
S u b - b a s i n t o an I m m e d i a t e l y Downstream
S u b - b a s i n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ®. . . ®.
SI
S i m u l a t i o n o f R e s e r v o i r i n t h e LP Mo d e l . . . . . . . . .
65
3.
6.
7.
8.
9.
12.
13.
14.
15.
x ii
A bstract
A p a r t i t i o n e d l i n e a r p r o g r a m m i n g model o f t h e
Y ellow stone R iver B asin i s developed.
The model m a x i m i z e s
r e t u r n s over v a r i a b l e c o s t s t o a v e c to r of a l t e r n a t i v e
i r r i g a t e d a g r i c u l t u r a l crops.
Demands f o r w a t e r i n m u n i c i ­
p a l u s e , e n e r g y p r o d u c t i o n and minimum i n s t r e a m f l o w s a r e
i n c l u d e d i n t h e model a s model c o n s t r a i n t s .
W ith t h e b a s i c m odel a s a b e n c h m a rk , a number o f
s c e n a r i o s r e f l e c t i n g a l t e r n a t i v e w a t e r m an agem en t p o l i c i e s
and c h a n g e s i n i m p o r t a n t v a r i a b l e s a r e e v a l u a t e d .
S p ecific
sc e n a rio s include in cre ased l e v e ls of i r r i g a t i o n e f f i c ­
i e n c y , i n c r e a s e d i r r i g a t e d a c r e a g e i n t h e b a s i n , be lo w
a v e r a g e l e v e l s o f r i v e r f l o w w h i c h w o u ld be a s s o c i a t e d w i t h
d r y y e a r s and i n c r e a s e d , l e v e l s o f p r i c e s f o r a g r i c u l t u r a l
products.
The r e s u l t s o f t h e b a s i c m o d e l i n d i c a t e t h e p r e s e n c e
o f t i m e and s i t e s p e c i f i c w a t e r s c a r c i t i e s w h i c h a r e e x a g ­
g e ra te d in th e s c e n a rio s of in c re a s e d a g r i c u l t u r a l p r ic e s
o r b e lo w a v e r a g e f l o w s . The r e s u l t s a l s o i n d i c a t e t h a t
w a t e r m anagem ent p o l i c i e s d e s i g n e d t o i n c r e a s e t h e l e v e l o f
i r r i g a t i o n w a t e r u s e e f f i c i e n c y w i l l , w i t h i n some r a n g e ,
r e s u l t in i n c r e a s e s in r e t u r n s over v a r i a b l e c o s t s to
i r r i g a t e d a g r i c u l t u r a l production.
However, t h e c o s t s o f
in c re a s in g i r r i g a t i o n e f f ic ie n c y a re not c a lc u la te d in the
m o d e l. Model r e s u l t s i n d i c a t e t h a t i n c r e a s i n g i r r i g a t i o n
e f f i c i e n c y may r e s u l t i n s i g n i f i c a n t income r e d i s t r i b u t i o n ,
betw een s e c t o r s w i t h i n th e b a s in .
I
Chapter I
In troduction
I s s u e s r e g a r d i n g w a t e r r e s o u r c e s have r e c e i v e d much
a t t e n t i o n in the U nited S ta te s in re c e n t y e a rs.
Increasing
s c a r c i t y o f w a t e r due t o i n c r e a s i n g demands a n d / o r d e c r e a s ­
i n g q u a l i t y h a s i n c r e a s e d t h e c o n f l i c t s among w a t e r u s e r s ,
e n v i r o n m e n t a l c o n c e r n s and w a t e r f o r e n e r g y , a g r i c u l t u r a l ,
m u n i c i p a l and o t h e r i n d u s t r i a l u s e s .
T his problem i s
p a r t i c u l a r l y a c u t e i n many a r e a s o f t h e W e s t e r n U n i t e d
S t a t e s where a h i s t o r y of p u r e ,
a b u n d a n t w a t e r s u p p l i e s and
a m y r i a d o f w a t e r r e l a t e d l a w s and l e g a l i s s u e s ,
often
c o n f u s i n g and c o n f l i c t i n g a n d , i n many c a s e s , j u d i c i a l l y
te s te d for the f i r s t
tim e o n ly r e c e n t l y , have combined t o
b r i n g w a t e r p o l i c y c o n s i d e r a t i o n s t o t h e f o r e f r o n t of
p ublic
attention.
I n a 1960 p u b l i c a t i o n ,
H i r s h l e i f e r , DeHaven, and
M illim an c o r r e c t l y noted t h a t w ater r e l a t e d i s s u e s are
o f t e n a p p r o a c h e d w i t h more e m o t i o n t h a n c l e a r t h i n k i n g .
They s t a t e :
Much n o n s e n s e h a s b e en w r i t t e n on t h e u n i q u e
im p o rtan c e of w a t e r su p p ly to th e n a tio n , or to
p a r tic u la r regions.
G r a n t e d t h a t t h e n a t i o n , or
any i n d i v i d u a l t h e r e o f , c o u l d n o t s u r v i v e w i t h o u t
w a t e r , t h a t d o e s n o t show u n i q u e n e s s . No human
can s u r v i v e w i t h o u t fo o d , w i t h o u t oxygen,
and w i t h o u t a v a r i e t y o f o t h e r s u p p o r t i n g
2
e n v i r o n m e n t a l c o n d i t i o n s many n o t ev en f u l l y .
k n o w n t o d a y (p .4 ).
However, t h i s d o e s n o t i m p l y t h a t w a t e r r e s o u r c e s a r e .
undeserving of s c i e n t i f i c in q u iry .
W h il e no m ore a ’’n e c e s ­
s i t y " t h a n many o t h e r g o o d s , w a t e r r e s o u r c e s a r e p l a g u e d
w i t h a c e r t a i n u n i q u e n e s s due t o t h e many c o m p e t i n g and
o v erlapping uses of w ater, th e e x t e r n a l i t i e s a sso c ia te d
w ith w ater use, th e absence of m arkets to a l l o c a t e w ater in
many c a s e s ,
and t h e h a z y n a t u r e o f w a t e r o w n e r s h i p and u se
r i g h t s d u e t o t h e s p a t i a l and i n t e r t e m p o r a l c o m p l e x i t i e s o f
h y d ro lo g ic system s.
T h u s, a s c o n c e r n and a t t e n t i o n t o t h e s e i s s u e s
i n c r e a s e s and s o l u t i o n s become i m p e r a t i v e , much i n f o r m a t i o n
w i l l be r e q u i r e d f o r s o c i e t y t o a r r i v e a t s a t i s f a c t o r y
so lu tio n s.
Issu es regarding w ater reso u rces are in v a ria b ly
u n i q u e t o a s p e c i f i c l o c a l i t y and c o m p l e t e s o l u t i o n s w i l l
involve s i t e s p e c i f i c study.
A ccordingly t h i s study i s
c o n c e n t r a t e d on s p e c i f i c r i v e r m an ag em en t a l t e r n a t i v e s i n
t h e Y e l l o w s t o n e R i v e r B a s i n i n Montana.
How ever, i t i s
hoped t h a t t h e methods used i n t h i s stu d y w i l l p r o v id e
i n s i g h t s i n t o w a t e r m an ag em en t i s s u e s t h a t w i l l a p p l y t o
o th er a re a s as w e ll.
B a ck g ro u n d
The Y e l l o w s t o n e R i v e r , a t r i b u t a r y o f t h e M i s s o u r i
R i v e r , h a s i t s h e a d w a t e r s i n n o r t h w e s t e r n Wyoming, t h e s i t e
o f Y e l l o w s t o n e N a t i o n a l P a r k , and f l o w s i n a g e n e r a l l y
3
n o r t h e a s t e r l y d i r e c t i o n a c r o s s s o u t h e a s t e r n Montana and a
s m a l l p o r t i o n o f N o r t h D a k o ta t o i t s c o n f l u e n c e w i t h t h e
M issouri River,
F r e e - f l o w i n g f o r t h e f u l l 670 m i l e r e a c h
o f t h e m a i n s t e m , t h e Y e l l o w s t o n e s u p p o r t s some o f t h e
f i n e s t s p o r t f i s h e r i e s in th e U nited S t a te s ,
Some 550
m i l e s o f t h e m a i n s t e m a r e l o c a t e d i n Montana.
The m a j o r
t r i b u t a r i e s o f t h e Y e l l o w s t o n e : t h e C l a r k s Fo rk o f t h e
Y ellow stone?
t h e B ig h o r n ? t h e Tongue? and t h e Powder r i v e r s
l i k e w i s e h a v e t h e i r h e a d w a t e r s i n Wyoming and f l o w n o r t h ­
w a r d i n t o Montana b e f o r e j o i n i n g t h e Y e l l o w s t o n e .
Thus?
over o n e -h a lf of th e w a ter sup p ly of th e Y ello w sto n e River
i s p r o d u c e d i n Wyoming.
The Y e l l o w s t o n e R i v e r B a s i n i n Montana? w i t h w h i c h t h i s
s t u d y i s c o n c e r n e d ? d r a i n s a b o u t 35?000 s q u a r e m i l e s w h ic h
is
roughly h a l f of th e t o t a l d ra in a g e of th e b a s in .
The
b a s i n i s g e o g r a p h i c a l l y a l a n d o f e x t r e m e s r a n g i n g fro m t h e
snow -capped peaks o f t h e w e s t e r n p o r tio n ? where t h e Y ellow ­
s t o n e R i v e r e n t e r s Mon tana f r o m Y e l l o w s t o n e Park? t o t h e
r o l li n g p la in s of the e a s te rn p o rtio n .
E le v a t i o n s range
fro m o v e r 12?000 f e e t i n t h e m o u n t a i n s t o a b o u t 2?000 f e e t
w h e r e t h e r i v e r l e a v e s Montana.
The c l i m a t e o f t h e b a s i n
d i s p l a y s v a r i a t i o n t o match t h e geography.
Average annual
p r e c i p i t a t i o n r a n g e s f r o m a b o u t 6.6 i n c h e s i n p a r t o f
C a rb o n County? t h e d r i e s t p o r t i o n o f t h e b a s i n ?
t o 24
i n c h e s i n P a r k County? w h i c h h a s t h e h i g h e s t a v e r a g e a n n u a l
p r e c i p it a ti o n in the basin.
Average t e m p e r a t u r e s range
4
f r o m 15,2 d e g r e e s f a r e n h e i t i n t h e w i n t e r t o 75 d e g r e e s
f a r e n h e i t i n t h e summer.
The b a s i n t h u s m a i n t a i n s a v a s t
number o f d i f f e r e n t m i c r o c l i m a t e s and s u p p o r t s a w i d e
v a r i e t y o f f l o r a and f a u n a .
The p r i m a r y s o u r c e o f w a t e r f o r t h e Y e l l o w s t o n e r i v e r
i s sn ow pack t h a t a c c u m u l a t e s i n t h e m o u n t a i n s o f t h e h e a d ­
w aters.
Average an n u al flow o f th e Y e llo w sto n e R iver a t
S i d n e y , M o n ta n a , f o r t h e y e a r s 1 9 34-1980 i s 8.9 mmaf
( m i l l i o n a c r e - f e e t ) w i t h a v a r i a t i o n o f f l o w s f r o m 4.2 mmaf
t o 15.4 mmaf.1
S n o w m e lt r u n o f f i n t h e b a s i n u s u a l l y b e g i n s
a b o u t A p r i l and r e a c h e s a p e ak i n May and J u n e .
A v e rag e
m o n t h l y f l o w s t h r o u g h o u t t h e y e a r w i l l r a n g e f ro m l e s s t h a n
.4 mmaf t o a b o u t 2 mmaf a t S i d n e y w i t h t h e l o w f l o w s ,
o c c u r r i n g i n t h e l a t e summer and f a l l .
The b a s i n i s a s p a r s e l y p o p u l a t e d r e g i o n c o v e r i n g some
f o u r t e e n c o u n t i e s i n t h e s o u t h c e n t r a l and s o u t h e a s t e r n p a r t
of th e s t a t e .
B illin g s,
in Y ellow stone county, i s th e
l a r g e s t c i t y in the b asin.
T h e r e a r e tw o I n d i a n r e s e r v a ­
t i o n s i n t h e Y e l l o w s t o n e B a s i n ; t h e Crow R e s e r v a t i o n , 1
1The u s e o f a v e r a g e s can be v e r y m i s l e a d i n g .
Average
flow s of th e Y ellow stone a re e x tre m e ly s e n s i t i v e to the
t i m e p e r i o d upon w h i c h t h e y a r e b a s e d . For e x a m p l e ,
a v e ra g e a n n u a l f l o w s a t Sidney f o r th e 5 y e a r p e r io d 19341 9 3 8 w e r e 6 .7 mmaf a n d f o r t h e 5 y e a r p e r i o d 1 9 7 4 - 1 9 7 8
w e r e 10.6 mmaf. I n a d d i t i o n , some a u t h o r s p r e f e r t o a d j u s t
t h e raw h i s t o r i c a l a v e r a g e t o r e f l e c t a p a r t i c u l a r l e v e l o f
developm ent.
The DNRC (1 977a, pg. 17) r e p o r t a v e r a g e f l o w s
a t S i d n e y o f 8.8 mmaf w h e n a d j u s t e d t o t h e 1 9 7 0 l e v e l o f .
d e v e l o p m e n t , and B o r i s and K r y t i l l a (1980, pg, 62) r e p o r t
f l o w s o f 8 . 4 5 mmaf w h e n a d j u s t e d f o r t h e 1975 l e v e l o f
developm ent.
5
l o c a t e d i n B i g h o r n and Y e l l o w s t o n e c o u n t i e s , and t h e Nor­
t h e r n Cheyenne r e s e r v a t i o n ,
im m ediately a d ja c e n t to the
Crow r e s e r v a t i o n t o t h e e a s t i n B i g h o r n and Rose bud
co u n ties.
A g r ic u ltu r e , i s t h e most im p o r ta n t i n d u s t r y in
the b asin.
A p p r o x i m a t e l y 570,000 o f t h e n e a r l y 2 5 ,0 0 0 ,0 0 0
a c r e s in th e b a s in a re p r e s e n t l y under i r r i g a t i o n . 2
D e p a r t m e n t o f N a t u r a l R e s o u r c e s and C o n s e r v a t i o n
The
(DNRC)
(1977b) p r o j e c t s a maximum i n c r e a s e i n e c o n o m i c a l l y f e a s i ­
b l e i r r i g a t e d a c r e a g e o f a b o u t 2 3 7 ,0 0 0 a c r e s .
Irrig ated
a g r i c u l t u r e i s by f a r t h e m a j o r u s e r o f w a t e r i n t h e
Y ellow stone B asin w ith v i r t u a l l y a l l i r r i g a t i o n w ater
c o m in g f r o m s u r f a c e s u p p l i e s .
P r e s e n t consum ptive use of
w a t e r f o r i r r i g a t i o n i s a b o u t 1.1 m m a f / y . 3
The o t h e r m a j o r p r i m a r y i n d u s t r y i n t h e b a s i n i s c o a l
m ining.
C u r r e n t l y c o a l m ining ra n k s f a r behind a g r i c u l t u r e
i n e c o n o m i c i m p o r t a n c e b u t h a s t h e p o t e n t i a l t o become a
very s i g n i f ic a n t in d u s try .4
I n 1977,
some 29.3 m i l l i o n
t o n s o f c o a l w e r e r e p o r t e d m in e d i n t h e b a s i n ,
rep resenting
a b o u t a 3 0 - f o l d i n c r e a s e o v e r m i n i n g 10 y e a r s p r e v i o u s l y .
T h e r e a r e a n e s t i m a t e d 50 b i l l i o n t o n s o f c o a l r e s e r v e s i n
2
T hes e a r e f u l l y i r r i g a t e d a c r e s a s r e p o r t e d by t h e SCS
(1978, T a b l e I l i a ) , and do n o t i n c l u d e w a t e r s p r e a d i n g
acreage.
3 The 1.1 mmaf was r e p o r t e d by t h e SCS-USDA (1978, pg.
24).
The DNRC (19 7 7 a, pg. 33) r e p o r t s i r r i g a t e d
a g r i c u l t u r a l c o n s u m p t i v e u s e a s 1 . 5 mmaf.
4See DNRC (1977d, p p . 1 1 -36) f o r e n e r g y r e l a t e d
developm ent p r o j e c t i o n s .
6
e a s t e r n M ontana, w h i c h a r e p r e s e n t l y e c o n o m i c a l l y f e a s i b l e
t o m i n e , i n d i c a t i n g t h a t t h e c o a l i n d u s t r y h a s much room
t o grow.
C o a l m i n i n g by i t s e l f u s e s a l m o s t no w a t e r . 5
In
a d d i t i o n , c u r r e n t l e v e l s o f i n s t a t e e n e r g y p r o d u c t i o n from
coal i s a lso a r e l a t i v e l y i n s i g n i f i c a n t w ater user.
How­
e v e r , d e p e n d i n g on t h e f o rm o f t e c h n o l o g y a p p l i e d , e n e r g y
p ro d u c tio n in th e f u t u r e could r e p r e s e n t a s i g n i f i c a n t
demand f o r w a t e r
( B o r i s and K r u t i l l a ,
pp. 1 0 4 - 1 3 0 ) .
The
s i t u a t i o n a p p e a rs p a r t i c u l a r l y a c u t e g iv en t h a t t h e bulk of
M o n t a n a 's c o a l r e s e r v e s a r e l o c a t e d i n t h e r e l a t i v e l y w a t e r
s c a r c e Tongue and Powder s u b - b a s i n s .
L ikew ise, c u rr e n t
w a t e r de mands f o r m u n i c i p a l and o t h e r i n d u s t r i a l u s e s a r e
in sig n ifican t rela tiv e
to a g r i c u l t u r a l uses.
Legal Issu e s
O w n e r s h i p o f M o n t a n a 's w a t e r r e s o u r c e s i s a l a b y r i n t h
of ta n g le d le g a l is s u e s a t the s t a t e ,
federal
in te rstate ,
and
lev els.5
S t a t e W ater Law
A ll w a t e r i n t h e s t a t e i s d e c l a r e d t o be p u b l i c
p r o p e r t y by t h e s t a t e l e g i s l a t u r e a l t h o u g h t h i s i s c l o u d e d
by l a r g e l y u n s p e c i f i e d f e d e r a l c l a i m s ( d i s c u s s e d l a t e r i n
5See B o r i s and K r u t i l l a (1980, pp. 9 4 -104) f o r a d e s c r i p ­
t i o n o f t h e c o a l m i n i n g p r o c e s s and r e l a t e d w a t e r u s e .
5A good d e s c r i p t i o n o f w a t e r r e l a t e d l a w s and l e g a l
i s s u e s c a n b e f o u n d i n B o r i s a n d K r u t i l l a ( 1 9 8 0 , c h . 2 & 3)
and DNRC (19 7 7 n , p p . 4 5 - 5 4 ) .
7
t h i s chapter)
However,
estab lish
(M o n t. Code A n n o t . , 1 9 7 9 , 8 5 - 2 - 1 0 1 , s e c t . I ) .
s t a t e l a w a l l o w s i n d i v i d u a l s and e n t i t i e s t o
t h e r i g h t t o d i v e r t and u se w a t e r i n t h e s t a t e .
W a t e r u s e r i g h t s a r e b a s e d on t h e d o c t r i n e o f p r i o r a p p r o ­
p riatio n .
T his d o c tr in e ,
a d o p t e d i n Montana i n 18 6 5 ,
e s s e n t i a l l y s t a t e s t h a t r i g h t s to use w a te r a re c h ro n o lo g i­
c a l l y o r d e r e d , w ith t h e o l d e s t r i g h t s having t h e h i g h e s t
p r i o r i t y , i.e ., " f i r s t in tim e , f i r s t in rig h t".
Use
r i g h t s under p r i o r a p p r o p r i a t i o n a r e a l s o s u b j e c t to a
number o f o t h e r c o n d i t i o n s ,
t h e p r i m a r y one b e i n g t h a t t h e
w a t e r be p u t t o " b e n e f i c i a l u s e " ,
(Mont. Code A n n o t . ,
1979,
a s d e f i n e d by t h e s t a t e
85-2-102,
sect.
2).
The p r o c e s s
by w h i c h w a t e r r i g h t s a r e e s t a b l i s h e d h a s gone t h r o u g h some
m o d if ic a tio n s over tim e.
Many o f t h e e a r l y w a t e r r i g h t s
w e r e e s t a b l i s h e d s i m p l y by p u t t i n g t h e w a t e r t o u s e (Bowman
and L e s s l e y , p. 4 ).
I n many c a s e s t h e r e was no r e c o r d of
d a t e or q u a n t i t y o f w a t e r a s s o c i a t e d w i t h t h e s e r i g h t s .
L a t e r o n , r i g h t s w e r e e s t a b l i s h e d by p o s t i n g n o t i c e o f
i n t e n t t o d i v e r t w a t e r and f i l i n g t h e n o t i c e w i t h t h e
c o u n t y c l e r k and r e c o r d e r
T hes e use r i g h t s ,
(Bowman and L e s s l e y ,
p. 4).
accum ulated over the y e a rs , a re often
c o n f u s i n g and o v e r l a p p i n g .
The Montana W a t e r Use A ct o f
1973 s e t i n m o t i o n a s t a t e - w i d e p e r m i t s y s t e m f o r use
r i g h t s and m a n d a t e d a c o m p l e t e a d j u d i c a t i o n o f e x i s t i n g
w ater
rig h ts
(Mont. Code A n n o t . ,
1979,
8 5 - 2 , p a r t 2).
8
The a d j u d i c a t i o n p r o c e s s r e q u i r e s t h a t h o l d e r s o f
w a t e r r i g h t s p r i o r t o J u l y I , 1973 f i l e n o t i c e o f s u c h
r i g h t s w i t h t h e DNRC s o t h a t a l l r i g h t s e x i s t i n g a s o f t h a t
d a t e c a n be e v a l u a t e d and q u a n t i f i e d s i m u l t a n e o u s l y by a
c o u rt proceeding.
From t h a t p o i n t on, new r i g h t s w i l l be
i s s u e d by t h e DNRC, and a l l a p p l i c a t i o n s w i l l be h a n d l e d by
th at
agency.
The W a t e r Use A c t o f 1973 a l s o r e c o g n i z e d a n d g r a n t e d
l e g a l s t a n d i n g f o r i n s t r e a m u s e s o f w a t e r and i n i t i a t e d t h e
p r o c e s s whereby governm ent a g e n c ie s , but n o t i n d i v i d u a l s ,
could apply f o r r e s e r v a t i o n of w a te r fo r p r e s e n t or f u t u r e
b e n e f i c i a l use.
T h ese r e s e r v a t i o n s c o u l d a p p l y t o b o t h
i n s t r e a m and w i t h d r a w a l u s e .
F e d e r a l l y R e s e r v e d W ater
F u rth er co m p lica tin g th e le g a l s ta tu s of w ater reso u r­
ces i s th e e x i s t e n c e of u n s p e c i f i e d q u a n t i t i e s of w a te r
r e s e r v e d f o r t h e Crow and N o r t h e r n Cheyenne I n d i a n r e s e r v a ­
tions,
T h e s e r e s e r v e d w a t e r s , h i n g e d on t h e W i n t e r s
D o c trin e of 1908, e s s e n t i a l l y g u a r a n te e a d e q u a te w a te r to
m e e t t h e f u t u r e demands o f t h e r e s e r v a t i o n , w h a t e v e r t h a t
f u t u r e demand may be.
T his p la c e s p o t e n t i a l l y l a r g e
de mands on t h e w a t e r o f t h e Y e l l o w s t o n e R i v e r and s p e c i f i ­
c a l l y on t h e B i g h o r n and Tongue s u b - b a s i n s .
The Wind R i v e r
I n d i a n R e s e r v a t i o n i n N o r t h e r n Wyoming a l s o h a s p o t e n t i a l
i m p a c t s on t h e i n f l o w o f t h e B i g h o r n R i v e r i n t o Montana i n
th is
regard.
9
O t h e r f e d e r a l e s t a b l i s h m e n t s i n t h e b a s i n , s u c h as
m ilita r y re s e rv a tio n s , n a tio n al f o r e s ts , w ilderness areas,
et cetera,
a re su b je c t to w ater r e s e r v a tio n s in a s im ila r
manner.
The Y e l l o w s t o n e R i v e r Compact
The f i n a l c o m p l i c a t i n g l e g a l a r e a w i t h r e g a r d t o t h e
Y ellow stone B asin i s i n t e r s t a t e
P rim arily,
com petition fo r w ater.
t h e i s s u e i s t h a t o f d e c i d i n g how t h e w a t e r o f
t h e Y e l l o w s t o n e and i t s t r i b u t a r i e s s h o u l d be d i v i d e d
b e t w e e n Montana and Wyoming.
T h is i s s u e i s embodied in t h e
Y e l l o w s t o n e R i v e r Compact (Mont. Code A n n o t . ,
1979,
85-20).
The c o m p a c t , r a t i f i e d by C o n g r e s s i n 19 5 1 , i s b e t w e e n t h e
tw o s t a t e s , b u t a l s o i n c l u d e d N o r t h D a k o ta a s a s i g n a t o r y
s t a t e s i n c e t h e a c t i o n s of t h e o t h e r two s t a t e s d i r e c t l y
a f f e c t w a te r a v a i l a b l e i n North Dakota.
The c o m p a c t , and
t h e c o m m i s s i o n s e t up t o a d m i n i s t e r i t ,
has th e s e prim ary
featu res:
first,
to recognize a p p ro p ria tiv e r i g h ts to
b e n e f i c i a l u se s o f w a te r in each s i g n a t o r y s t a t e a s of
January I ,
1950? s e c o n d , t o s p e c i f y t h e s h a r e s o f u n a p p r o ­
p r i a t e d w a t e r i n t h e t r i b u t a r i e s t o be a l l o c a t e d t o Montana
and Wyoming? t h i r d ,
t o g i v e e a c h s i g n a t o r y s t a t e v e t o power
over t r a n s f e r s of w ater out of th e b a sin .
Two c o n s e q u e n c e s a r e i m p o r t a n t r e g a r d i n g t h e
Y e l l o w s t o n e Compact.
F irst,
to d a t e , th e d i v i s i o n of
u n a p p r o p r i a t e d w a t e r b e t w e e n Montana and Wyoming a s s p e c i ­
f i e d i n t h e compact has n o t been a p p l i e d , bu t i t a p p e a rs
10
t h a t t h e t i m e i s r a p i d l y a p p r o a c h i n g when s u c h a p p l i c a t i o n
w i l l be n e c e s s a r y .
S e c o n d l y , t h e Compact h a s no i m p a c t on,
or le g a l sta n d in g w ith , the w a te rs re se rv e d fo r th e Indian
R e se rv a tio n s in th e b a sin ,
th e r e f o r e th e a b i l i t y of the
Compact t o r e s o l v e i n t e r s t a t e w a t e r i s s u e s i s h i n d e r e d .
The W ater Pro b lem
The q u e s t i o n o f t h e a d e q u a c y o f w a t e r i n t h e Y e l l o w ­
s t o n e B a s i n t o m e e t c u r r e n t and f u t u r e dem ands i s n o t an
e a s y one.
The a d j u d i c a t i o n o f c u r r e n t w a t e r . r i g h t s i n t h e
b a s i n i s u n d e r way b u t may t a k e a s l o n g a s 1 5 - 2 0 y e a r s t o
com plete.^
T h i s makes r e s o l u t i o n o f new a p p l i c a t i o n s f o r
r i g h t s very d i f f i c u l t in th e in te rim .
Thu s, t h e e x i s t e n c e
o f c o n f l i c t s b e t w e e n p r e s e n t u s e s , new u s e s and w a t e r
re s e r v e d f o r f u t u r e use i s u n c le a r .
I t is clear,
however,
t h a t t h e q u e s t i o n o f a d e q u a c y m u s t be a n s w e r e d i n t h e
c o n t e x t o f f l o w s a t s p e c i f i c l o c a t i o n s and p o i n t s i n t i m e .
T h e r e a r e t w o t i m e d i m e n s i o n s t o be d i s t i n g u i s h e d , t e m p o r a l
v ariatio n s,
i.e.,
v a r i a t i o n i n f l o w fr o m y e a r t o y e a r ,
intertem poral v a ria tio n s ,
the year.
Water s h o r t a g e s ,
i.e.,
and
v a r i a t i o n in flow w ith in
to the e x te n t th a t they e x is t
o r w i l l d e v e l o p , a r e t i m e and s i t e s p e c i f i c .
W h i l e i t may
be t r u e t h a t t h e r e i s enough w a t e r in t h e b a s i n t o m eet
^ P r e l i m i n a r y r e s u l t s w i l l be a v a i l a b l e i n t h e i m m e d i a t e
f u t u r e b u t f i n a l l e g a l d e c r e e s may be many y e a r s h e n c e .
( T e l e p h o n e c o n v e r s a t i o n w i t h Mike McLane, A d j u d i c a t i o n
P r o g r a m M a n ag e r, DNRC, S e p t e m b e r 1 3 , 1982).
.
11
demands i n t o t a l ,
basin th a t,
i t i s tr u e t h a t th e re a re a re a s in the
a t c e r t a i n tim es during th e y ear, p re s e n tly
appear to experience sh o rtag es of w ater.
In th e p l a i n s re g io n , c r i t i c a l l y
low f l o w s , approach™
i n g no f l o w s i n some s t r e a m s , o c c a s i o n a l l y o c c u r i n t h e
f a l l c a u s in g s e r i o u s w a te r a v a i l a b i l i t y problem s fo r both
irrig ato rs
and f i s h a nd w i l d l i f e
(DNRC 1977a, p. 17).
As
demands f o r w a t e r grow t h e s e s i t u a t i o n s w i l l w o r s e n .
I n t h e e a r l y 70®s , a b o u t t h e t i m e t h a t t h e Montana
W a t e r Use Act was p a s s e d ,
c o al developm ent in th e b a sin
began gro w in g a t a r a p i d r a t e .
T h i s r e s u l t e d i n a wave o f
c o n s t e r n a t i o n r e g a r d i n g w a t e r r e s o u r c e s i n t h e b a s i n and
was t h e s o u r c e o f much r e s e a r c h t o i d e n t i f y p o s s i b l e
s o l u t i o n s t o c o n f l i c t s among c o m p e t i n g w a t e r u s e r s .
o f t h e r e s e a r c h was c a r r i e d on by t h e DNRC.®
years,
Much
In re c e n t
t h e r a t e o f c o a l d e v e l o p m e n t h a s s l o w e d and w h i l e
th e p a n i c - o r i e n t e d c o n ce rn s i n i t i a l l y e x p re s s e d have no t
m a t e r i a l i z e d , t h e r e i s every i n d i c a t i o n t h a t coal develop­
m e n t w i l l c o n t i n u e t o grow a s w i l l o t h e r i n d u s t r i a l and
a g r ic u ltu r a l uses.
T h u s, s o l u t i o n s t o t h e s e p r o b l e m s a r e
as im p o rta n t as ev er.
T h es e s o l u t i o n s m u st d e a l w i t h two
c o m p o n e n t s ; t h e p h y s i c a l and h y d r o l o g i c a l c h a r a c t e r i s t i c s
of the b a sin ,
®Much
Study,
and a
1977a,
i.e.,
when and w h e r e w a t e r i s a v a i l a b l e ,
o f t h i s work i s e m b o d ie d i n t h e Y e l l o w s t o n e I m p a c t
a s e r i e s o f e l e v e n t e c h n i c a l r e p o r t s (DNRC, 1977d-n)
f i n a l r e p o r t (DNRC, 1 9 8 1 ).
See a l s o DNRC (1975,
1977b, 1 9 7 7 c ) .
12
and t h e l e g a l q u e s t i o n s o f t h e s i z e and p r i o r i t y o f r i g h t s
t o use t h e , a t t i m e s ,
l i m i t e d s u p p l y o f w ater.
P ossible Solutions
What k i n d s o f s o l u t i o n s a r e a v a i l a b l e t o s o l v e t h e s e
problem s?
The DNRC r e c o g n i z e s t h r e e p o s s i b l e s o l u t i o n s ?
w a t e r r e s e r v a t i o n s , a d d i t i o n a l s t o r a g e , and i m p r o v e d w a t e r
management ( 1 9 7 7 a , p .
71).
The u s e o f w a t e r r e s e r v a t i o n s , p r o v i d e d f o r i n t h e
W a t e r Use A ct o f 1973, a l l o w s p u b l i c a g e n c i e s t o p r o v i d e
f o r f u t u r e w a t e r demands a n d , i m p o r t a n t l y , r e c o g n i z e s and
p r o t e c t s i n s t r e a m u s e s f o r f i s h an d w i l d l i f e , h e a l t h , and
r e c r e a tio n a l purposes.
W ater r e s e r v a t i o n s w e r e d e s i g n e d t o
u n t a n g l e so m e o f t h e l e g a l h e a d a c h e s a n d t o p r o v i d e a
f r a m e w o r k f o r a l l o c a t i n g w a t e r among a l t e r n a t i v e u s e s .
I n c r e a s e d s t o r a g e c a p a c i t y p r o v i d e s a means o f s o l v i n g
some o f t h e s p a t i a l and i n t e r t e m p o r a l w a t e r d i s t r i b u t i o n
problem s.
However, t h e . i s s u e o f i n c r e a s e d s t o r a g e c a p a c i t y
r a i s e s much c o n c e r n o v e r who w i l l b u i l d , c o n t r o l , and
a d m in iste r the f a c i l i t i e s ,
who w i l l g e t t o u s e t h e w a t e r
and, p a r t i c u l a r l y , t h e p r e s e r v a t i o n o f f i s h e r i e s ,
h a b i t a t and l o w - l y i n g a g r i c u l t u r a l l a n d s .
w ild life
These i s s u e s
make i t a p p e a r t h a t i n s t r e a m s t o r a g e f a c i l i t i e s a r e
p o l i t i c a l l y i n f e a s i b l e in v i r t u a l l y a l l a re a s of the
13
b asin .9
T h i s r e q u i r e s t h e u s e o f more e x p e n s i v e o f f s t r e a m
s to r a g e to im plem ent t h e s to r a g e a l t e r n a t i v e .
I t would
a p p e a r t h a t t h e r e is. enough d i s a g r e e m e n t and d i s c o n t e n t
a b o u t i n c r e a s e d s t o r a g e t h a t i t w i l l n o t be a v i a b l e
a l t e r n a t i v e to so lv e a l l of th e w a ter problem s in th e
Y ellow stone Basin.
The t h i r d a l t e r n a t i v e p r o p o s e s b e t t e r m an ag em en t o f
w a ter being c u r r e n t l y used, p r i m a r il y fo r i r r i g a t i o n , to
c o n s e r v e w a t e r and i n c r e a s e a v a i l a b i l i t y f o r o t h e r u s e s .
C u r r e n tly , o v e r a l l i r r i g a t i o n e f f i c i e n c y in th e Y ellow stone
R i v e r B a s i n i s a b o u t 19 p e r c e n t (SCS-USDA, 1978, T a b l e
Ilia).
In o th e r w ords, l e s s th an o n e - f i f t h of th e w ater
d i v e r t e d f r o m t h e r i v e r i s u s e d c o n s u m p t i v e l y by a g r i c u l ­
t u r a l crops.
T h e r e i s much c o n c e r n o v e r t h e o t h e r
f o u r - f i f t h ' s t h a t i s taI o s t t5.
I t w o u ld a p p e a r t h a t t h e r e i s
i n d e e d some room f o r w a t e r c o n s e r v a t i o n t h r o u g h b e t t e r
r i v e r m an a g em en t.
I n c r e a s i n g t h e l e v e l of i r r i g a t i o n
e f f i c i e n c y would red u c e t h e d i v e r s i o n r e q u i r e m e n t f o r i r r i ­
gation.
However, t h e r e a r e some i m p l i c a t i o n s o f t h i s
c o n s e r v a t i o n t h a t h a v e , a t l e a s t t o some e x t e n t , b e e n
overlooked.
T h i s s t u d y p r o p o s e s t o e x a m in e and d e v e l o p ,
in
9The A l l e n s p u r dam s i t e , one o f t h e more p r o m i s i n g r e s e r ­
v o i r s i t e s f r o m a r i v e r m an ag em en t s t a n d p o i n t , was t h e
s u b j e c t o f a j o i n t r e s o l u t i o n o f t h e 1974 Montana L e g i s l a ­
t u r e a s b e i n g c o n t r a r y t o s t a t e g o a l s and o b j e c t i v e s (DNRC,
1975, pg. 2).
_________________________ :______________________________________________________________________
14
some d e t a i l ,
t h e s e i m p l i c a t i o n s , and e v a l u a t e t h e e c o n o m ic
i m p a c t o f a l t e r n a t i v e r i v e r m anagem ent p o l i c i e s on t h e
Y e l l o w s t o n e B a s i n and t h e s t a t e o f Montana,
I r r i g a t i o n and R e t u r n Flows
As s t a t e d p r e v i o u s l y , a p p r o x i m a t e l y 80 p e r c e n t o f t h e
w a t e r d i v e r t e d f r o m t h e r i v e r i s l o s t fro m t h e i r r i g a t i o n
s y s t e m b e f o r e b e i n g u s e d by a g r o n o m i c c r o p s .
However,
r o u g h l y 90 p e r c e n t o f t h a t t8I o s t ra w a t e r e v e n t u a l l y r e t u r n s
to th e r i v e r as r e t u r n flows.
The r e m a i n i n g w a t e r i s t r u l y
" lo s t* t o t h e s u r f a c e flow system because i t e v a p o r a te s ,
p e r c o l a t e s i n t o deep groundw ater a q u i f e r s ,
e t cetera.
The
r e t u r n f l o w s e n t e r t h e r i v e r a f t e r some t i m e d e l a y and
d o w n s t r e a m fr o m t h e o r i g i n a l d i v e r s i o n p o i n t .
T h es e r e t u r n f l o w s , a l t h o u g h s u b t l e i n t h e i r i n t e r ­
a c tio n w ith th e h y d ro lo g ic system , a re n e v e r th e le s s a
s i g n i f i c a n t f a c to r in th e flow of th e r i v e r .
I t has long
been rec o g n ize d t h a t w a te r r e e n t e r i n g th e r i v e r as r e tu r n
f l o w s can be r e u s e d .
in C a lifo rn ia ,
t h e same w a t e r ,
T e e l e , d e s c r i b i n g t h e S a n t a Ana R i v e r
i n 1915, s t a t e s ?
" I t i s thus e v id e n t t h a t
in p a s s i n g from m ountain t o s e a ,
a distance
o f n o t m o r e t h a n 100 m i l e s , may b e u s e d a t l e a s t e i g h t
t i m e s f o r p ower and i r r i g a t i o n
(pip. 2 3 - 2 4 ) S o i l C o n s e r ­
v a tio n S e rv ic e f i g u r e s in d ic a t e t h a t annual r e t u r n flow s in
t h e Y e l l o w s t o n e a r e a b o u t 3.1 mmaf, o v e r o n e - t h i r d o f t h e
av erag e an n u al flow of th e r i v e r as m easured a t Sidney
(SCS-USDA, 1 9 78).
15
More i m p o r t a n t . a r e t h e i m p l i c a t i o n s f o r t h e d i s t r i b u ­
t i o n of w a ter flow thoughout th e y e a r.
The m o s t c r i t i c a l
p e rio d re g a rd in g w ater a v a i l a b i l i t y „ a t th e p r e s e n t tim e,
a r e t h e m o n th s o f A u g u s t and S e p t e m b e r when r e l a t i v e l y lo w .
r i v e r flow i s coupled w ith high d i v e r s i o n of w ater for
irrig atio n .
G iv e n t h a t r e t u r n f l o w s a r e d e l a y e d som ewhat
a f t e r d i v e r s i o n , t h e b u l k o f w h i c h o c c u r s i n t h e May t o
Septem ber i n t e r v a l , s i g n i f i c a n t p o r t i o n s of th e p r e s e n t
l e v e l s o f l a t e summer f l o w of t h e r i v e r a r e due t o r e t u r n
flow s.
The DNRC ( 1 9 7 7 a ) , r e c o g n i z i n g t h e s i g n i f i c a n c e o f
re tu rn flow s s t a t e ,
" I n many a r e a s w a t e r u s e r s h ave l e g a l
r i g h t s t o w a t e r l o s t by i r r i g a t o r s a b o v e t h e m ,
and t h e i r
r i g h t s c o u l d b e a d v e r s e l y , a f f e c t e d b y t h e u s e o f mo r e
e fficien t
irrig atio n
p r a c t i c e s , (p.
72)".
W ater Q u a l i t y
The q u a l i t y o f r e t u r n f l o w w a t e r i s u s u a l l y l o w e r t h a n
i t was b e f o r e d i v e r s i o n due t o t h e i n t r o d u c t i o n o f s a l t s ,
p e s t i c i d e s , s e d i m e n t a r y m a t e r i a l a n d / o r o r g a n i c m a t t e r . 1®
I n some a r e a s o f i r r i g a t e d a g r i c u l t u r e i n t h e W e s t e r n
U nited S t a t e s ,
th is q u a lity issue is c r i t i c a l .
For
e x a m p l e , p o r t i o n s o f t h e Upper Rio Grande V a l l e y and much
o f t h e C o l o r a d o R i v e r B a s i n a r e c h a r a c t e r i z e d by s e v e r e
s a l i n i t y p r o b l e m s and t h e q u a l i t y c o m p o n e n t o f t h e r e t u r n 10
1 0 See Boone (1976) and DNRC ( 1 9 7 7 f , pp. 7 7-80) f o r more
d e t a i l e d d i s c u s s i o n s of w a te r q u a l i t y a s p e c ts of r e t u r n
flow s.
16
flow i s s u e i s c r i t i c a l .
The Y e l l o w s t o n e B a s i n i s somewhat
u n i q u e i n t h i s r e s p e c t f o r tw o r e a s o n s .
F irst,
th e basin
i s c h a r a c t e r i z e d by u n u s u a l l y h i g h q u a l i t y s u r f a c e w a t e r i n
g e n e r a l , and s e c o n d , t h e r e i s a l a c k o f i n d i c a t i o n o f
w idespread w ater q u a li t y d e g ra d a tio n throughout the basin.
W h i l e c e r t a i n a r e a s o f t h e b a s i n may p r e s e n t p o t e n t i a l
q u a l i t y problem s i t does n o t appear t h a t t r e a t i n g r e t u r n
f l ows in t he e n t i r e b a sin as p r i m a r i l y a q u a l i t y is s u e is
ap propriate.
Fo r t h i s r e a s o n t h i s s t u d y w i l l n o t d e a l w i t h
t h e q u a l i t y i s s u e and w i l l c o n c e n t r a t e i n s t e a d on t h e
q u a n t i t y and d i s t r i b u t i o n a l c o m p o n e n ts o f w a t e r i n t h e
Y ellow stone Basin.
The c o n s e r v a t i o n o f w a t e r t h r o u g h b e t t e r r i v e t manage­
m en t a s a s o l u t i o n t o t h e w a t e r p r o b l e m i n t h e Y e l l o w s t o n e
B a s i n h a s r e c i e v e d much a t t e n t i o n .
T his i s u n d e rs ta n d a b le
b e c a u s e i t a p p e a r s t o b e an o b v i o u s a l t e r n a t i v e .
I t allow s
c o n s e r v a t i o n o f w a t e r f o r a l t e r n a t i v e u s e s and s i m u l t a n e ­
o u sly c o n tr i b u te s to th e m aintenance of w ater q u a li t y .
In
a d d i t i o n , i t i s n o t p l a g u e d w i t h t h e l e g a l and p o l i t i c a l
c o n t r o v e r s i e s s u r r o u n d i n g t h e . w a t e r r e s e r v a t i o n and s t o r a g e
altern ativ es.
I t appears t h a t th e re a re s i g n i f i c a n t u n d e sirab le
e c o n o m ic i m p l i c a t i o n s o f p r o p o s e d r i v e r m an agem en t
p o licies.
S p e c i f i c a l l y , p o l i c i e s which a re d i r e c t e d to w a rd
im proving th e o v e r a l l e f f i c i e n c y of w ater used f o r i r r i g a ­
t i o n may r e s u l t i n a r e d u c t i o n i n t h e q u a n t i t y o f r e t u r n
17
flow i n th e r i v e r ,
i.e.,
may c h a n g e t h e d i s t r i b u t i o n o f
r i v e r flow throughout th e y ear.
T h e r e f o r e , p o l i c i e s of
i n c r e a s e d e f f i c i e n c y o f w a t e r u s e may a l t e r t h e a d e q u a c y o f
t h e r i v e r t o m e e t w i t h d r a w a l and i n s t r e a m u s e s ,
even a t
c u r r e n t e c o n o m i c l e v e l s and a v e r a g e r i v e r f l o w s .
Increased
e f f i c i e n c y p o l i c i e s a l s o have i m p l i c a t i o n s f o r o t h e r r i v e r
m an a g em en t p o l i c i e s s u c h a s , i r r i g a t i o n p r o j e c t d e v e l o p m e n t
and r e s e r v o i r c o n s t r u c t i o n .
T h es e i m p l i c a t i o n s a r e even
more e x a g g e r a t e d i n l i g h t o f o t h e r v a r i a b l e s s u c h as?
v ariatio n
in th e p h y s ic a l system ,
i.e.,
runoff, p re c ip ita ­
t i o n , e v a p o r a t i o n ? f u t u r e e c o n o m ic g r o w t h i n t h e b a s i n ? and
o t h e r economic c o n d i t i o n s ,
ag ricu ltu ral
i.e.,
l e v e l of p r i c e s fo r
products.
O bjectives
The p u r p o s e o f t h i s s t u d y i s t o e x a m in e t h e e c o n o m ic
i m p l i c a t i o n s o f c u r r e n t r i v e r m an ag em en t p o l i c i e s ,
Y ellow stone River B asin.
in the
T h i s w i l l be a c c o m p l i s h e d by
com pleting th e fo llo w in g o b je c tiv e s :
(1)
D e v e l o p m e n t o f a model o f t h e Y e l l o w s t o n e R i v e r
B a s i n , t h a t i n c o r p o r a t e s t h e a p p r o p r i a t e e c o n o m i c and
h y d r o l o g i c t h e o r y and p o l i c y f a c t o r s t o e v a l u a t e c u r r e n t
m an a g em en t p o l i c i e s .
(2)
E v a l u a t i o n of th e econom ic im p a c ts o f i n c r e a s e d
e f f i c i e n c i e s o f w a t e r u s e by p a r a m e t r i c a l l y i n c r e a s i n g t h e
l e v e l o f e f f i c i e n c y o f w a t e r u s e i n t h e m o d e l.
18
(3)
E v a l u a t i o n o f c u r r e n t m an ag em en t p o l i c i e s i n
l i g h t o f o t h e r p h y s i c a l and e c o n o m ic f a c t o r s , s u c h a s
low er-than-average r iv e r flow s, a lte r n a tiv e p ric e le v e ls
and f u t u r e a g r i c u l t u r a l d e v e l o p m e n t , and d i s c u s s i o n o f
t h e s e i m p l i c a t i o n s i n r e l a t i o n t o o t h e r m an ag em en t a l t e r n a
tiv es.
19
C hapter 2
Economic and H y d r o l o g i c T h eo ry
The p u r p o s e s o f t h i s c h a p t e r a r e t o s e t f o r t h t h e
h y d r o l o g i c and e c o n o m i c t h e o r y a p p r o p r i a t e t o an u n d e r ­
s t a n d i n g o f t h e s i t u a t i o n p r e s e n t e d i n C h a p t e r I and t o
d i s c u s s . (I) t h e i m p l i c a t i o n s and l i m i t a t i o n s o f s u c h t h e o r y
i n t h e l i g h t o f d a t a a v a i l a b i l i t y and o t h e r f a c t o r s and (2)
t h e a d a p t a t i o n s n e c e s s a r y in o rd e r to use t h e t h e o r y to
achieve q u a n t i f ic a t i o n of the s t a te d o b je c tiv e s .
H y d ro lo g ic Theory
An u n d e r s t a n d i n g o f t h e e c o n o m ic i m p a c t s o f a l t e r n a ­
t i v e r i v e r m an a g em en t p o l i c i e s r e q u i r e s a t l e a s t a c u r s o r y
u n d e rstan d in g of th e h y d ro lo g ic p ro c e sse s involved.
The
h e a r t of t h e problem s e t f o r t h in C hapter I i s h y d rology.
C o n s e q u e n t l y , t h i s s e c t i o n o f t h e c h a p t e r w i l l be d e v o t e d
to a g en eral in tro d u c tio n to hydrologic th eo ry , a d isc u s­
sio n of stream flo w hydrology in p a r t i c u l a r ,
and an
i n t r o d u c t i o n t o t h e r e s p o n s i v e n e s s o f t h e h y d r o l o g i c system
I
t o human i n t e r v e n t i o n . 1
1The g e n e r a l h y d r o l o g y and r u n o f f s e c t i o n s draw h e a v i l y
on Ward ( 1 9 7 5 , c h s . 1 , 8 ) .
20
W a t e r o c c u r s s i m u l t a n e o u s l y on, u n d e r and ab o v e t h e
e a r t h ' s s u r f a c e in a v a r i e t y of f o rm s , each of which i s a
c o m p o n e n t o f a c o m p l e x , c o n t i n u o u s l y moving h y d r o l o g i c
cycle.
Figure I d e p ic ts a s im p lif ie d re p r e s e n ta tio n of the
m a j o r c o m p o n e n ts o f t h e h y d r o l o g i c c y c l e .
T his study i s
p r i m a r i l y c o n c e r n e d w i t h t h e o c c u r r e n c e o f w a t e r on o r n e a r
t h e e a r t h ' s s u r f a c e and i t s
a v a i l a b i l i t y fo r use.
G r o u n d w a t e r p u m pin g i n t h e Y e l l o w s t o n e B a s i n r e p r e ­
s e n t s a r e l a t i v e l y i n s i g n i f i c a n t q u a n t i t y o f w a t e r and
v i r t u a l l y no g r o u n d w a t e r i s pumped f o r i r r i g a t i o n .
fore,
There­
a d e q u a t e m o d e l i n g o f h y d r o l o g y and w a t e r u s e i n t h e
Y e l l o w s t o n e B a s i n , f o r p u r p o s e s o f t h i s s t u d y , c a n be
a c c o m p l i s h e d w i t h a h y d r o l o g i c a l model t h a t c o n c e n t r a t e s on
t h e s t r e a m f lo w or r u n o f f component o c c u r r i n g i n th e b a s i n .
I g n o r i n g g r o u n d w a t e r pumping r e p r e s e n t s a s i g n i f i c a n t
s i m p l i f i c a t i o n of t h e r e t u r n flow problem b ecau se groundw a t e r and s t r e a m f l o w s y s t e m s a r e v e r y o f t e n i n t e g r a l l y
r e l a t e d v i a t h e r e t u r n flow mechanism.
B u r t (1964) p r e ­
s e n t e d t h e a p p l i c a t i o n o f d y n a m i c p r o g r a m m in g t o p r o b l e m s
o f c o n j u n c t i v e g r o u n d and s u r f a c e w a t e r .
B redehoeft
Young and
(1972) a d d r e s s e d i s s u e s o f c o n j u n c t i v e g r o u n d
and s u r f a c e w a t e r u se a lo n g t h e S outh P l a t t e R iv e r in
C o l o r a d o a s d i d McConnen and Menon (1968) and Boyd (1968)
in the G a lla tin V alley,
M ontana.
21
Interception
W ater vapour
Soil- m o i s t u r e
Gr oundwa t e r
flow
Figure I.
Sirplified Diagram of the Hydrological Cycle.
(Fran Ward, 1975)
22
Runoff
R u n o f f i s t h e g r a v i t a t i o n a l l y m o t i v a t e d movement o f
w a t e r i n t o and t h r o u g h c h a n n e l s on t h e e a r t h ’s s u r f a c e .
H y d r o l o g i c a l l y f r u n o f f o c c u r s when p r e c i p i t a t i o n e x c e e d s
e v a p o t r a n s p i r a t i o n and s t o r a g e i n and on t h e g r o u n d
surface.
However, an i m p o r t a n t a s p e c t o f r u n o f f i s t h a t , ,
w h i l e t h e o c c u r r e n c e of p r e c i p i t a t i o n t e n d s t o be v e ry
d i s j o i n t and i r r e g u l a r ,
th e r e s u l ti n g stream flow tends to
be r e l a t i v e l y c o n s t a n t .
T h i s i s due p r i m a r i l y t o t h e
s t o r a g e c a p a c i t y o f t h e u p p e r l a y e r s o f s o i l on t h e e a r t h
w h i c h s m o o t h and d e l a y s u b s u r f a c e c o n t r i b u t i o n s t o s t r e a m flow .
F ig u re 2 p r e s e n t s a d i a g r a m a t i c r e p r e s e n t a t i o n of
t h e s p e c i f i c c o m p o n e n ts o f r u n o f f .
T h es e a r e c h a n n e l
p r e c i p i t a t i o n , o v e r l a n d f l o w , i n t e r f l o w and g r o u n d w a t e r ,
flow .
Channel p r e c i p i t a t i o n ,
i.e.,
p recip itatio n d irectly
onto th e stream channel i s u s u a lly a r e l a t i v e l y sm a ll
component of r u n o f f , b e in g d i r e c t l y p r o p o r t i o n a l to th e
a r e a o f t h e c a t c h m e n t b a s i n t h a t i s o c c u p i e d by s t r e a m
channels,
in s e m i- a r id re g io n s l i k e th e Y ello w sto n e Basin,
t h i s p ro p o rtio n i s q u ite sm all.
w ater f a i l s to i n f i l t r a t e
O v e r l a n d f l o w o c c u r s when
t h e s o i l and t r a v e l s o v e r t h e
s u rfa c e to the stream channel.
F a i l u r e t o i n f i l t r a t e can
o c c u r f o r a number o f r e a s o n s ? i m p e r v i o u s s o i l s u b s t a n c e
(bedrock,
e tc .),
s o il s a tu ra tio n during.high p r e c ip ita tio n
or fro z e n s o i l s u r f a c e .
O verland flo w i s a l s o u s u a l l y a
23
BASIN PRECIPITATION
(excluding s t o r a g e interception
and o t h e r los se s)
INFILTRATION
CHANNEL
PRECIPITATION
INTERFLOW
(subsurface
stemflow)
OVERLAND
FLOW
RAPID
INTERFLOW
GROUNDWATER
FLOW
DE L A/ED
INTERFLOW
chonnel
f l ow
channel
j
~h,_____ T
L
SURFACE
RUNOFF I
SUBSURFACE
RUNOFF
X
QUICKFLOW
BASEFLOW
I
( d i r ec t runoff)
(Dose r u no f f )
i
I
I
I
TOTAL RUNOFF
( s t r e o m f l ow a t Dos m o u t ' e t )
Figure 2.
Diagrammatic Representation of the Runoff
Process.
(Fran Ward, 1975)
24
r e l a t i v e l y s m a l l com pon en t o f r u n o f f b e c a u s e t h e a f o r e m e n ­
t io n e d c o n d it io n s r a r e ly occur over la r g e area s for
e x t e n s iv e p erio d s of tim e.
in d icate
How ever, f l o o d s , f o r e x a m p l e ,
t h a t th e r e are im portant e x c e p t io n s to t h i s .
The w a t e r w h i c h i n f i l t r a t e s t h e s o i l w i l l become
e i t h e r i n t e r f l o w , w h i c h i s t h e s h a l l o w l a t e r a l movement o f
s u b s u r f a c e w a t e r , or g ro u n d w a te r.
d e fin e d as subsurface ru n o ff.
n ents,
T hes e two c o m p o n e n ts a r e
Of a l l t h e r u n o f f compo­
i n t e r f l o w i s th e most im p o r ta n t c o n t r i b u t o r to t o t a l
runoff,
h a v i n g i m p a c t s on i m m e d i a t e r u n o f f ( r a p i d
i n t e r f l o w ) and d e l a y e d r u n o f f
(delayed i n t e r f l o w ) .
Ward
c i t e s e m p i r i c a l h y d r o l o g ic s t u d i e s which i n d i c a t e t h a t
i n t e r f l o w may a c c o u n t f o r 85 p e r c e n t o f s t r e a m f l o w
p.
(Ward,
241).
R u n o f f i s a l t e r n a t i v e l y s u b d i v i d e d i n t o q u i c k f l o w or
storm p e rio d ru n o f f ,
which c o n s i s t s of c h an n e l p r e c i p i ­
t a t i o n , o v e r l a n d f l o w , and r a p i d i n t e r f l o w ; and b a s e f l o w or
d r y p e r i o d r u n o f f , w h i c h c o n s i s t s o f d e l a y e d i n t e r f l o w and
groundw ater c o n t r i b u t i o n t o stre a m flo w .
I t is th is
b a s e flo w which a c c o u n ts f o r th e r e l a t i v e c o n sta n c y of
stream flow d e s p ite i n t e r m i t t e n t p r e c i p i t a t i o n p a tte rn s .
These f a c t o r s i n f l u e n c e th e a n n u al d i s t r i b u t i o n of s tr e a m f l o w t y p i c a l o f t h e Y e l l o w s t o n e and many o t h e r s e m i - a r i d
r e g i o n s of th e West.
S p r i n g and e a r l y summer f l o w s a r e
v e r y h i g h , b e i n g p r e d o m i n a n t l y q u i c k f l o w r e s u l t i n g from
s n o w m e l t and s e a s o n a l r a i n f a l l i n t h e s p r i n g and e a r l y
25
summer.
L a t e summer, f a l l and w i n t e r f l o w s a r e l o w a s i s
p r e c i p i t a t i o n d u r i n g t h a t p e r i o d and s t r e a m f l o w i s
s u s t a i n e d a l m o s t e n t i r e l y by b a s e f l o w .
Hydrograp hs
One o f t h e t o o l s u s e d i n r u n o f f a n a l y s i s i s a h y d r o graph.
A hydrograph i s a g r a p h ic a l p r e s e n t a ti o n of
s t r e a m f l o w volum e p e r u n i t t i m e o v e r t i m e .
A lthough used
i n o t h e r c o n t e x t s , such as i n d i v i d u a l storm r u n o f f a n a l y ­
s i s , t h e h y d r o g r a p h i s a v e r y c o n v e n i e n t way t o i l l u s t r a t e
r i v e r flow thoughout th e y e a r .
The. h y d ro g r a p h o f a v e r a g e
m onthly flo w s of th e Y ello w sto n e R iver a t Sidney for th e
p e r i o d 1934 t o 1980 a r e p r e s e n t e d i n F i g u r e 3.
H y d r o g r a p h s , s u c h a s F i g u r e 3 , a r e an i m p o r t a n t
f o u n d a t i o n upon w h i c h w a t e r m an ag em en t and c o n t r o l p o l i c i e s
are form ulated.
W hile h y d ro g ra p h s s e r v e as a u s e f u l
benchmark of a v a i l a b l e w a te r s u p p l i e s ,
i t i s im perative
t h a t o t h e r f a c t o r s be c o n s i d e r e d i n c o n j u n c t i o n w i t h t h e
hydrograph.
An u n d e r s t a n d i n g o f t h e c o m p o n e n ts i n c l u d e d i n
f l o w s m e a s u r e d i n a h y d r o g r a p h , t h e s t o c h a s t i c n a t u r e of
r u n o f f , and t h e v a r i a t i o n i n f l o w s a t d i f f e r e n t p o i n t s
a l o n g t h e r i v e r m u s t be c o n s i d e r e d a s w e l l .
S t r e a m f l o w and I r r i g a t i o n
H isto rica lly ,
i n many o f t h e a r i d and s e m i - a r i d
r e g i o n s o f t h e w o r l d , t h e q u a n t i t y and d i s t r i b u t i o n o f
s t r e a m f l o w p l a c e d q u i t e r e s t r i c t i v e l i m i t a t i o n s on t h e
26
2250
.
Figure 3.
Average Monthly Flow of the Yellowstone River
at Sidney, Montana, for Water Years 1934-1980.
27
n a t u r e and e x t e n t o f e c o n o m i c a c t i v i t y .
In much o f t h e
W estern U n ited S t a t e s t h i s i s p a r t i c u l a r l y t r u e .
im p o r ta n t, though l e s s o b v io u s , i s
Also very
t h e f a c t t h a t human
a c t i v i t i e s h ave i m p a c t s w h i c h f e e d back i n t o t h e p h y s i c a l
hyd rologic system .
An i m p o r t a n t e x a m p le o f t h i s i s
irri-
/
gated
agricu ltu re.
A g r i c u l t u r a l i r r i g a t i o n s y ste m s t y p i c a l l y d i v e r t water
f r o m t h e r i v e r and c o n v e y i t t o f i e l d s t h r o u g h a n e t w o r k o f
can als,
d i t c h e s and o c c a s i o n a l l y p i p e s .
H owev er , n o t a l l
o f t h e w a t e r d i v e r t e d from t h e r i v e r i s d e l i v e r e d t o th e
fie ld .
Some i s t r a n s p i r e d by d i t c h b a n k f l o r a ,
through o p e r a t io n a l s p i l l s ,
some s e e p s i n t o s u b s u r f a c e
a q u i f e r s and some e v a p o r a t e s .
c a l d e liv e r y system ,
some i s l o s t
The e f f i c i e n c y o f t h e p h y s i ­
conveyance e f f i c i e n c y
(Ec ) ,
i s d efin ed
as th e r a t io of th e q u a n tity of w ater d e liv e r e d to the
f i e l d t o t h e q u a n t i t y o f w a t e r d i v e r t e d f r o m t h e r i v e r or
Ec =
w a t e r deLivet^_±(i_thm_jEl@JLA
Water d i v e r t e d from t h e r i v e r
L ik ew ise, not a l l of the w ater d e liv e r e d to the f i e l d
w i l l b e b e n e f i c i a l l y u s e d by c r o p s .
Some w i l l r u n o f f due
t o e f f e c t s o f t o p o g r a p h y ( s l o p e ) , some w i l l s e e p i n t o
s u b s u r f a c e a q u i f e r s and some w i l l e v a p o r a t e from t h e f i e l d
surface.
T h e s e e f f e c t s can be e x a g g e r a t e d i n some
i n s t a n c e s due t o management i n e f f i c i e n c y t h a t r e s u l t s i n
i m p r o p e r i r r i g a t i o n t i m i n g and q u a n t i t y o f a p p l i c a t i o n .
28
The e f f i c i e n c y o f t h i s c o m b i n a t i o n o f p h y s i c a l and mana­
g e r i a l f a c t o r s a t t h e farm l e v e l
un it e ffic ie n c y .
efficien cy.
i s d efin ed as i r r i g a t i o n
This i s so m etim es r e f e r r e d t o as f i e l d
S p ecifica lly
i r r ig a t io n unit e f f i c i e n c y
(Eu)
i s t h e r a t i o o f t h e q u a n t i t y o f w a t e r b e n e f i c i a l l y u s e d by
c r o p s t o t h e q u a n t i t y o f w a t e r d e l i v e r e d t o t h e f i e l d or
Eu =
W a te r u s e d bv c r o p s
Water d e l i v e r e d t o t h e f i e l d
Ec a n d Eu c a n b e c o m b i n e d t o e x p r e s s a n o v e r a l l
irrig a tio n efficien cy
(E1 ) t h a t i s t h e r a t i o o f t h e q u a n ­
t i t y o f w a t e r b e n e f i c i a l l y u s e d by c r o p s t o t h e q u a n t i t y o f
w a t e r d i v e r t e d f r o m t h e r i v e r or
E
1
-
Water u s e d bv c r o p s
Water d i v e r t e d from t h e r i v e r
T h e s e e f f i c i e n c i e s a r e b a s e d on d e f i n i t i o n s fr o m J e n s e n
(19 67 ).
Brosz
(1981) p r o v i d e s a good summary o f t h e
f a c t o r s involved in i r r i g a t i o n
efficien cy .
The n u m e r o u s s o u r c e s o f l o s s e s f ro m c o n v e y a n c e and
f i e l d s y s t e m s c a n b e g r o u p e d i n t o tw o c a t e g o r i e s ?
a b l e and n o n r e c o v e r a b l e .
recover­
F i g u r e 4 shows t h e b r e a k d o w n o f
i r r i g a t i o n s y s t e m l o s s e s i n t o t h e p r i m a r y c o m p o n e n ts and
th e r e s u l tin g c ateg o ry of rec o v erab le lo sse s.
Recoverable
l o s s e s i n t h i s u s a g e s i m p l y means t h o s e l o s s e s t h a t w i l l
e v e n tu a lly r e tu r n to th e n a t u r a l stre am flo w system .
a r e a l s o known a s r e t u r n f l o w s .
These
S p e c i f i c a l l y r e t u r n flow s
supply source
diversions
losses
crop evapotranspiration
subsurface
surface
“''■-'-.canal evaporation
I
\phreatophyte and
hydrophyte evapotranspiration
seepage from
conveyance system
deep percolation
from fields
operational spills
groundwater
aquifer
tailwater runoff
surface drainages
shallow groundwater
discharge into streamflow
recoverable losses
return flows available
for reuse downstream
Figure 4.
Ccrnponents of Water Loss From Irrigation Systems.
deep groundwater
supplies
30
a r e d e f i n e d , f o r p r e s e n t p u r p o s e s , a s . t h e sum o f s u r f a c e
and s u b s u r r a c e l o s s e s f r o m c o n v e y a n c e and f i e l d s y s t e m s
t h a t r e e n t e r the stre am flo w system .
Figure 5 p rovides a
good r e p r e s e n t a t i o n o f t h e i r r i g a t i o n and r e t u r n f l o w
s y s t e m s and t h e i r r e l a t i o n t o t h e r i v e r or s t r e a m f l o w
system .
R e t u r n f l o w s a r e a c o m p l e x h y d r o l o g i c a l phenomenon.
C o n s e q u e n t l y , w h i l e t h e p r i m a r y c o m p o n e n ts o f r e t u r n f l o w
are id e n tifie d ,
th e c o m p lex ity of r e t u r n flo w s coupled w ith
t h e c o m p l e x i t y o f t h e n a t u r a l h y d r o l o g i c s y s t e m m akes q u a n ­
t i f i c a t i o n of re tu rn flow s d i f f i c u l t .
N i c k l i n and
B r u s t k e r n (1981) d i s c u s s t h e p r o b l e m s f a c e d by h y d r o l o g i s t s
a tte m p tin g to q u a n tify re tu rn flow s.
T h i s b eco m es i m p o r ­
t a n t m e t h o d o l o g i c a l l y i f one p r o p o s e s t o i n v e s t i g a t e t h e
i m p a c t o f r e t u r n f l o w s on t h e n a t u r a l s t r e a m f l o w s y s t e m .
C o n c e p t u a l l y , r e t u r n f l o w s a r e an e x a m p le o f manmade
o v e r l a n d f l o w and s u b s u r f a c e f l o w t h a t c o n t r i b u t e s t o
q u i c k f l o w and b a s e f l o w i n h y d r o l o g i c a l l y t h e same way a s do
n a tu ra l sources.
Of c o u r s e ,
th e q u a n t i t y of r e t u r n flow i s
p r o p o r t i o n a l t o t h e l e v e l of i n e f f i c i e n c y i n t h e c o n v e y a n c e
and f i e l d s y s t e m s and c o n s e q u e n t l y can be c o n t r o l l e d by
changes i n th e l e v e l of t e c h n i c a l e f f i c i e n c y of th e i r r i g a ­
t i o n system .
How ever, one o f t h e c o m p o n e n ts o f t h e
hydrograph of r i v e r flo w s
( F i g u r e 3),
i s r e t u r n flow .
To
th e e x t e n t t h a t a hydrograph i s view ed as a "benchmark” of
a v a ila b le w ater su p p lie s,
i t c a n be m i s l e a d i n g i n t h i s
Precipitation
Inflow to
Canals
Evopotronspirahon
from Crops
Evaporation
from Canals
Upstream
River
Flow
Groundwater
Contribution
Surface Runoff from
Non-lrnaated Land
Diverted
for
Irrigation
Applied to
Irrigated Land
Other
Evapotranspiration
from Irrigated Land
Irrigation
Return Flow
River Flow
Downstream
Ind & Mun.
Wastes
Figure 5.
Natural
Inflow
Conceptual Diagram of the Irrigation Return Flow System. (Fran Waller, 1976)
32
s i t u a t i o n b e c a u s e t h e benchmark w i l l ch a n g e a s t h e q u a n t i t y
o f return f lo w s in th e system changes.
Economic T h e o r y .
The f o l l o w i n g s e c t i o n o f e c o n o m i c t h e o r y s h o u l d accom­
p lish
several goals.
F irst,
it
should e s t a b l i s h th e
g e n e r a l t h e o r e t i c a l n o t i o n o f w a t e r a s an e c o n o m i c good
w i t h r e s p e c t t o b o t h t h e q u a n t i t y and q u a l i t y a s p e c t s o f
water use.
issu e,
W h i l e t h i s s t u d y a b s t r a c t s from t h e q u a l i t y
i t i s an i m p o r t a n t on e t h a t m u st u l t i m a t e l y be
a d d r e s s e d and s h o u l d be i n c l u d e d i n t h e t h e o r e t i c a l f r a m e ­
wo rk,
Second,
th e th e o r y should e s t a b l i s h th e co n cep tu a l
lin k a g e between th e l e v e l of i r r i g a t i o n e f f i c i e n c y
t h e q u a n t i t y and q u a l i t y a s p e c t s o f w a t e r u s e .
(E1) and
Third,
the
t h e o r y s h o u l d d e l i n e a t e b e t w e e n p r i v a t e l y and p u b l i c l y
p e r c e i v e d i m p a c t s o f c h a n g e s i n t h e l e v e l o f E1.
t h e s e ends,
Towards
b e n e f i t / c o s t a n a l y s i s p r o v i d e s an a p p r o p r i a t e
b a s i s f o r e v a l u a t i o n o f c h a n g e s i n t h e l e v e l o f E1.
B e n e f i t / C o s t Framework
When w a t e r i s u s e d a s an i n p u t i n t o t h e p r o d u c t i o n
p r o c e s s o f some p r o d u c t (as o p p o s e d t o i t s v a l u e a s a
c o n s u m p t i o n g o o d ) t h e dem and f o r w a t e r i s s a i d t o b e a
d e r i v e d demand.
That i s ,
i t s v a l u e i s d e r i v e d from t h e
v a l u e o f t h e p r o d u c t s f o r w h i c h w a t e r i s an i n p u t .
t h e demand f o r w a t e r i n a l t e r n a t i v e u s e s i s
Thus,
r e la t e d to the
m a r g i n a l v a l u e p r o d u c t i v i t y (MVP) o f w a t e r i n e a c h u s e .
33
S p ecifically ,
t h e demand f u n c t i o n f o r w a t e r a s an i n p u t
w i l l be e q u a l . t o t h e i n v e r s e . m a r g i n a l v a l u e p r o d u c t i v i t y
c u r v e i n t h e s h o r t r u n when o n l y w a t e r i s a v a r i a b l e
facto r.
In th e lo n g er run,
when o t h e r f a c t o r s a r e v a r i a b l e
and w i l l be s u b s t i t u t e d f o r w a t e r ,
t h e demand f u n c t i o n f o r
w a t e r w i l l b e m o r e e l a s t i c t h a n t h e MVP c u r v e .
re tic a l settin g ,
.
In a th e o ­
where o p tim a l a l l o c a t i o n o f water, i s
a s s u m e d t o o c c u r , o p t i m a l i t y i s a c h i e v e d when t h e m a r g i n a l
value p r o d u c tiv ity of w ater in a l l uses a re equal.
From
t h e s t a n d p o i n t o f w a t e r m an ag em en t p o l i c y , t h e demands f o r
w a t e r a r e e x o g e n o u s l y d e t e r m i n e d and a r e f i x e d i n t h e s h o r t
run.
I t was e x p o u n d ed e a r l i e r t h a t u s e o f w a t e r d e p e n d s on
when and w h e r e w a t e r i s a v a i l a b l e .
I n a more a b s t r a c t
s e n s e , t h i s can be r e s t a t e d t o s a y t h a t t h e v a l u e o f w a t e r
a s p e r c e i v e d by t h e w a t e r p o l i c y p l a n n e r , i s d e p e n d e n t on
q u a n t i t y and q u a l i t y o f w a t e r a v a i l a b l e , g i v e n t h e e x o g e n ­
o u s l y d e t e r m i n e d demands f o r w a t e r , a t a g i v e n t i m e and
place.
A b s t r a c t i n g f r o m t h e t i m e and s p a c e d i m e n s i o n s , t h e
t o t a l b e n e f i t s o f w a t e r can be d e f i n e d ,
in g e n e r a l mathe­
m a t i c a l n o t a t i o n as
(I)
TBw - £(QW, Kw)
w h e r e Qw r e p r e s e n t s t h e q u a n t i t y o f w a t e r a nd Kw r e p r e s e n t s
34
the q u a lity of w ater.
T o t a l c o s t s o f w a t e r c a n be d e f i n e d
i n t h e same g e n e r a l n a t u r e a s
(2)
TGw = g (Qwr Kw)
At t h i s p o i n t ,
a f t e r m aking t h e u s u a l a s s u m p t i o n s
a b o u t f i r s t and s e c o n d o r d e r c o n d i t i o n s ,
i.e.,
dim inishing
m a r g i n a l b e n e f i t s and i n c r e a s i n g m a r g i n a l c o s t s ,
th e m argi­
n a l c o s t and b e n e f i t r e l a t i o n s h i p s c a n be d e f i n e d a s
(3)
MBw = ^ T B w
doT"
and
(4)
MCw = ^ T C w
T his s t r a ig h t f o r w a r d b e n e f i t / c o s t a n a ly s is
( s e e F i g u r e 6)
h a s b e e n r e c o g n i z e d , f o r e x a m p l e , by t h e DNRC a s p e r t a i n i n g
to th e Y ellow stone R iver Basin
(DNRC 1977n and 1981).
However, t h e s p e c i f i c i m p a c t s o f t h e l e v e l o f r e t u r n
f l o w s a n d , t h e r e f o r e , t h e l e v e l o f E1 a r e n o t f o r m a l l y
taken in to account in
(3) and ( 4 ) .
T herefore,
it
i s neces­
s a r y t o p u r s u e f u r t h e r t h e q u a n t i t y and q u a l i t y a s p e c t s o f
w ater.
From p r e v i o u s s e c t i o n s on h y d r o l o g y t h e m a j o r d e t e r m i ­
n a n ts of th e q u a n t i t y of w ater a v a i l a b l e a re i d e n t i f i e d as
n a t u r a l s tr e a m f lo w or r u n o f f , stre a m a u g m e n ta tio n w ith
i
35
Figure 6.
Marginal Benefits
of Water Use.
(MBw ) and Marginal Costs
(MCv )
36
storage f a c i l i t i e s ,
and r e t u r n f l o w s fro m i r r i g a t i o n .
That
is,
(5)
Qw = k ( R , S , Rf)
where R r e p r e s e n t s n a t u r a l r u n o f f , S r e p r e s e n t s a r t i f i c i a l
s t o r a g e and Rf r e p r e s e n t s r e t u r n f l o w from i r r i g a t i o n .
W ater q u a l i t y i s a f u n c t i o n of n a t u r a l q u a l i t y co n d i­
t i o n s i n t h e r u n o f f s y s t e m and a r t i f i c i a l ,
i m p a c t s t h a t may b e p o s i t i v e
ie.,
(w ater tr e a tm e n t) or n e g a tiv e
( p o i n t and n o n - p o i n t s o u r c e s o f p o l l u t i o n ) .
purposes,
For p r e s e n t
t h e q u a l i t y i m p a c t s o f r e t u r n f l o w w i l l be s e p a ­
r a t e d from o t h e r a r t i f i c i a l q u a l i t y im p a c ts.
q u ality
human,
T h u s, w a t e r
(Kw) c a n b e e x p r e s s e d a s
(6)
Kw = z (R, A, Rf)
where R r e p r e s e n t s q u a l i t y f a c t o r s in n a t u r a l r u n o f f , A
re p re s e n ts a r t i f i c i a l q u a lity f a c to r s other than i r r i g a t i o n
r e t u r n f l o w s , and Rf r e p r e s e n t s q u a l i t y f a c t o r s o f r e t u r n
flow s.
I t was s t a t e d e a r l i e r t h a t r e t u r n f l o w s (Rf) a r e
d i r e c t l y p ro p o rtio n a l to the le v e l of i r r i g a t i o n e f f i ­
cien cy , or in g en eral
(7)
Rf =
h (E1 )
I
C onsequently,
t h e l i n k b e t w e e n E1 and w a t e r b e n e f i t s and
costs is estab lish ed .
In g e n e r a l,
su b stitu tin g
(7)
into
37
(6) a n d (5) a n d s u b s t i t u t i n g
(6) a n d (5) i n t o
( I ) a n d (2) -
r e s u l t s in
(8)
TBw = f {k IR, S , K E 1 )] ,
Z
ER. Ar h (Ej ) ] }
(9)
TCw = g{k ER- S. I ( E 1 )]
Z
ER. A- h (Ej ) ] ]
-
The m a r g i n a l i m p a c t s o f c h a n g e s i n t h e l e v e l o f E
1
can
be a p p r o p r i a t e l y d e f i n e d a s
(10)
MBe s = d TBw
and
(11)
MCfis= a TCw
6 * 7
T his m a rg in a l a n a l y s i s ,
( s e e F i g u r e 7) i n c o n t r a s t
w i t h F i g u r e 6, c o n c e p t u a l i z e s t h e o p t i m a l l e v e l o f i r r i g a ­
tio n efficien cy
r a t h e r t h a n t h e q u a n t i t y o f w a t e r use.
I t i s im p o r t a n t t o u n d e rs ta n d th e d i s t i n c t i o n betw een
p r i v a t e l y and p u b l i c l y p e r c i e v e d b e n e f i t s and c o s t s o f t h e
l e v e l of i r r i g a t i o n e f f i c i e n c y .
p o sitiv e
and n e g a t i v e i m p a c t s ,
The e f f e c t s o f b o t h t h e
i.e ., a b e t t e r d i s t r i b u t i o n
t h r o u g h t i m e and q u a l i t y d e g r a d a t i o n , o f a l o w e r l e v e l of
i r r i g a t i o n e f f ic ie n c y are alm ost e n t i r e l y e x te r n a l to the
in d iv id u a l w ater user.
T he.preceeding b e n e f i t / c o s t analy­
s i s i s m u l t i d i m e n s i o n e d i n t i m e and s p a c e and o n l y i n t h i s
l i g h t i s th e i n d i v i d u a l w a te r u s e r viewed in p ro p er p e r ­
sp e c tiv e to th e e n t i r e basin.
I n e c o n o m ic p a r l a n c e , t h e r e
38
Figure 7.
Marginal Benefits and Marginal Costs of
Irrigation Efficiency (Ej).
39
a r e b o t h p o s i t i v e and n e g a t i v e e x t e r n a l i t i e s a s s o c i a t e d
w ith th e l e v e l of E j0
Thus, t h e r e i s a d i v e r g e n c e i n t h e
p u b l i c and p r i v a t e p e r c e p t i o n s o f b o t h t h e m a r g i n a l b e n e f i t
and c o s t c u r v e s o f F i g u r e 7 a s d e p i c t e d i n F i g u r e 8.
T h e r e a r e tw o i m p o r t a n t i m p l i c a t i o n s i m p l i e d i n F i g u r e
8.
F irst,
t h e r e i s a d i v e r g e n c e i n t h e p r i v a t e and p u b l i c
m a r g i n a l b e n e f i t and c o s t f u n c t i o n s and t h e r e f o r e w i l l
r e s u l t i n a d i f f e r e n t l e v e l o f E1 b e i n g v i e w e d a s o p t i m a l
a t t h e p r i v a t e and p u b l i c l e v e l s , e x c e p t i n t h e u n l i k e l y
case where th e y j u s t happen t o c o in c id e .
Second, g iv en
t h a t t h e r e i s a d i v e r g e n c e i n b o t h t h e m a r g i n a l b e n e f i t and
cost functions,
it
i s n o t obvious t h a t t h e r e i s a r i g i d ,
c o n s t a n t r e l a t i o n s h i p i n t h e tw o l e v e l s o f E1.
In o th e r
w o r d s , i t i s n o t c l e a r w h i c h o n e w i l l be h i g h e r a n d w h e t h e r
o r n o t t h e r e l a t i o n s h i p b e t w e e n t h e tw o w i l l a l w a y s be t h e
same.
I t is lik ely th at site
sp e c ific conditions,
e.g=,
h e i g h t o f p u m p in g , e n e r g y c o s t s , w h e t h e r or n o t t h e s i t e i s
p a r t of a p u b lic ly su pported i r r i g a t i o n p r o j e c t ,
e t cetera,
w i l l d e t e r m i n e w h e t h e r t h e p r i v a t e l e v e l o f E1 i s h i g h e r or
low er th an t h e p u b l i c l y o p tim a l l e v e l .
In g e n e r a l, th e
p red o m in a n tly nonm arket environm ent of w ater use as w e ll as
t h e n a t u r e o f i n s t i t u t i o n a l r e g i m e s w o u ld l i k e l y r e s u l t i n
p r i v a t e l y d e te r m in e d l e v e l s of e f f i c i e n c y t h a t a r e low er
t h a n w o u l d be p u b l i c l y o p t i m a l .
T h e r e a r e a number o f h y d r o l o g i c and e c o n o m i c i m p l i c a ­
t i o n s of p o l i c i e s which a t t e m p t t o change th e l e v e l of
40
(Private)
E x (Public)
(Private)
Et
EJ
Private Public
Figure 8.
Public and Private Marginal Benefits and Marginal
Costs of Irrigation Efficiency (Ej).
41
i r r i g a t i o n e f f i c i e n c y and s u b s e q u e n t l y c h a n g e t h e l e v e l o f
r e t u r n flo w s in th e system ,
A n d e r s o n (1975) d i s c u s s e s t h e
i m p l i c a t i o n s of r e t u r n flo w s w i t h i n a w a te r r i g h t s regim e
of p r io r a p p ro p ria tio n for i r r i g a t e d a g r i c u l t u r a l
producers.
J o h n s o n , G i s s e r and W e r n e r (1981) d e a l w i t h
r e t u r n f l o w s i n t h e i r d i s c u s s i o n o f a g e n e r a l model o f
e f f i c i e n t w ater a llo c a tio n .
Dudek and H o r n e r
(1981)
d i s c u s s t h e e f f e c t s o f r e t u r n f l o w c o n t r o l p o l i c i e s on
in com e d i s t r i b u t i o n among i r r i g a t o r s .
An A l t e r n a t i v e M e t h o d o l o g i c a l A p p ro a ch
C onceptually the foregoing theory i s s tra ig h tfo rw a rd .
However, e m p i r i c a l a p p l i c a t i o n o f t h e t h e o r y w o u ld r e q u i r e
a p o n d e r o u s am ount o f d a t a i n c l u d i n g ; d e f i n i t i o n and v a l u a ­
t io n of a l l w ater uses,
k n o w l e d g e and m o d e l i n g c a p a b i l i t y
o f b o t h q u a n t i t y and q u a l i t y a s p e c t s o f t h e h y d r o l o g i c
system ,
d a t a r e g a r d i n g t h e c o s t and m a i n t e n a n c e o f i r r i g a ­
t i o n c o n v e y a n c e and f i e l d s y s t e m s a t a l t e r n a t i v e l e v e l s o f
e f f i c i e n c y , and t h e d e f i n i t i o n o f an a p p r o p r i a t e p l a n n i n g
h o r i z o n and d i s c o u n t f a c t o r t o i m p l e m e n t b e n e f i t / c o s t
analysis.
The c o m p l e x i t i e s and s t o c h a s t i c n a t u r e o f t h e
h y d ro lo g ic system , th e f a c t t h a t w a ter re s o u rc e s o p e ra te in
a p r e d o m i n a n t l y n o n - m a r k e t e n v i r o n m e n t and c o n s e q u e n t l y
preclude r e l i a b l e v a lu a tio n d a ta ,
some u s e s ,
i.e.,
a e s th e tic s etc.,
and t h e n e b u l u s n a t u r e o f
make t h i s a m ore o n e r o u s
t a s k t h a n can be a d e q u a t e l y h a n d l e d i n t h i s s t u d y .
42
An a l t e r n a t i v e m o d e l i n g a p p r o a c h t h a t w i l l p r e s e n t an
a p p r e c i a t i o n o f t h e i m p a c t s o f t h e l e v e l o f e f f i c i e n c y , and
r e l a t e d f a c t o r s w h i l e p r e c l u d i n g an a c t u a l d e t e r m i n a t i o n o f
c o s t s and b e n e f i t s i s t o u s e a “t y p i c a l year*9 m o d e l.
The
" t y p i c a l y e a r " m o d e l , b a s e d l o o s e l y on t h e M a r s h a l l i a n
co n cep t of a r e p r e s e n t a t i v e f i r m
a l l o w s us t o a b s t r a c t ,
in pro d u ctio n th eo ry ,
i n i t i a l l y a t l e a s t , from th e s t o ­
c h a s t i c n a tu r e of th e h y d ro lo g ic sy stem ,
of planning h o rizo n s,
and t h e p r o b l e m s
d i s c o u n t i n g , and d e f i n i n g ,
and p r o j e c t i n g l e v e l s o f a l l w a t e r uses.®
valuing
T h is approach
u t i l i z e s a l i n e a r p r o g r a m m i n g f r a m e w o r k t o m o d el a " t y p i c a l
y e a r " t h a t c o n c e n t r a t e s on i r r i g a t e d a g r i c u l t u r e ,
the
p r i m a r y c o n s u m p t i v e u s e r o f w a t e r , and a v e r a g e l e v e l s o f
r i v e r flow i n th e b a s in .
O ther, l e s s c l e a r l y d e fin e d uses
of w a te r a re e n te r e d as c o n s t r a i n t s in th e m odel, but not
e x p l i c i t l y valued.
S n y d e r (1976) u t i l i z e d l i n e a r p r o g r a m ­
m ing i n h i s m o d el t o d e t e r m i n e t h e v a l u e o f w a t e r f o r
i r r i g a t i o n in th e Y ellow stone R iver Basin.
The p a r t i t i o n e d
l i n e a r p r o g r a m m i n g f r a m e w o r k was a l s o u t i l i z e d by Boyd
(1968) and McConnen and Menon (1968) i n w a t e r m o d e l i n g
ap p licatio n s.
^ C o n c e r n i n g t h e r e p r e s e n t a t i v e f i r m , Rima (1967) s t a t e s ,
"The f i r m i s n o t an a c t u a l f i r m , b u t r a t h e r an a n a l y t i c a l
t o o l which M a rs h a ll c o n c i e v e d . . . "
43
Chapter 3
The Model
I n o r d e r t o c o n s t r u c t an a n a l y t i c a l model a c c o r d i n g t o
t h e g u i d e l i n e s o f C h a p t e r 2, w h i c h w i l l f u l f i l l t h e o b j e c ­
t i v e s of Chapter I f t h r e e p r e c e p t s serv ed as g u i d e l i n e s .
F irst,
t h e model m u s t a d e q u a t e l y s i m u l a t e t h e h y d r o l o g y o f
the basin.
W h i l e t h e o b j e c t i v e s p r e s c r i b e an e c o n o m ic
e v a l u a t i o n o f t h e i m p a c t o f a l t e r n a t i v e r i v e r m anagem ent
p o licies,
s u c h i m p a c t s a r e t h e r e s u l t of i n t e r a c t i o n s w i t h
th e p h y s i c a l h y d r o lo g ic system .
T h e r e f o r e , e c o n o m ic
e v a l u a t i o n i s c o n t i n g e n t upon s a t i s f a c t o r i l y m o d e l i n g t h e
hydrologic pro cesses.
S e c o n d , e c o n o m ic e v a l u a t i o n of r i v e r
m an ag em en t p o l i c i e s i s c o n t i n g e n t upon s a t i s f a c t o r i l y
e s t a b l i s h i n g t h e l i n k a g e b e t w e e n t h e e c o n o m ic phenomenon,
w h i c h i n t h i s s t u d y i s i r r i g a t e d a g r i c u l t u r e , and t h e
hydrology of th e b a s in .
T hird,
th e conceptual id e a s in
C h a p t e r 2 i n d i c a t e a number o f a p p l i e d p o l i c y i s s u e s w h i c h
a r e b ey o n d t h e s c o p e of t h i s t h e s i s , b u t m e r i t f u r t h e r
in v estig atio n .
A c c o r d i n g l y , t h e m odel was d e v e l o p e d w i t h
enough f l e x i b i l i t y t o a l l o w t h e s e i s s u e s t o be d e a l t w i t h
a t a l a t e r d a te w ith o u t s i g n i f i c a n t m o d if i c a t io n of the
b a s i c mod el p r e s e n t e d h e r e .
44
The r e m a i n d e r o f t h i s c h a p t e r i s d i r e c t e d t o w a r d s
p r e s e n t i n g t h e g e n e r a l l i n e a r p r o g r a m m in g f r a m e w o r k and t h e
a d a p t a t i o n of t h i s fram ework t o th e s p e c i f i c problem d e a l t
w ith in t h i s study.
The S t a n d a r d L i n e a r Programming Pro b lem .
L i n e a r p r o g r a m m in g (LP) i s a m a t h e m a t i c a l t e c h n i q u e
t h a t seeks to o p tim iz e a s p e c i f i c c r i t e r i o n over a v e cto r
of a l t e r n a t i v e a c t i v i t i e s s u b j e c t t o a s e t of l i n e a r
co n strain ts.
L e t j = ( 1 , 2 , 3 ,o.,N) r e p r e s e n t a s e t o f N a c t i v i t i e s ,
w h e r e Xj i s t h e q u a n t i t y o f t h e j t h a c t i v i t y a n d
i=(l,2,3,...M )
represent
a s e t o f M r e s o u r c e s or
in p u ts
i n t o t h e N a c t i v i t i e s w h e r e b^ i s t h e l e v e l o f t h e i t h
resource a v a ila b le .
The i n t e r d e p e n d e n c i e s b e t w e e n t h e X j ' s
and b ^ ' s can be e x p r e s s e d a s a s y s t e m of M x N l i n e a r
e q u a t i o n s o f t h e fo rm s
a I l x I + a 12x 2 + • ° °a l n xn = b I
a 12x l + a 22x 2 + • • ®a 2 n x n = b 2
amlx l + am2x 2 + • e • amnx n
where
Xj
2. o,
j —( l , 2 , o e e N)
bm
45
The a j j ' s a r e t h e c o e f f i c i e n t s o f p r o p o r t i o n a l i t y ,
i e . f the
te c h n ic a l c o e f f i c i e n t s r e l a ti n g th e ith input to th e jth
a ctiv ity .
The s o l u t i o n t o t h e s y s t e m o f e q u a t i o n s i s
o b t a i n e d u s i n g an a l g o r i t h m known a s t h e s i m p l e x p r o c e d u r e
(D antzig,
1963).
The s y s t e m o f e q u a t i o n s a r e o p t i m i z e d a c c o r d i n g t o a
s p e c i f i c o b j e c t i v e f u n c t i o n Z.
For e x a m p l e , t o m a x i m iz e a
s e t of a c t i v i t i e s X j, (j = l ,2 ,...N ) , each w ith a v a lu e of
c-i, ( j = l , 2 , . . . N ) , t h e o b j e c t i v e f u n c t i o n i s
J
M
max (Z) =
Cj x ^
J=I
The s t a n d a r d l i n e a r p r o g r a m m i n g p r o b l e m i s s u b j e c t t o
four g e n eral assum ptions
(I)
P ro p o rtio n ality :
(D antzig,
1963,
I n t h e LP m o d e l ,
pp.
32-33).
th e l e v e l s of
r e s o u r c e s used a re alw ay s p o r p o r t i o n a l t o th e a c t i v i t y
lev el.
(2)
N onnegativity:
A c t i v i t i e s a r e alw ays r e s t r i c t e d to
z e r o or p o s i t i v e
lev els.
(3)
The a d d i t i v i t y a s s u m p t i o n r e q u i r e s t h a t
A d d itiv ity :
e a c h r e s o u r c e or i n p u t be c o m p l e t e l y a c c o u n t e d f o r i n t h e
m o d e l , i e . t h e t o t a l amoun t o f i n d i v i d u a l r e s o u r c e use
i m p l i e d by t h e sum o f a l l a c t i v i t i e s m u s t b e e q u a l t o t h e
to tal
(4)
amou nt o f e a c h r e s o u r c e a v a i l a b l e .
L inear O b je c tiv e F unction:
Each o f t h e a c t i v i t i e s
in
t h e LP p r o b l e m m u s t c o n t r i b u t e t o t h e o b j e c t i v e f u n c t i o n i n
a l i n e a r f a s h i o n r e g a r d l e s s o f t h e l e v e l of t h e a c t i v i t y .
46
In a d d itio n ,
t h e g e n e r a l LP f r a m e w o r k i m p l i e s t h a t
t h e r e a r e a f i n i t e number of a c t i v i t i e s and r e s o u r c e s and
th a t th ese are i n f i n i t e l y d iv is ib le .
In a d d i t i o n to d e te rm in in g th e o p tim al a l l o c a t i o n of
s c a r c e r e s o u r c e s among a l t e r n a t i v e u s e s , t h e LP s o l u t i o n
w i l l i n c l u d e c a l c u l a t e d shadow p r i c e s f o r e a c h r e s o u r c e
co n strain t.
T h ese shadow p r i c e s r e p r e s e n t t h e i m p u t e d
v a l u e s of a m a r g i n a l u n i t o f e a c h o f t h e r e s o u r c e s .
More
s p e c i f i c a l l y , t h e shadow p r i c e o f a p a r t i c u l a r r e s o u r c e i s
t h e v a l u e o f an a d d i t i o n a l u n i t o f t h e r e s o u r c e u s e d i n t h e
h i g h e s t v a l u e d a c t i v i t y m in u s t h e o p p o r t u n i t y c o s t o f t h e
resource in a lte r n a tiv e uses.
T herefore,
o p tim al a l l o c a t i o n of re s o u rc e s,
i n l i g h t of an
t h e c a l c u l a t e d shadow
p r i c e of a r e s o u r c e r e p r e s e n t s t h e m a r g i n a l v a l u e of t h a t
resource.
The v a l i d i t y o f t h e shadow p r i c e a s an e s t i m a t e
of th e t r u e m a r g in a l v a lu e of t h a t r e s o u r c e t o s o c i e t y
d e p e n d s on t h e c o m p l e t e n e s s o f t h e model i n r e f l e c t i n g
so c ia l opportu n ity
costs.
The l i n e a r p r o g r a m m i n g f r a m e w o r k i s w e l l s u i t e d t o t h e
needs of the study.
As a m e t h o d o l o g i c a l a p p r o a c h i t f u l ­
f i l l s two c r i t i c a l needs of t h e s tu d y .
F irst,
it is a
model o f t h e a l l o c a t i o n o f a s c a r c e r e s o u r c e among a number
of a l t e r n a t i v e uses.
criterio n ,
Se c o n d , by o p t i m i z i n g a s p e c i f i c
i t p r o v i d e s t h e m ec h an ism w h e r e b y t h e i m p a c t s of
f a c t o r s a f f e c t i n g t h e s c a r c e r e s o u r c e can be m e a s u r e d .
However, a s e s t a b l i s h e d i n C h a p t e r s I and 2, b o t h t h e
47
s c a r c i t y o f w a t e r r e s o u r c e s and t h e i m p a c t s o f r e t u r n f l o w s
i n t n e Y e l l o w s t o n e $ a s i n a r e f u n c t i o n s o f t i m e and s p a c e
dim ensions.
Thus t h e a d a p t a t i o n o f t h e l i n e a r p ro g r a m m in g
m o d el t o i n c l u d e t h e s e d i m e n s i o n s i s a f i r s t p r e r e q u i s i t e .
S p a t i a l Dimension
To f a c i l i t a t e t h e m o d e l i n g o f an a r e a a s v a s t a s t h e
Y e llo w sto n e B a sin , th e r e g io n i s d iv id e d i n t o n in e sub­
basins.
T h ese n i n e s u b - b a s i n s
( s e e F i g u r e 9 and T a b l e I)
r e p r e s e n t t h e m a j o r t r i b u t a r y and m a i n s t e m r e g i o n s o f t h e
Y e l l o w s t o n e B a s i n and a r e b a s e d on a g g r e g a t i o n s o f h y d r o l o ­
g i c s u b d r a i n a g e s u s e d by t h e DNRC (1970).
The d r a i n a g e
b a s in c o m p o s itio n of th e nine a r e a s a re a ls o l i s t e d in
T able I.
Each o f t h e n i n e s u b - b a s i n s i s m o d eled i n d i v i d u a l l y i n
t h e l i n e a r p r o g r a m m in g f r a m e w o r k and c o m b i n e d , a l o n g w i t h
a p p r o p r i a t e l i n k a g e s among t h e s u b - b a s i n s , i n a p a r t i t i o n e d
l i n e a r programming fram ew ork.
The Y e l l o w s t o n e R i v e r B a s i n ,
i n t n e c o n t e x t o f m a i n s t e m r i v e r f l o w and t r i b u t a r y i n f l o w ,
can be v i e w e d s p a t i a l l y a s a n e t w o r k s i m i l a r t o F i g u r e 10
a n d , when a d a p t e d t o t h e p a r t i t i o n e d LR f r a m e w o r k ,
resu lts
i n a m a t r i x f o r m a t s i m i l a r t o F i g u r e 11 w h e r e t h e s u b - b a s i n
s u b m a tr i c e s a r e s e q u e n t i a l l y l i n k e d t o form t h e b a s in - w id e
model.
The l i n e a r p r o g r a m m in g m o d el w h i c h was d e v e l o p e d
t r e a t s a l l a c t i v i t i e s w i t h in a su b -b a s in as i f th ey occur
a t one p o i n t i n s p a c e .
Thus t h e m odel a c t s a s i f t h e n i n e
Y e II o w s t o n e R iver B asin
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i.lO
wSTO
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e . vc * BAS N
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Clorks Fork Yellowstone
Billings Area
Bighorn
Mid-Yellowstone
Tongue
Kinsey Area
Powder
Lower Yellowstone
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N A T I O N A L
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Figure 9.
.J L .
Fiqunt I
The Nine Planning Sub-basins of the Yellowstone River Basin
(From D N R C , 1977d)
49
Sub-basin
•h ia
Table I .
The N i n e S u b - b a s i n s o f t h e Y e l l o w s t o n e R
B a s i n and A s s o c i a t e d H y d r o l o g i c D r a i n a g e
Name
H ydrologic Basin
I
Upper
Y ellow stone
43A , 43B , 43C ,
4 3 B J , 43QJ
2
C l a r k s Fo rk
43D
3
B illin g s
43Q,
4
Bighorn
43N, 43P,
5
M id-Y ellow stone
43KJ f 42A
6
Tongue
42B ,
7
Kinsey
42K
8
Powder .
421, 42J
9
Lower
Y ellow stone
42L, 42M
43E
42C
430
43BV,
Ul
O
Figure 10.
The Nine Planning Sub-basins as a Network.
O b l e c t i v e Row
S ub-basin L
Sub-basin 2
S ub-basin 3
lin k a g e s
S ub-basin 4
S ub-basin 5
I
Linkages
S ub -b asin 6
S ub-basin 7
I
Ul
Linkages
H
S ub-basin 6
Sub-basin 9
I
Figure 11.
Linkages
The Nine Sub-basins Submatrices in the Partitioned Linear Programming Framework
52
s u b - b a s in s of the Y e llo w s to n e B a sin are nine i n d i v i d u a l
p o in ts in space.
F u r t h e r s p a t i a l r e a l i s m c o u l d be added t o
t h e model by f u r t h e r d i v i d i n g t h e s u b - b a s i n s i n t o s m a l l e r
regions.
The n i n e a r e a b r e a k d o w n was c h o s e n f o r t h r e e r e a s o n s .
F irst,
t h e n in e a r e a breakdown i s c o m p a tib le w i t h o t h e r
a n a l y t i c a l work done i n t h e Y e l l o w s t o n e B a s i n ( B o r i s and
K r u t i l l a f 1980 and DNRCf 1977 d). T h e r e f o r e ,
t h e r e s u l t s of
t h i s s t u d y w i l l be c o m p a t i b l e w i t h t h o s e o f o t h e r s t u d i e s .
T his w i l l f a c i l i t a t e th e a b i l i t y of w ater p la n n in g o f f i ­
c i a l s to i n t e r p r e t th e r e s u l t s p re se n te d here.
Seco n d ,
the
n in e a r e a breakdown w orks q u i t e w e l l t o f a c i l i t a t e th e
m eshing of a l t e r n a t i v e d a t a s o u r c e s .
Much o f t h e e c o n o m ic
and a g r i c u l t u r a l d a t a a r e c o u n t y b a s e d w h e r e a s t h e h y d r o l o g i c d a t a a r e b a s e d on h y d r o l o g i c s u b - b a s i n s .
a d d itio n a l sub-basin s u b s ta n tia lly
t h e b a s i n - w i d e model.
T herefore,
T hird,
each
in c r e a s e s th e s iz e of
i n o r d e r t o c o n s e r v e on
b o t h c o m p u t a t i o n a l t i m e and t i m e s p e n t i n m odel c o n s t r u c ­
t i o n , t h e model s h o u l d be no l a r g e r t h a n r e q u i r e d t o d e a l
w i t h th e problem under i n v e s t i g a t i o n .
Time D i m e n s io n
W h i l e i t i s t h e i n t e n t o f t h i s s t u d y t o u t i l i z e an
a n n u a l " t y p i c a l y e a r " t y p e mod el u t i l i z i n g
o f annual r i v e r f l o w s ,
average l e v e l s
t h e n a t u r e o f t h e h y d r o l o g i c and
a g r i c u l t u r a l p r o c e s s e s n e c e s s i t a t e m odeling th e c h a r a c t e r ­
i s t i c s of flo w w i t h in th e y e a r . . This i s a cco m p lish ed in
53
t h e LP mod el by r e p l a c i n g s i n g l e a c t i v i t i e s and c o n s t r a i n t s
b a s e d on a n n u a l v a l u e s w i t h a s e r i e s r e p r e s e n t i n g m o n t h l y
values.
For p u r p o s e s o f t h i s s t u d y t h e LP m odel c o n t a i n s 5
t i m e i n t e r v a l s r e p r e s e n t i n g t h e 5 m o n th s . May t h r o u g h
S eptem ber, th e r e b y r e p r e s e n t i n g th e m a j o r i t y of t h e i r r i g a ­
t i o n season.
I n s t e a d o f one ( a n n u a l ) w a t e r b a l a n c e
e q u a tio n f o r each s u b - b a s in ,
th e re a re f iv e balance
e q u a t i o n s , one f o r e a c h o f t h e f i v e m o n th s o f t h e i r r i g a ­
t i o n s e a s o n . The h y d r o l o g y o f t h e b a s i n r e q u i r e s t h a t t h e s e
f i v e t i m e i n t e r v a l s be i n t e r r e l a t e d due t o t h e n a t u r e o f
r e t u r n f l o w s and c r o p c o n s u m p t i v e u s e o f w a t e r .
Expansion
of th e model to encom pass a l l p e r i o d s of th e y e a r i s
s t r a i g h t f o r w a r d and c o u l d be a c c o m p l i s h e d by an i n c r e a s e
i n d i m e n s i o n o f t h e m o d e l.
The H y d r o l o g i c Model
The movement o f w a t e r t h r o u g h t i m e and s p a c e i s s i m u ­
l a t e d m a t h e m a t i c a l l y by m a t e r i a l b a l a n c e e q u a t i o n s .
I)
O u t f l o w t = I n f l o w t - U se t
E q u a tio n I i s a s im p le v e r s i o n of such a b a la n c e e q u a tio n
w h i c h s a y s t h a t t h e o u t f l o w o f w a t e r fr o m a s u b - b a s i n i n
t i m e i n t e r v a l t m u s t be e q u a l t o t h e i n f l o w m in u s t h e u se
in tim e i n t e r v a l t.
In t h i s exam ple,
i n f l o w and o u t f l o w
m u s t be i n t e r p r e t e d more b r o a d l y t h a n j u s t s t r e a m f l o w t o
i n c l u d e " e f f e c t i v e " i n f l o w and o u t f l o w su c h a s i n t e r n a l
p r e c i p i t a t i o n , t e m p o r a r y g r o u n d w a t e r i n f i l t r a t i o n , and
54
storage.
Of c o u r s e "Use^" c a n be s e p a r a t e d i n t o c a t e g o r i e s
f o r any number o f a l t e r n a t i v e u s e s .
R ew riting eq u atio n I
as
la)
Uset + O u t f l o w t = I n f l o w t
s e t s th e s ta g e f o r i n c o r p o r a t i o n of th e m a t e r i a l b a la n c e
e q u a t i o n i n t o t h e l i n e a r programming fram ew ork where in f lo w
i s a s p e c i f i e d r i g h t - h a n d s i d e (RHS) and u s e s and o u t f l o w
are a c t i v i t i e s .
By f o r c i n g t h e s t r i c t e q u a l i t y ,
flow becomes a r e s i d u a l a c t i v i t y such t h a t ,
"used",
th e out­
any w a t e r n o t
m u s t become o u t f l o w and move i n t o t h e n e x t s u b -
b a s i n d o w n s tr e a m ? t h u s s i m u l a t i n g t h e " f l o w " o f t h e r i v e r .
F i g u r e 12 i s a r e p r e s e n t a t i o n o f t h e m a j o r c o m p o n e n ts
of t h e model u se d i n t h i s s t u d y .
A ll of th e w a t e r w hich
e n t e r s a s u b - b a s i n m u s t e i t h e r be d i v e r t e d f o r i r r i g a t i o n ,
u s e d f o r e n e r g y p r o d u c t i o n , m u n i c i p a l , o r minimum f l o w
( in s tr e a m ) r e q u i r e m e n t s or s e n t dow nstream as u n d i v e r t e d
flow .
In t h i s c a s e , th e u n d iv e r te d flow i s t h e r e s i d u a l
a c t i v i t y t o e n s u r e t h a t t h e w a t e r e q u a t i o n b a l a n c e s , and
t h e r e f o r e i s a component of o u t f lo w .
Minimum f l o w r e p r e ­
s e n t s minimum r i v e r l e v e l s r e q u i r e d t o m a i n t a i n w i l d l i f e
h a b i t a t and w a t e r q u a l i t y and i s one of t h r e e c a t e g o r i e s of
e x o g e n o u s u s e s , b u t , a s i t i s an i n s t r e a m u se i t
i s also a
component of o u tf lo w .
The e x o g e n o u s u s e c a t e g o r i e s ?
energy p ro d u c tio n ,
m u n i c i p a l , and minimum f l o w e n t e r t h e model a t s p e c i f i e d
In a
T
Diversion
—
V
Energy use
Requirements
for
Agricxilture
Municipal use
Reqxiirements
Minimum flew
Requirements
Y~
Not
Diverted
-^Outflow
L
Conveyance
Loss
Return flow
from Conveyance
Conveyance
to Field
V
Inflow to
next
Sub-basin
Total Return
flow/sub-basirr
A
L Loss during
field use
Use in
field
Figure 12.
Return flow from
rield xose
Meet net irrigation
Requirements
Flow Chart of t h e
Principal C o m p o n e n t s of t h e
.
LP Model.
Maximum returns
to Agricultxire
Crops
56
l e v e l s , by t i m e i n t e r v a l a n d s u b - b a s i n , i n t h e f o r m o f row
c o n s t r a i n t s w h i c h m u s t be s a t i s f i e d *
Minimum f l o w c o n ­
s t r a i n t s , b a s e d on i n s t r e a m r e s e r v a t i o n s f o r f i s h , w i l d l i f e ,
and w a t e r q u a l i t y m a i n t e n a n c e g r a n t e d by t h e B o a r d o f
N a t u r a l R e s o u r c e s and C o n s e r v a t i o n ,
represent a sig n ific a n t
p o r tio n of th e w ater a v a i la b l e in th e r i v e r .
E n erg y and
m u n ic i p a l use of w a t e r a t th e p r e s e n t tim e a r e s m a ll r e l a ­
t i v e to t o t a l r iv e r flow .
However, t h e i n c l u s i o n of t h e s e
c o m p o n e n t s i n t h e m od el g r e a t l y i n c r e a s e s i t s f l e x i b i l i t y
t o s im u la te s c e n a r i o s of in c re a s e d l e v e l s of th e s e a l t e r n a ­
tiv e
uses.
The I r r i g a t e d A g r i c u l t u r e Model
M o d e l in g t h e movement o f i r r i g a t i o n w a t e r f r o m t h e
r i v e r t o t h e p l a n t t h r o u g h t h e c o n v e y a n c e and f i e l d s y s t e m s
i s a c c o m p l i s h e d v i a a n e t w o r k o f t r a n s f e r a c t i v i t i e s and
balance e q u a tio n s.
The c o n v e y a n c e and f i e l d u s e p r o c e s s e s
a r e s i m u la t e d w ith t r a n s f e r a c t i v i t i e s which d i v e r t w a ter
f ro m t h e " r i v e r " ,
(the w ater b a la n ce e q u a tio n ),
and d e l i v e r
a p o r t i o n of t h a t w a te r t o t h e p l a n t fo r i t s use.
Not a l l
of th e d i v e r t e d w a t e r i s d e l i v e r e d because of conveyance
and f i e l d l o s s e s ,
th a t is,
b e c a u s e c o n v e y a n c e and f i e l d
e f f i c i e n c i e s a r e l e s s t h a n 100 p e r c e n t .
The d i v e r s i o n ,
c o n v e y a n c e , f i e l d u s e , and c r o p n e t i r r i g a t i o n r e q u i r e m e n t
p o r t i o n o f t h e l i n e a r p r o g r a m m i n g model i s d e p i c t e d c o n c e p ­
tu ally
i n t h e t a b l e a u p r e s e n t e d i n F i g u r e 13.
presents,
as detached c o e f f i c i e n t s ,
The t a b l e a u
t h o s e p o r t i o n s of t h e
D ivert
Water
F i e l d Use
o f Water
Crop
A ctivity
RHS
Inflow
Water B a l a n c e E q u a t i o n
1
Conveyance E q u a t i o n
-E c
I
^
F i e l d Use E q u a t i o n
I
=
0
=
0
—>
-
EU
^ /
N^I.R.
Ec = c o n v e y a n c e e f f i c i e n c y
Eu = i r r i g a t i o n u n i t e f f i c i e n c y
N .I.R . = net i r r i g a t i o n requirem ents
F i g u r e 13.
"Movement" o f W ater From t h e R i v e r t o Cro p s i n t h e LR Model
58
r e l e v a n t e q u a t i o n s w h i c h show how t h e model e s t a b l i s h e s t h e
l i n k a g e b e t w e e n t h e c r o p p i n g a c t i v i t i e s and r i v e r f l o w v i a
t h e c o n v e y a n c e and f i e l d s y s t e m s .
Thus,
i n an a b s t r a c t
s e n s e , t h e "m ovem ent" of w a t e r f ro m t h e r i v e r t o t h e c r o p
i s m o d e l e d a s d e p i c t e d by t h e d i r e c t i o n a l a r r o w s .
For
i l l u s t r a t i o n e a s e , t h e t a b l e a u o n l y shows t h e e q u a t i o n s f o r
a s in g le tim e i n t e r v a l .
R e f e r r i n g t o F i g u r e 13, and a s s u m i n g f o r s i m p l i c i t y
t h a t conveyance e f f i c i e n c y
efficien cy
(Ec ) and i r r i g a t i o n
(Eu ) a r e b o t h 50 p e r c e n t ,
w a t e r i s d i v e r t e d from th e r i v e r ,
w i l l be d e l i v e r e d t o t h e f i e l d .
unit
(field)
i f one a c r e - f o o t o f
then o n e -h a lf a c r e - f o o t
Of t h e w a t e r d e l i v e r e d t o
t h e f i e l d , o n e - h a l f w i l l be d e l i v e r e d t o t h e p l a n t f o r
c o n su m p tiv e use.
Thus, o f t h e o r i g i n a l one a c r e - f o o t
d i v e r t e d fr o m t h e r i v e r ,
o n l y o n e - q u a r t e r a c r e - f o o t was
u l t i m a t e l y u s e d by t h e p l a n t .
A d i f f e r e n t s e t of th e se
ro w s and a c t i v i t i e s e x i s t s f o r e a c h t i m e i n t e r v a l (month)
and s u b - b a s i n .
A l t e r n a t i v e i r r i g a t e d c r o p s c a n be p r o d u c e d
in the su b -b asin s.
The c r o p p i n g a c t i v i t i e s a r e l i n k e d t o
t h e h y d r o l o g i c m o d el v i a n e t i r r i g a t i o n r e q u i r e m e n t s f o r
e a c h c r o p w h i c h a r e s p e c i f i e d by m onth and m u s t be s a t i s ­
f i e d i n o r d e r t o "grow" a p a r t i c u l a r c r o p .
In t h i s sense
t h e model i s l i m i t e d t o a s i n g l e i r r i g a t i o n schem e f o r e a c h
c ro p in each su b -b a sin .
I n o t h e r w o r d s , t h e c u r r e n t model
does n o t p e r m i t a c ro p to have a lo w e r y i e l d and hence
59
re q u ire l e s s w ater.
However, t h e model c o u l d be e x p a n d e d
t o i n c l u d e such a l t e r n a t i v e s i f d a t a were a v a i l a b l e .
The model d o e s n o t a t t e m p t t o s i m u l a t e t h e e n t i r e
a g r i c u lt u r a l production process for
W ith th e e x c e p t i o n o f w a t e r ,
each of t h e cro p s.
t h e model a s s u m e s t h a t a l l
o t h e r p r o d u c t i o n i n p u t s a r e a v a i l a b l e and p r o d u c t i o n
re q u ire m e n ts a re s a t i s f i e d f o r each crop.
The t o t a l number
of i r r i g a t e d a c r e s in each su b -b a s in a re c o n s tr a in e d ,
but
t h e o p tim u m c r o p p i n g p a t t e r n i s d e t e r m i n e d by t h e l i n e a r
program m ing model.
The m odel i m p l i c i t l y a s s u m e s t h a t e a c h s u b - b a s i n i s
c h a r a c t e r i z e d by hom ogeneous s o i l t y p e s , f a r m i n g s y s t e m s ,
m an a g em en t l e v e l s ,
etc.
Thus,
i t t a c i t l y assum es t h a t each
s u b - b a s i n i s compo sed o f a s e r i e s o f a v e r a g e o r t y p i c a l
farm s t h a t are a l l a lik e .
The O b j e c t i v e F u n c t i o n
The o b j e c t i v e f u n c t i o n i s t h e d r i v i n g f o r c e o f t h e
l i n e a r p r o g r a m m i n g m o d e l.
In t h i s model, t h e o b j e c t i v e
f u n c t i o n i s s p e c i f i e d t o m axim ize r e t u r n s over v a r i a b l e
c o s t s to th e v e c to r of cro p s in each a re a .
In a d d it i o n th e
o b j e c t i v e f u n c t i o n c o n t a i n s a n o m i n a l c h a r g e o f $5.00 p e r
a c re -fo o t for div ersio n a c t i v i t i e s .
T his i s c o n s t a n t f o r
a l l s u b - b a s i n s and i s n o t an a c t u a l d i v e r s i o n c o s t b u t i s
i n t e n d e d t o i n s u r e t h a t t h e model i s e f f i c i e n t ,
ie.,
d o e s n ' t d i v e r t any more w a t e r t h a n n e c e s s a r y f o r c r o p u s e . .
60
The B a s i n - w i d e Model
The l i n k a g e s b e t w e e n t h e n i n e s u b - b a s i n s t h a t r e s u l t
i n a b a s i n - w i d e model o f r i v e r f l o w c o n s i s t o f two compo­
n e n t s ; i n s t r e a m f l o w b e t w e e n s u b - b a s i n s and r e t u r n f l o w s
from i r r i g a t i o n .
R i v e r f l o w f ro m an u p s t r e a m s u b - b a s i n t o
an i m m e d i a t e l y d o w n s t r e a m s u b - b a s i n c o n s i s t s o f tw o o u t f l o w
components.
The tw o o u t f l o w c o m p o n e n ts of a s u b - b a s i n a r e
t h e u n d i v e r t e d w a t e r w h i c h s a t i s f i e s t h e minimum f l o w
r e q u i r e m e n t s and t h e r e s i d u a l a c t i v i t y ,
v e rte d flow .
i.e.,
other
undi­
T h ese o c c u r i n t h e l i n e a r p r o g r a m m i n g model
as a t r a n s f e r betw een th e w a te r b a la n c e e q u a t io n s of th e
u p s t r e a m and d o w n s t r e a m s u b - b a s i n s by t i m e i n t e r v a l .
F i g u r e 14 i s a c o n c e p t u a l t a b l e a u r e p r e s e n t i n g t h i s t r a n s ­
f e r o f i n s t r e a m f l o w f ro m an u p s t r e a m s u b - b a s i n t o an
im m e d ia te ly downstream s u b - b a s i n f o r a g iv en tim e i n t e r v a l .
The t a b l e a u i s a s i m p l i f i e d r e p r e s e n t a t i o n o f t h i s t r a n s f e r
p r o c e s s and i n c l u d e s o n l y t h e n e c e s s a r y p o r t i o n s o f t h e
equations
involved.
Thus, i n F i g u r e 1 4 , e a c h a c r e - f o o t o f w a t e r e n g a g e d by
t h e minimum f l o w a c t i v i t y o f t h e u p s t r e a m a r e a ,
t o m ee t t h e
minimum f l o w c o n s t r a i n t s f o r t h a t s u b - b a s i n , w i l l be t r a n s ­
f e r r e d t o th e b a la n c e e q u a tio n of th e s u b - b a s in im m e d ia te ly
dow nstream .
S i m i l a r l y , f o r e a c h a c r e - f o o t o f w a t e r en g ag ed
by t h e r e s i d u a l u n d i v e r t e d f l o w a c t i v i t y of t h e u p s t r e a m
s u b - b a s i n , t o b a l a n c e t h e w a t e r b a l a n c e e q u a t i o n , an
Minimum
Flow
"Not
D iverted"
RHS
Water B a l a n c e E q u a t i o n
Inflow
U p s tr e a m S u b - b a s i n
W ater B a l a n c e E q u a t i o n
Inflow
Downstream S u b - b a s i n
F i g u r e 14
"Movement" o f I n s t r e a m Flow From an U p s tr e a m S u b - b a s i n
t o an I m m e d i a t e l y Downstream S u b - b a s i n .
p
62
a c r e - f o o t w i l l be t r a n s f e r r e d t o t h e w a t e r b a l a n c e e q u a t i o n
of th e s u b - b a s i n im m e d ia te ly downstream .
The s i g n c o n v e n t i o n o f t h e LP m o d e l i n t h i s s t u d y
u s e s p o s i t i v e c o e f f i c i e n t s t o r e p r e s e n t " d e m a n d e r s " and
n e g a t i v e c o e f f i c i e n t s t o r e p r e s e n t " s u p p l i e r s 61 f o r t r a n s f e r
a c t i v i t i e s and b a l a n c e e q u a t i o n s .
T h e r e f o r e t h e minimum
f l o w and t h e r e s i d u a l u n d i v e r t e d f l o w a c t i v i t i e s a r e
"d em a n d in g " w a t e r f r o m t h e u p s t r e a m s u b - b a s i n and
" s u p p l y i n g " w a t e r t o t h e s u b - b a s i n i m m e d i a t e l y d o w n s tr e a m .
I f t h e d o w n s t r e a m s u b - b a s i n h a s no i n t e r n a l s t r e a m f l o w
s o u r c e , t h e n t h e RHS o f t h e w a t e r b a l a n c e e q u a t i o n w i l l b e
z e r o s i n c e t h e i n f l o w i n t o t h a t s u b - b a s i n e n t e r s oh t h e
l e f t s i d e of th e w a te r b a la n c e e q u a t io n ,
from th e u p stre am s u b - b a s in .
i.e.,
the outflow
A ll of th e t r i b u t a r y sub­
b a s i n s and t h e u p p e r m a i n s t e m h a v e w a t e r e n t e r i n g a c r o s s
t h e s t a t e l i n e f r o m Wyoming a n d / o r g e n e r a t e s i g n i f i c a n t
q u a n t i t i e s o f s t r e a m f l o w w i t h i n t h e s u b - b a s i n and t h e r e f o r e
h av e p o s i t i v e RHS on t h e w a t e r b a l a n c e e q u a t i o n s .
However,
most of th e m ainstem s u b - b a s i n s a r e l o c a t e d in th e p l a i n s
region of the b a sin ,
i.e.,
they a re not headw ater a re as,
and t h e r e f o r e do n o t make s i g n i f i c a n t c o n t r i b u t i o n s t o
stream flow .1
The r e t u r n f l o w s t h a t r e e n t e r t h e s u r f a c e f l o w s y s t e m
a r e so m e w h at more c o m p l i c a t e d b o t h w i t h r e g a r d t o t h e t i m e
1 T h i s a s s u m p t i o n i s m o d i f i e d so m e w h at i n t h e c a l i b r a t i o n
pro ce d u re d e s c r i b e d in C hapter 5,
63
an d s p a c e d i m e n s i o n s .
S p a t i a l l y , i t i s assumed i n t h i s
m o d el t h a t i n t h e t r i b u t a r y and u p p e r m a i n s t e m s u b - b a s i n s ,
(1,2,4,6,8),
w a t e r i s d i v e r t e d by i n d i v i d u a l u s e r s w h i c h
a r e s c a t t e r e d hom ogeneously th r o u g h o u t t h e s u b - b a s i n s such
t h a t v i r t u a l l y a l l o f t h e r e t u r n f l o w fr o m i r r i g a t i o n i s
a v a ila b le for
r e u s e by an i r r i g a t o r
Most o f t h e m a i n s t e m s u b - b a s i n s
i n t h a t same s u b - b a s i n .
(3,5,7,9),
in c o n tr a s t ,
are
c h a r a c t e r i z e d by d i s t i n c t d i v e r s i o n p o i n t s f o r l a r g e i r r i ­
g a t i o n p r o j e c t s and c o n s e q u e n t l y r e t u r n f l o w s a r e n o t
a v a i l a b l e u n t i l t h e n e x t s u b - b a s in downstream .
The m ajo r
e x c e p t i o n t o t h i s a s s u m p t i o n i s s u b - b a s i n 3, t h e B i l l i n g s
a r e a , which i s som eth in g of a t r a n s i t i o n a re a .
Conse ­
q u e n t l y , i n t h e B i l l i n g s s u b - b a s i n i t i s a s s u m e d t h a t 60
p e rc e n t of i t s i n t e r n a l l y g e n e ra te d r e tu r n flo w s a re
a v a i l a b l e f o r r e d i v e r s i o n w i t h i n s u b - b a s i n 3 and 40 p e r c e n t
w i l l n o t be a v a i l a b l e f o r r e u s e u n t i l s u b - b a s i n 5 , w hich i s
im m e d ia te l y dow nstream .
R etu rn f l o w s a l s o c r o s s over tim e i n t e r v a l s because of
t h e i r delayed n a tu re .
sion,
T h u s, r e t u r n f l o w s fr o m a May d i v e r - .
f o r e x a m p l e , w i l l c o n t r i b u t e t o t h e May w a t e r b a l a n c e
eq u ation,
th e June w ater balance e q u atio n ,
e t cetera.
R eservoirs
The m o d el a l s o i n c l u d e s s i m u l a t i o n s o f t h e tw o l a r g e s t
r e s e r v o i r s i n t h e b a s i n , t h e Y e l l o w t a i l Dam on t h e B i g H orn
River
( s u b - b a s i n 4) and t h e Tongue R e s e r v o i r on t h e Tongue
R iver
(sub-basin
6).
64
The a c t i o n s o f a r e s e r v o i r a r e s i m u l a t e d by a s e r i e s
o f t r a n s f e r a c t i v i t i e s and b a l a n c e e q u a t i o n s .
F i g u r e 15
d e p ic ts c o n c e p tu a lly th e s im u la tio n of r e s e r v o ir a c t i v i ­
t i e s fo r a p a r t i c u l a r tim e i n t e r v a l .
in terv al t,
For e x a m p l e , i n t i m e
t h e w a t e r " s u p p l i e d " t o t h e r e s e r v o i r comes
f r o m e i t h e r w a t e r h e l d i n t h e p r e v i o u s t i m e i n t e r v a l and
n o t r e l e a s e d or w a t e r h e l d f r o m r i v e r f l o w i n t h i s t i m e
in terv al.
The b a l a n c e e q u a t i o n f o r r e s e r v o i r u s e i n e a c h
tim e i n te r v a l
are su b je ct to a s t r i c t e q u a lity ,
i.e.,
all
o f t h e w a t e r " s u p p l i e d " m u s t be demanded i n some a c t i v i t y .
Thus, t h e w a t e r " s u p p l i e d " t o t h e r e s e r v o i r ,
in terv al,
sub-basin,
in each tim e
cart be "demanded" f o r e i t h e r r e u s e i n t h a t same
r e l e a s e t o t h e s u b - b a s i n im m e d ia te ly dow nstream ,
or t r a n s f e r r e d t o t h e n e x t t i m e i n t e r v a l a s r e s e r v o i r
storage.
In o th e r words,
th e r e s e r v o ir balance e quation
f o r a p a r t i c u l a r t i m e i n t e r v a l s a y s t h a t t h e sum o f t h e
q u a n t i t y of w a ter h e ld over from th e p r e v io u s tim e i n t e r v a l
p l u s t h e q u a n t i t y h e l d fr o m r i v e r f l o w i n t h i s t i m e i n t e r ­
v a l m ust e q u a l th e amount of w a te r used in th e s u b - b a s in in
t h i s tim e i n t e r v a l p l u s t h e amount r e l e a s e d downstream in
t h i s tim e i n t e r v a l p l u s t h e amount h e ld over i n t o t h e n e x t
tim e i n t e r v a l .
The use o f p o s i t i v e and n e g a t i v e C j "s i n t h e o b j e c t i v e
f u n c t i o n a l l o w s t h e m odel t o s i m u l a t e any number o f p o s ­
s i b l e r e s e r v o i r m anagem ent s c e n a r i o s ,
w h i c h may be d e s i r e d ,
a g a i n c o n t r i b u t i n g t o t h e f l e x i b i l i t y of t h e m o d el.
Transfer
water from
t-1 to t
Water Balance Equation (t)
Reservoir Balance Equation (t-1)
Reservoir Balance Equation (t)
Store
water in
t
Release
water
downstream
in t
I
I
-I
-I
RHS
= Inflow
I
Reservoir Balance Equation (t+1)
t = time interval
Figure 15.
Release
Transfer
water
water from
back into t to t+1
sub-basin
in t
Simulation of Reservoir Actions in the L P Model.
I
=
0
. I
=
0
-I
=
0
66
C hapter 4
D a t a S o u r c e s an d P r e p a r a t i o n
The B a s i c Model
The l i n e a r p r o g r a m m i n g m o d el r e q u i r e s t h r e e b a s i c
ty p e s of data?
th e v a lu e s of t h e r e s o u r c e c o n s t r a i n t s
r i g h t hand s i d e s ,
c ien ts
RHS), t h e v a l u e s o f t h e m a t r i x c o e f f i ­
(the a ^ j 's ) ,
function
(the C j's).
t h i s model a r e ?
(the
and t h e v a l u e s i n t h e o b j e c t i v e
The m a j o r
reso u rce c o n s t r a i n t s for
the w ater flow ing in to the the b a sin ,
i.e.,
t h e RHS o f t h e w a t e r b a l a n c e e q u a t i o n s , a c r e a g e r e s t r i c ­
tio n s,
and t h e v a l u e s o f t h e e x o g e n o u s u s e a c t i v i t i e s .
T h es e i n c l u d e minimum i n s t r e a m f l o w f o r f i s h and w i l d l i f e
h a b i t a t a nd w a t e r q u a l i t y m a i n t e n a n c e , w a t e r u s e d i n e n e r g y
production,
and w a t e r f o r m u n i c i p a l u s e . The p r i m a r y a ^ ' s
a r e t h e c o n v e y a n c e and f i e l d e f f i c i e n c i e s , r e t u r n f l o w
c o e f f i c i e n t s , t h e n e t i r r i g a t i o n r e q u i r e m e n t s f o r t h e crop-,
p i n g a c t i v i t i e s and t h o s e f o r l a n d u s e . The r e s t o f t h e
a ^ j ' s a r e r e q u i r e d f o r t h e f u n c t i o n i n g of m a t e r i a l b ala n ce
e q u a t i o n s and t r a n s f e r a c t i v i t i e s .
The m a j o r o b j e c t i v e
f u n c t i o n v a l u e s a r e t h e r e t u r n s o v e r v a r i a b l e c o s t s (ROVC)
f o r e a c h o f t h e c r o p s grown i n e a c h s u b - b a s i n .
67
H y d ro lo g ic Data
S t r e a m f l o w g a u g i n g d a t a on t h e Y e l l o w s t o n e R i v e r was
o b t a i n e d f r o m t h e U. S. G e o l o g i c a l S u r v e y ' s c o m p u t e r i z e d
d a t a ban k .
The y e a r s 1963 t o 1977 w e r e u s e d a s a b a s e
p e r i o d f o r t h e c a l i b r a t i o n m o d e l a n d a s t h e b a s i s o f com­
p a ris o n for subsequent a p p lie d runs.
The t i m e p e r i o d o f
1 9 6 3 -1 9 7 7 i s n o t i n k e e p i n g w i t h t h e a s s u m p t i o n a b o u t a
"ty p ic a l year",
in term s of riv e r flow s,
sin c e th e average
flo w s f o r t h i s p e r io d of y e a r s i s g r e a t e r th a n th e lo n g run
average of r i v e r f l o w s .^
The p r o b l e m s i n d e t e r m i n i n g
"average" flo w s were d i s c u s s e d i n Chapter I .
T his p a r t i c ­
u l a r b a s e p e r i o d was c h o s e n b e c a u s e i t c o i n c i d e d w i t h t h e
b a s e p e r i o d o f o t h e r h y d r o l o g i c d a t a and w i t h a v a i l a b l e
c r o p p i n g d a t a and t h e r e b y f a c i l i t a t e d t h e c a l i b r a t i o n
procedure.
The m o d el r e q u i r e s t h a t t h e " i n f l o w s " i n t o t h e t r i b u ­
t a r y and m a i n s t e m s u b —b a s i n s be s p e c i f i e d a s RHS.
However,
t h e m a t h e m a t i c a l n a t u r e o f l i n e a r p r o g r a m m in g t r e a t s e a c h
su b -b a sin as a p o in t in space,
o c c u r a t t h e same p o i n t .
Thu s,
i.e.,
i n f l o w s and o u t f l o w s
in a r e a l i s t i c sense,
it is
n e c e s s a r y t o t r e a t th e w a te r which flo w s out of a p a r t i c u ­
l a r s u b -b a sin as being a v a i l a b l e fo r d iv e r s io n throughout
t h a t s u b - b a s i n and t h e r e f o r e i s t r e a t e d a s i n f l o w .
In1
1The 1 9 6 3 -1 9 7 7 a v e r a g e a n n u a l f l o w a t S i d n e y was 10.3
mmaf c o m p a r e d w i t h t h e 1 9 34-1980 a v e r a g e a n n u a l f l o w o f 8.9
mmaf.
^
>'
68
s u b - b a s i n s where v e ry l i t t l e
t h e s u b - b a s i n and o u t f l o w ,
ences,
stream flow i s g en erate d w ith in
i n t h e a b s e n c e o f human i n f l u ­
i s n e a r l y t h e same a s i n f l o w , t r e a t i n g o u t f l o w a s
in flo w i s of l i t t l e
consequence.
However, i n s u b - b a s i n s
where t h e r e i s s u b s t a n t i a l i n t e r n a l r u n o f f ,
lim itin g speci­
f i e d i n f l o w t o m e a s u r e d s t r e a m i n f l o w would s e r i o u s l y
u n d e r e s t i m a t e t h e w a t e r a v a i l a b l e i n t h a t s u b —b a s i n .
In c o n ju n c tio n w ith the p rev io u s n o tio n ,
i t i s im pera­
t i v e t o k e e p i n m in d t h a t t h e h i s t o r i c a l l y m e a s u r e d o u t f l o w
f r o m a s u b —b a s i n , on a m o n t h l y b a s i s , a l r e a d y r e f l e c t s . a
h i s t o r i c a l p a t t e r n o f d i v e r s i o n and r e t u r n f l o w w h i c h
o c c u r r e d i n t h a t s u b —b a s i n .
More c o r r e c t l y ,
i t reflects
t h e n e t d i f f e r e n c e o f d i v e r s i o n i n t h a t month and r e t u r n
f l o w s t h a t r e t u r n e d i n t h a t m onth.
Thus, w h a t i s r e a l l y
r e q u i r e d a s a. RHS i s t h e p r i s t i n e f l o w o f t h e r i v e r , t h a t
i s , t h e f l o w o f t h e r i v e r i n t h e a b s e n c e o f h u m an i n f l u ­
ences.
E s t i m a t e s o f p r i s t i n e r i v e r f l o w s w e r e p r o v i d e d by
P h i l F a m e s o f t h e Montana o f f i c e o f S o i l C o n s e r v a t i o n
Service,
U.S. D e p a r t m e n t o f A g r i c u l t u r e .
Conv eyanc e and F i e l d E f f i c i e n c i e s
Con veyance and f i e l d e f f i c i e n c i e s f o r t h e n i n e s u b ­
b a s i n s w e r e o b t a i n e d f r o m SCS-USDA (1978).
C urrent le v e ls
o f c o n v e y a n c e and f i e l d e f f i c i e n c i e s u s e d i n t h e b a s i c
m o d el a r e p r e s e n t e d i n T a b l e 2 a l o n g w i t h i n c r e a s e d l e v e l s
of e f f i c i e n c i e s f o r th e o t h e r s c e n a r i o s which a r e d i s c u s s e d
later
in t h i s chapter.
69
Table 2.
Model /
Scenario
C u r r e n t and F u t u r e L e v e l s o f Conveyance and
F i e l d E f f i c i e n c i e s . (From SCS-DSDAr 1978)
I
2
3
4
Sub - b a s i n
5 , 6
7
8
9
C o n veyance
BI
(1980)
43
40
50
50
50
50
50
50
32
El
(1990)
56
54
59
59
59
59
60
60
44
E2 (2000)
68
67
68
68
68
68
69
69
56
E3 (2010)
81
81
77
77
77
77
79
79
68
F ield
BI (1980)
40
40
46
42
45
45
51
50
. 51
(1990)
47
51
51
48
50
50
58
57
53
E2 (2000)
54
61
55
54
54
54
64
64
55
ES (2010)
61
72
60
60
59
59
71
71
. 57
El
70
R e t u r n Flows
The d e t e r m i n a t i o n o f t h e g e n e r a l p a t t e r n o f r e t u r n
f l o w s was a m o s t d i f f i c u l t e m p i r i c a l t a s k .
To t h e e x t e n t
t h a t t h e r e h a s b e e n h y d r o l o g i c work t o d e t e r m i n e r e t u r n
flow p a t t e r n s ,
i t h as alw ays been e x tre m e ly s i t e - s p e c i f i c
s t u d i e s w h e r e h y d r o l o g i s t s can a c c o u n t f o r f a c t o r s s u c h a s
s o i l t y p e s , t o p o g r a p h y , and t h e g e o m o r p h o l o g y o f t h e l o c a l ­
ity ,
What w as n e e d e d f o r t h i s s t u d y was a g e n e r a l p a t t e r n
of r e t u r n flo w s,
i.e.,
a p a t t e r n which r e p r e s e n t s th e
a v erag e r e t u r n flo w p a t t e r n over th e range of s o i l ty p es
and t o p o g r a p h i c a l f e a t u r e s f o u n d i n a b a s i n .
S u b s t a n t i a l t i m e was s p e n t i n c o n j u n c t i o n w i t h t h i s
study a tte m p tin g to e m p iric a lly e s tim a te a g e n eral p a tte rn
of r e t u r n flow fo r th e Y ellow stone Basin,
W hile n o t
e n t i r e l y s u c c e s s f u l , work d i d l e a d t o i n d i c a t i o n s o f t h e
p a t t e r n of r e t u r n f l o w s found i n t h e Y e llo w sto n e B asin,
T h e s e i n d i c a t i o n s t e n d e d t o be c o n f i r m e d by d a t a f r o m t h e
Bureau of Reclam ation-USDI ab out r e t u r n flo w p a t t e r n s in
t h e S h o s h o n e P r o j e c t i n Wyoming a nd l e d t o t h e a d o p t i o n o f
t h e r e t u r n f l o w p a t t e r n shown i n T a b l e 3 f o r u s e i n t h i s
stu d y ,^
^The B u r e a u o f R e c l a m a t i o n - U S D I d a t a i s c o n t a i n e d i n a
l e t t e r f r o m t h e Upper M i s s o u r i R e g i o n a l o f f i c e . B u r e a u o f
R e c l a m a t i o n - U S D I , B i l l i n g s , M o n t a n a , Au g u st 1 3 , 1982,
71
T able 3.
R e t u r n Flow P a t t e r n Used i n t h e LP Model=
------ ------- 1
-----------
R e t u r n flo w
occurring:
P e r c e n t of t o t a l
lo sses:
Same month a s
d iv er sion
40
1 s t month a f t e r
div ersio n
12
2nd month a f t e r
d iversion
10.4
3 r d month a f t e r
div ersio n
6.4
4 t h month a f t e r
div ersio n
3.2
5 month t o t a l -3
72.
Minimum Flow R e q u i r e m e n t s
The minimum f l o w r e q u i r e m e n t s f o r e a c h a r e a , f o r e a c h
o f t h e f i v e m o n th s i n t h e m o d e l , a r e l i s t e d i n T a b l e 4.
The v a l u e s u s e d a r e t h e i n s t r e a m r e s e r v a t i o n a m o u n t s
g r a n t e d by t h e Bo a rd o f N a t u r a l R e s o u r c e s and C o n s e r ­
v a tio n .4
3 I n o t h e r w o r d s , 72 p e r c e n t o f t h e l o s s e s f r o m c o n v e y a n c e
and f i e l d s y s t e m s h a s r e t u r n e d i n 5 m o n th s .
The r e m a i n i n g
28 p e r c e n t i s composed o f l o s s e s w h i c h a r e e i t h e r n o n r e c o v e r a b l e o r w i l l r e t u r n a f t e r t h e f i f t h m o n th .
^Minimum f l o w r e q u i r e m e n t s a r e b a s e d on t h e f i n a l
i n s t r e a m r e s e r v a t i o n s p u b l i s h e d i n B o r i s and K r u t i l l a
(198 0, T a b l e 7 -1 ) e x c e p t f o r t h e B i l l i n g s A r e a w h e r e r e c e n t
a d j u s t m e n t s h a v e b e e n made. The v a l u e s f o r t h e B i l l i n g s
A r e a a r e c o n t a i n e d i n a l e t t e r from R i c h a r d Moy, C h i e f ,
W a t e r Management B u r e a u , DNRC, S e p t e m b e r 14, 1982.
Table 4.
Minimum Instream Flows (acre-feet)
I
2
3
4
Sub-basin
5
6
7
8
9
26,000
735,500
May
180,454
1,000
469,309
233,600
755,000
4,600
755,000
June
489,800
3,420 1,093,122
309,300
1,558,000
4,500
1,558,000
July
232,000
I ,400
370,392
221,000
632,000
4,600
632,000
4,000
647,000
August
120,000
381
215,205
■172,000
237,000
4,600
237,000
900
164,000
92,508
346
184,878
155,000
267,000
4,500
267,000
500
195,000
September
11,000 1,496,000
'- j
tv
73
M u n i c i p a l & Energy R e l a t e d Water Us e
At t h e p r e s e n t t i m e ,
w a t e r u s e d f o r m u n i c i p a l and
energy r e l a t e d a c t i v i t i e s i s i n s i g n i f i c a n t r e l a t i v e to
t o t a l flow .
V a l u e s f o r t h e s e u s e s a r e b a s e d on e s t i m a t e s
o f w a t e r u s e i n t h e s e c a t e g o r i e s by B o r i s and K r u t i l l a
( 1 9 8 0 ).5
E n erg y r e q u i r e m e n t s o f 3500 a c r e - f e e t / m o n t h a r e
u s e d i n s u b —b a s i n s 5 , 5, and 8 w h i c h e n c o m p a s s p r e s e n t
l o c a tio n s of coal r e l a te d in d u s try in the basin.
s u b - b a s in s have z e ro energy r e l a t e d w a ter use.
A ll other
R equire­
m e n t s f o r m u n i c i p a l u s e a r e 500 a c r e - f e e t / m o n t h f o r t h e
Upper Y e l l o w s t o n e , 3000 a c r e —f e e t / m o n t h f o r t h e B i l l i n g s
Area,
120 a c r e - f e e t / m o n t h f o r t h e M i d - Y e l l o w s t o n e and 140
a c r e - f e e t / m o n t h f o r t h e Lower Y e l l o w s t o n e .
The i n c l u s i o n
o f b o t h o f t h e s e a c t i v i t i e s i s f a r more i m p o r t a n t m e t h o d ­
o l o g i c a l l y t h a n f o r r e a s o n s o f p r e s e n t s i g n i f i c a n c e as
d i s c u s s e d i n C h a p t e r 3.
I r r ig a te d Acres
I r r i g a t e d a c re a g e fo r each of th e n ine s u b - b a s i n s i s
b a s e d on e s t i m a t e s o b t a i n e d f ro m SCS-USDA (1978).
T hes e
e s t i m a t e s t e n d t o be h i g h e r t h a n a c t u a l m e a s u r e m e n t s o f
5The e n e r g y r e l a t e d w a t e r use v a l u e s i n t h e m o d el a r e
b a s e d on e s t i m a t e d c o a l p r o d u c t i o n i n t h e i m m e d i a t e f u t u r e
( a p p r o x i m a t e l y 72 m i l l i o n t o n s ) , s e e B o r i s and K r u t i l l a
(1 980, T a b l e 5 - 7 ) .
The v a l u e s f o r w a t e r f o r m u n i c i p a l
u s e a r e b a s e d on w a t e r r e s e r v a t i o n s g r a n t e d f o r m u n i c p a l
u s e and a d e p l e t i o n r a t e o f 50 p e r c e n t o f d i v e r s i o n , s e e
B o r i s and K r u t i l l a ( 1 9 8 0 , T a b l e 6 - 8 ) .
74
i r r i g a t e d a c r e s i n any g i v e n y e a r t h a t w o u ld be o b t a i n e d
f r o m t h e Montana D e p a r t m e n t o f A g r i c u l t u r e b e c a u s e i t
in clu d es a cres th a t are i r r ig a te d
in term itten tly .®
The
h i g h e r e s t i m a t e s w e r e u s e d b e c a u s e i t was f e l t t h a t i t more
c o r r e c t l y r e p r e s e n t s th e c u r r e n t l y i r r i g a b l e acrea g e in the
basin.
A t o t a l o f 5 6 9 ,1 0 0 i r r i g a t e d a c r e s a r e u s e d i n t h e
m o d e l.
The i r r i g a t e d a c r e s f o r e a c h s u b - b a s i n a r e p r e ­
s e n t e d i n T a b l e 5.
I r r i g a t e d Crops
The v e c t o r o f a l t e r n a t i v e i r r i g a t e d c r o p s f o r e a c h of
t h e n i n e s u b - b a s i n s was c h o s e n , b a s e d on h i s t o r i c a l d a t a ,
t o be t n o s e p r i n c i p a l c r o p s w h i c h , c o l l e c t i v e l y , w i l l
a c c o u n t f o r a p p r o x i m a t e l y 95 p e r c e n t o r more of t h e i r r i ­
g a te d a c r e s in th e county.
T h i s was b a s e d on d a t a fro m t h e
Montana D e p a r t m e n t o f A g r i c u l t u r e f o r a l l c r o p s e x c e p t
i r r i g a t e d p a s t u r e w h i c h was b a s e d on i n f o r m a t i o n f r o m t h e
Bureau of Census.
The a l t e r n a t i v e c r o p s f o r e a c h o f t h e
nine su b -b a sin s a re l i s t e d
i n T a b l e 6.
I t i s a p p r o p r i a t e t o view th e b a r l e y c ro p p in g a c t i v i t y
as a proxy fo r a l l i r r i g a t e d s p r i n g g r a i n s ( o a ts ,
spring
w heat, e t c e te r a ) because of c lo s e s i m i l a r i t i e s of the crops
w ith regard to i r r i g a t e d production.
For t h e c a l i b r a t i o n
m o d e l , w h e r e a h i s t o r i c a l c r o p p i n g p a t t e r n was s p e c i f i e d a s
®For e x a m p l e , t h e 1977 Montana A g r i c u l t u r a l S t a t i s t i c s
l i s t s a t o t a l o f 4 34,555 i r r i g a t e d a c r e s i n t h e Y e l l o w s t o n e
B asin.
75
Table 5.
I r r i g a t e d A c r e a g e s o f t h e Nine S u b - b a s i n s Used .
i n t h e LP M odel. (From SCS-USDAr 1978)
#
Sub-basin
Name
I r r i g a t e d Acres
I
Upper Y e l l o w s t o n e
148,208
2
C l a r k s Fo rk
93,532
3
B illin g s
94,490
4
Bighorn
61,110
5
M id-Y ellow stone
58,800
6
Tongue
11,635
7
Kinsey
19,590
8
Powder
11,075
9
Lower Y e l l o w s t o n e
70,660
Basin T o ta l
569,100
.
76
Table 6 .
A l t e r n a t i v e Crops f o r t h e N in e S u b - b a s i n s .
Upper Y e l l o w s t o n e
b a r l e y ? a l f a l f a hay? o t h e r hay?
p a stu r e , sugar b e e t s
C l a r k s Fork
b a r l e y ? a l f a l f a hay? o t h e r hay
p a s t u r e ? s u g a r b e e t s ? b ean s?
corn s i l a g e
B illin g s
b a r l e y , a l f a l f a hay? o t h e r h a y ,
p a s t u r e , sugar b eets? corn (grain) ?
c o rn s i l a g e ? b e a n s
B ig h o r n
b a r l e y ? a l f a l f a hay? o t h e r hay?
pasture? sugar b e e ts? corn ( g r a i n ) ?
c o rn s i l a g e , b e a n s
M id-Y ellow stone
b a r l e y ? a l f a l f a hay? o t h e r hay?
p astu re? sugar b e e t s , corn ( g r a i n ) ?
c o rn s i l a g e ? b e a n s
Tongue
b a r l e y ? a l f a l f a hay? o t h e r hay
pasture? corn s i l a g e
Kinsey
b a r l e y ? a l f a l f a hay? o t h e r hay?
p a s t u r e , sugar b e e ts? corn ( g r a i n ) ?
corn s i l a g e ? beans
Powder
b a r l e y ? a l f a l f a hay? o t h e r hay?
pasture? sugar beets? corn (grain) ?
co rn s i l a g e
Lower Y e l l o w s t o n e
b a r l e y ? a l f a l f a hay? o t h e r h a y ,
p a s t u r e , sugar b e e ts? corn ( g r a i n ) ?
corn s i l a g e ? beans
77
a p a r t of th e c a l i b r a t i o n p ro c e d u r e ,
the b a rle y a c t i v i t y
was e x p l i c i t l y a p r o x y and i n c l u d e d a c r e a g e s o f o a t s and
s p r i n g wheat in th e c a l c u l a t i o n of the c ro p p in g p a t t e r n .
R e t u r n s Over V a r i a b l e C o s t
(ROVC)
The o b j e c t i v e f u n c t i o n o f t h e model i s t o m a x i m iz e
ROVCgS o f t h e d i f f e r e n t c r o p s w h i c h can be g ro w n i n t h e
basin.
The ROVCs u s e d i n t h i s model a r e b a s e d on m o d i f i e d
e n t e r p r i s e b u d g e t s p r e p a r e d by t h e C o o p e r a t i v e E x t e n s i o n
S ervice.
The m o d i f i e d b u d g e t s a r e l i s t e d
i n A p p e n d ix A.
S u g a r B e e t and Bean A c r e a g e R e s t r i c t i o n s
In a d d i t i o n to th e o v e r a l l acrea g e r e s t r i c t i o n s in a
s u b - b a s i n , r e s t r i c t i o n s w e r e p l a c e d on t h e maximum a c r e a g e s
o f b e a n s and s u g a r b e e t s .
Bo th s u g a r b e e t s and b e a n s a r e
s p e c i a l i z e d c r o p s g ro w n u n d e r i n t e n s i v e m an ag em en t and
p ro d u ctio n regim es.
The l a r g e o b j e c t i v e f u n c t i o n v a l u e s o f
t h e s e c r o p s w o u ld r e s u l t i n a b n o r m a l l y h i g h a c r e a g e s i f
th e y were l e f t u n r e s t r i c t e d .
T h e r e f o r e e x o g e n o u s c on­
s t r a i n t s w e r e u s e d t o r e s t r i c t a c r e a g e s o f t h o s e tw o c r o p s
t o more r e a l i s t i c l e v e l s .
Sugar b e e t a c re a g e i s l i m i t e d to
t h e number o f a c r e s c o n t r a c t e d w i t h t h e b u y er i n t h e Y el­
low stone b asin .
T h e r e f o r e s u g a r b e e t a c r e a g e i n t h e model
i s l i m i t e d t o t h e a v erag e h i s t o r i c a l a c re a g e s which approx­
i m a t e s t h e number o f c o n t r a c t a c r e s .
Beans a r e a l s o
l i m i t e d to th e average h i s t o r i c a l acreage in th e basin.
78
Net I r r i g a t i o n R equirem ents
The q u a n t i t y o f w a t e r r e q u i r e d f o r e a c h c r o p f o r e a c h
month o f t h e g r o w i n g s e a s o n a r e b a s e d on t h e n e t i r r i g a t i o n
r e q u i r e m e n t s p u b l i s h e d by t h e SCS-USDA,
T his le a v e s i n t a c t
t h e SCS a s s u m p t i o n s a b o u t t h e o c c u r r e n c e of e f f e c t i v e r a i n ­
f a l l t h a t are i m p l i c i t in t h a t p u b lic a tio n .
Each o f t h e
n i n e s u b - b a s i n s h ad t o be c l a s s i f i e d a c c o r d i n g t o c l i m a t i c
zon e
( s e e A p p e n d ix B) and t h e n n e t i r r i g a t i o n r e q u i r e m e n t s
f o r each c ro p in each a r e a a re d e te rm in e d .
These r e q u i r e ­
m e n t s a r e p r e s e n t e d i n A p p e n d ix B.
Since i r r i g a t i o n re q u ire m e n ts a re not p u b lis h e d fo r
t h e " o t h e r hay" c a t e g o r y ,
( g r a s s and n a t i v e hay) i t was
a s s u m e d t h a t " o t h e r hay" i s i r r i g a t e d e x a c t l y l i k e a l f a l f a
h a y e x c e p t t h a t i r r i g a t i o n s t o p s a t t h e end o f J u l y a f t e r
one c u t t i n g h a s b e e n h a r v e s t e d .
W hile i t i s u n d o u b ted ly
t r u e t h a t some p o r t i o n o f t h i s c a t e g o r y i s i r r i g a t e d a f t e r
J u l y , a t l e a s t f o r p a s t u r e , i t a l s o se em s l i k e l y t h a t many
" o t h e r h ay" a c r e s a r e i r r i g a t e d f r o m s t r e a m s w h e r e f l o w s
a r e r e s t r i c t e d i n l a t e summer.
A lte r n a tiv e Scenarios
Increased I r r ig a tio n E f f ic ie n c y Scenarios
E s t i m a t e s o f c u r r e n t l e v e l s o f c o n v e y a n c e and f i e l d
e f f i c i e n c i e s a l o n g w i t h e s t i m a t e s of i n c r e a s e s t o be
a c h i e v e d by t h e y e a r 2000 w e r e t a k e n fr o m SCS-USDA (1978).
An i n t e r m e d i a t e l e v e l was e x t r a p o l a t e d by t a k i n g t h e
79
c u r r e n t l e v e l plus, h a l f th e d i s t a n c e betw een th e c u r r e n t
and y e a r 2000 l e v e l .
Also,
a h i g h l e v e l was e x t r a p o l a t e d
a s b e i n g e q u a l t o t h e y e a r 2000 l e v e l p l u s h a l f t h e
d i s t a n c e b e t w e e n t h e c u r r e n t and y e a r 2000 l e v e l s .
This
provides th re e scen ario s fo r increased i r r i g a t i o n e f f i c ­
iency in a d d it i o n t o th e c u r r e n t v a lu e s.
W h i l e t h e r e i s no
g u a r a n t e e t h a t t h e s e i n c r e a s e d l e v e l s w i l l be a c h i e v e d a t
t h e i m p l i e d t i m e s , a p p r o x i m a t e l y y e a r s 1 9 9 0 , 2 0 0 0 , and
2010, th e y p ro v id e a r e a s o n a b le b a s i s f o r s p e c u l a t i o n ab o u t
a t t a i n a b l e l e v e l s from a t e c h n i c a l s t a n d p o in t .
The v a l u e s
o f c o n v e y a n c e and f i e l d e f f i c i e n c i e s u s e d i n t h e s e s c e ­
n a rio s are l i s t e d
i n T a b l e 2.
Dry Year S c e n a r i o s
V a r i a t i o n in a v a i l a b l e w a te r s u p p l i e s from year to
year i s a c r i t i c a l f a c to r a f f e c t i n g the p o s s i b i l i t i e s fo r
r i v e r m an a g em en t.
Thus, i t was deemed i m p o r t a n t t o i n d i ­
c a te th e im pacts of dry y e a rs .
The p h y s i c a l i m p a c t o f d r y
y e a r s a r e s i m u l a t e d i n tw o j o i n t a s p e c t s o f t h e m o d e l ,
d e c r e a s e d r i v e r f l o w s and i n c r e a s e d n e t i r r i g a t i o n r e q u i r e ­
m ents.
The i n c r e a s e d n e t i r r i g a t i o n r e q u i r e m e n t s w e r e
n e c e s s a r y i n t h i s model b e c a u s e t h e b a s i c model i n c o r ­
p o r a t e s t h e a s s u m p tio n of norm al l e v e l s of e f f e c t i v e
r a i n f a l l in d ete rm in in g the n e t i r r i g a t i o n req u ire m e n ts.
For p r e s e n t p u r p o s e s ,
a d j u s t m e n t s w e r e made i n r i v e r
f l o w s and r a i n f a l l t h a t w o u ld be i n d i c a t i v e o f t h e i m p a c t s
involved.
Using a n n u al f lo w s of t h e Y e llo w sto n e R iv er f o r
80
a p e r i o d o f 55 y e a r s a t S i d n e y a s a g u i d e , and a s s u m i n g a
normal d i s t r i b u t i o n of r i v e r flo w s ,
i t is estim ated th a t
f l o w s g r e a t e r t h a n 6.9 mmaf w o u l d o c c u r more t h a n 90 p e r ­
c e n t o f t h e t i m e a n d f l o w s g r e a t e r t h a n 8 . 8 7 mmaf w o u l d
o c c u r more t h a n 80 p e r c e n t of t h e t i m e .
In r e a l i t y ,
the
r i v e r f l o w s do n o t a p p e a r t o be d i s t r i b u t e d n o r m a l l y .
A c t u a l f r e q u e n c y c a l c u l a t i o n s f r o m t h e 55 y e a r p e r i o d i n d i ­
c a t e t h a t f lo w s g r e a t e r than or eq u al to t h e s p e c i f i e d
f l o w s w o u l d o c c u r a b o u t 75 a n d 54 p e r c e n t o f t h e t i m e
resp ectiv ely .
In o t h e r words,
flow used th e s e s c e n a r i o s
flow s l e s s than th e " d r i e s t 0
(6.9 mmaf) a c t u a l l y o c c u r r e d 46
p e r c e n t of th e tim e in t h e h i s t o r i c a l p e rio d .
U s i n g d a t a p r o v i d e d by C a p r i o , S n y d e r , and G r u n w a ld
(1 9 8 0 ), r e d u c t i o n s i n r a i n f a l l w h i c h would o c c u r 90 and 80
p e r c e n t of th e tim e were a l s o e s t i m a t e d .
The e s t i m a t e s o f
th e n e t i r r i g a t i o n r e q u ire m e n ts were then a d ju s te d
a c c o rd in g t o th e lo w e r l e v e l s of r a i n f a l l .
The a d j u s t m e n t s i n r i v e r f l o w and r a i n f a l l w e r e g e n e r ­
a l i z e d i n t o c o n s t a n t p e r c e n t a g e c h a n g e s i n r i v e r f l o w s and
n e t i r r i g a t i o n r e q u i r e m e n t s and a p p l i e d p r o p o r t i o n a l l y i n
a l l sub-basins.
The f i r s t d r y y e a r s c e n a r i o i s b a s e d on
d e c r e a s e s i n r i v e r f l o w s o f 14 p e r c e n t a n d i n c r e a s e s i n n e t
i r r i g a t i o n r e q u i r e m e n t s o f 13 p e r c e n t .
The s e c o n d d r y y e a r
s c e n a r i o i s b a s e d on r i v e r f l o w . d e c r e a s e s o f 33 p e r c e n t a n d
i n c r e a s e s i n n e t i r r i g a t i o n r e q u i r e m e n t s o f 21 p e r c e n t .
81
I n c r e a s e d L evel of A g r i c u l t u r a l P r i c e s
Values a s s o c i a t e d w ith w ater fo r i r r i g a t e d a g r i c u l ­
t u r a l u s e a r e i m p u t e d v a l u e s d e r i v e d fro m t h e v a l u e o f t h e
a g r i c u l t u r a l p r o d u c ts produced w ith w ater.
Thus, a ch an g e
i n th e l e v e l of p r i c e s f o r a g r i c u l t u r a l p r o d u c ts w i l l
c h a n g e t h e v a l u e o f w a t e r and w i l l have e c o n o m ic i m p a c t s
p e r t i n e n t t o w a t e r m anagem ent p o l i c i e s i f w a t e r i s a s c a r c e
resource.
A d j u s t m e n t s i n p r i c e s w e r e made b a s e d on r a t i o s
o f t h e p r i c e s p a i d and p r i c e s r e c i e v e d i n d i c e s .
For exam­
p l e , a s an a p p r o x i m a t i o n t o t h e l e v e l o f r e t u r n s t o
a g r i c u l t u r e w h i c h p r e v a i l e d i n 1973, t h e r a t i o o f t h e 1973
p r i c e s r e c i e v e d and p r i c e s p a i d i n d i c e s w e r e c o m p a r e d t o
t h e 19 80 r a t i o o f t h e s e i n d i c e s a n d t h e n t h e a d j u s t m e n t s o f
t h e p r i c e s r e c i e v e d i n t h e 1980 b u d g e t s i n o r d e r t o a p p r o x ­
i m a t e t h e 1974 r a t i o can be c a l c u l a t e d . . T h i s p r o c e d u r e
r e s u l t e d i n i n c r e a s e d p r i c e s r e c i e v e d i n t h e 1980 b u d g e t s
o f a b o u t 42 p e r c e n t .
T h i s was u s e d a s t h e f i r s t h i g h e r
a g r ic u ltu r a l p ric e s scenario.
A second s c e n a r i o based
l o o s e l y on p r o j e c t i o n s of t h e p r i c e s p a i d and r e c i e v e d
i n d i c e s w h i c h w o u ld e x i s t i f t h e r e was an i n c r e a s e i n t h e
p r i c e s o f a g r i c u l t u r a l c r o p s i n t h e 1980 b u d g e t s o f a b o u t
70 p e r c e n t .
Indexing th e p r i c e s re c ie v e d alone a ls o r e s u l t s in
c h a n g e s i n th e r e l a t i v e v a lu e s of c r o p s as w e l l , w hich i s
t o be e x p e c t e d .
How ever,
i t i s d e s ir a b le in t h i s a n a ly s is
t o look a t th e im p act of h ig h e r l e v e l s of a g r i c u l t u r a l
82
re tu rn s c e t e r i s p e rIbus » i.e .,
including the r e la tiv e
constant.
T herefore,
holding e v ery th in g e l s e ,
r a n k i n g o f t h e ROVCs o f t h e c r o p s
th e i n c r e a s e s in p r i c e s r e c e i v e d were
t r a n s l a t e d i n t o c o n s t a n t p e r c e n t a g e c h a n g e s i n t h e ROVC1s
and a p p l i e d t o a l l c r o p s .
The tw o s c e n a r i o s r e s u l t e d i n
p r o p o r t i o n a t e i n c r e a s e s i n ROVCs o f 78 and 134 p e r c e n t
resp ectiv ely .
In c rea sed I r r i g a t e d Acreage S c e n a r io s
Three s c e n a r i o s of a d d i t i o n a l i r r i g a t e d a c r e a g e were
a ls o developed.
The f i r s t tw o s c e n a r i o s a r e b a s e d on p r o ­
j e c t i o n s of e c o n o m ic a lly f e a s i b l e a d d i t i o n a l a c re a g e a t a
"low" and " i n t e r m e d i a t e " l e v e l o f f u t u r e d e v e l o p m e n t done
by t h e DNRC (1977d).
tio n al
i r r i g a t e d a c r e a g e s o f 7 9 ,1 6 0 and 1 58,310 a c r e s
resp ectiv ely .
increase
lev el
T h ese two s c e n a r i o s r e p r e s e n t a d d i ­
A th ir d scenario,
w h i c h r e p r e s e n t s an
i n i r r i g a t e d a c r e a g e e v e n beyond t h e DNRC "high"
(237,4 80 a c r e s ) ,
i s b a s e d on t h e t o t a l number o f
a d d i t i o n a l a c r e s f o r w h i c h w a t e r r e s e r v a t i o n s h a v e be en
granted,
2 65,881 a c r e s .
In each of th e s e s c e n a r i o s th e
a d d itio n a l a c re s a re d i s t r i b u t e d throughout th e b a sin
according to the d i s t r i b u t i o n
of c u r r e n t l y i r r i g a t e d a c r e s .
83
C hapter 5
R esults
The r e s u l t s o f u s i n g t h e LP m o d e l t o g e n e r a t e a s o l u ­
t i o n f o r t h e b a s i c Y e l l o w s t o n e R i v e r B a s i n m od el and f o r a
s e r i e s of a lt e r n a t iv e scen a rio s are presented in t h i s
chapter.
The a l t e r n a t i v e s c e n a r i o s i n v o l v e f a c t o r s w h ic h
a f f e c t e i t h e r p h y s i c a l or e c o n o m i c v a r i a b l e s w h i c h have
i m p l i c a t i o n s f o r w a t e r management p o l i c i e s .
Each o f t h e
s c e n a r i o s i s b a s e d on a v a r i a t i o n o f one major co m p on en t o f
t h e m od el w h i l e t h e r e m a i n i n g c o m p o n e n ts a r e h e l d c o n s t a n t .
The p u r p o s e i s t o a n a l y z e t h e i m p a c t o f c h a n g e s o f t h a t
co m p on en t on t h e r e s t o f t h e s y s t e m .
The f o l l o w i n g i s a s u m m a r y o f t h e b a s i c m o d e l a n d t h e
s c e n a r i o s w h i c h w e r e d e v e l o p e d i n C h a p t e r s 3 and 4 and t h e
n o t a t i o n used in p r e s e n t i n g t h e r e s u l t s .
The B a s i c Model
BI
T h i s i s . t h e m odel o f t h e Y e l l o w s t o n e
River B asin a t the p r e s e n t tim e.
It
i n c o r p o r a t e s c u r r e n t l e v e l s of conveyance
and f i e l d e f f i c i e n c i e s ( r e p r e s e n t i n g a
b a s i n - w i d e i r r i g a t i o n e f f i c i e n c y o f 19
p ercen t), cu rren tly irrig a te d acres,
r e t u r n s o v e r v a r i a b l e c o s t s b a s e d , o n 1980
c ro p b u d g e ts , s p e c i f i e d r e t u r n flow
p a t t e r n , c u r r e n t minimum i n s t r e a m f l o w
r e q u i r e m e n t s , and a d j u s t e d r i v e r f l o w
v a l u e s fr o m t h e c a l i b r a t i o n p h a s e .
84
Increased I r r ig a tio n E ffic ie n c y Scenarios
El
Conve yanc e and f i e l d e f f i c i e n c i e s a r e
i n c r e a s e d a b o u t 43 p e r c e n t o v e r t h e b a s i c
m odel l e v e l s t o a b a s i n - w i d e i r r i g a t i o n
e f f i c i e n c y 28 p e r c e n t .
E2
Conveyance and f i e l d e f f i c i e n c i e s a r e
i n c r e a s e d a b o u t 92 p e r c e n t o v e r t h e b a s i c
m odel l e v e l s t o a b a s i n - w i d e i r r i g a t i o n
e f f i c i e n c y o f 37 p e r c e n t .
T his l e v e l of
e f f i c i e n c y i s t h a t p r o j e c t e d by t h e SCS
t o be a c h i e v e d f o r t h e y e a r 2000.
E3
Conveyanc e and f i e l d e f f i c i e n c i e s a r e
i n c r e a s e d a b o u t 150 p e r c e n t o v e r t h e
b a s i c m o d el l e v e l s t o a b a s i n - w i d e
i r r i g a t i o n e f f i c i e n c y o f 48.5 p e r c e n t .
Dry Year S c e n a r i o s ( c o m p a red t o t h e b a s i c m odel w h i c h i s
b a s e d on an a n n u a l f l o w a t S i d n e y o f 10.2 mmaf, t h e
a v e r a g e f l o w f o r t h e 1 9 6 3 -1 9 7 7 p e r i o d . )
Dl
S p e c i f i e d r i v e r f l o w s a r e d e c r e a s e d 14
p e r c e n t and n e t i r r i g a t i o n r e q u i r e m e n t s
i n c r e a s e d 13 p e r c e n t f r o m t h e b a s i c
m o d e l . T h i s r e p r e s e n t s an a n n u a l f l o w of
8 . 8 7 mmaf a t S i d n e y w h i c h i s o n l y
s l i g h t l y b e lo w t h e 1 9 34-1980 h i s t o r i c a l
a v e r a g e o f 8.9 mmaf. F l o w s l o w e r t h a n
t h i s l e v e l o c c u r r e d h i s t o r i c a l l y 23 o u t of
55 y e a r s i n t h e 1 9 2 4 -1 9 8 0 p e r i o d .
D2
S p e c i f i e d r i v e r f l o w s a r e d e c r e a s e d 33
p e r c e n t and n e t i r r i g a t i o n r e q u i r e m e n t s
i n c r e a s e d 21 p e r c e n t f r o m t h e b a s i c
m o d e l . T h i s r e p r e s e n t s an a n n u a l f l o w a t
S i d n e y o f 6.9 mmaf. F l o w s l o w e r t h a n t h i s
l e v e l o c c u r r e d h i s t o r i c a l l y 13 o u t o f 55
y e a r s i n t h e 1924 -1 9 8 0 p e r i o d .
I n c r e a s e d I r r i g a t e d Acreage S c e n a r io s
Al
I r r i g a t e d a crea g e of th e b a s in i s
i n c r e a s e d by 7 9 ,1 6 0 a c r e s , a b o u t 14
p e r c e n t over th e b a s i c model.
A2
I r r i g a t e d a c re a g e of th e b a s in i s
i n c r e a s e d by 15 8 ,3 1 0 a c r e s , a b o u t 28
p e r c e n t o v e r t h e b a s i c m o d e l.
85
A3
I r r i g a t e d a c re a g e of th e b a s in i s
i n c r e a s e d by 2 6 5 ,8 8 1 a c r e s , a b o u t 47
p e rc e n t over th e b a s i c model„
Increased A g ric u ltu ra l P ric es S cenarios
Pl
R e tu rn s over v a r i a b l e c o s t s of a l l c ro p s
a r e i n c r e a s e d 78 p e r c e n t o v e r t h e b a s i c
m od el l e v e l s . T h i s a p p r o x i m a t e s t h e l e v e l
o f ROVC's f o r a g r i c u l t u r a l p r o d u c t s i n
1973.
P2
R eturns over v a r i a b l e c o s ts of a l l crops
a r e i n c r e a s e d 134 p e r c e n t o v e r t h e b a s i c
m odel l e v e l s .
C a l i b r a t i n g The Model
The Y e l l o w s t o n e R i v e r B a s i n i s f e d by a m u l t i t u d e o f
ungauged, s t r e a m s w h i c h c o n t r i b u t e t o s t r e a m f l o w a s s t r e a m
augm entation.
A l s o , r i v e r f l o w i s s u b j e c t t o l o s s e s due t o
d e e p p e r c o l a t i o n f r o m t h e r i v e r b ed and e v a p o r a t i o n fro m
the stream su rfa c e .
N et s t r e a m a u g m e n t a t i o n (NSA) i s
d e f i n e d a s t h e sum o f s t r e a m a u g m e n t a t i o n and s t r e a m
lo sses,
f o r a p a r t i c u l a r r e a c h o f r i v e r and t i m e i n t e r v a l .
Net s t r e a m a u g m e n t a t i o n can be e i t h e r p o s i t i v e or n e g a t i v e
d e p e n d i n g on w h e t h e r t h e l o s s e s o u t w e i g h t h e a u g m e n t a t i o n s
in a given tim e i n t e r v a l .
I n s p e c t i o n o f g a u g i n g d a t a shows
t h a t i n w i n t e r m o n th s a c t u a l m e a s u r e d o u t f l o w s f r o m some
a re a s a re l e s s than in flo w s i n d ic a t i n g t h a t n e t stream
a u g m e n t a t i o n c a n become n e g a t i v e a t c e r t a i n t i m e s .
N e i t h e r s t r e a m a u g m e n t a t i o n s o r s t r e a m l o s s e s have
been e m p i r i c a l l y m easured along th e Y e llo w sto n e R iv er.
b a lan ce e q u a tio n of r i v e r flow for a p a r t i c u l a r tim e
A
86
i n t e r v a l t h a t a c c o u n t s f o r n e t s t r e a m a u g m e n t a t i o n and
re tu rn flow s i s
O utflow -
( I n f l o w + D i v e r s i o n ) = (NSA + R e t u r n f lo w )
R e a s o n a b l e e s t i m a t e s o f t h e q u a n t i t y (NSA + R e t u r n flo w )
c a n be o b t a i n e d u s i n g o b s e r v e d v a l u e s o f i n f l o w and o u t f l o w
and c a l c u l a t e d d i v e r s i o n s ,
irrig a tio n efficien cies,
w h i c h a r e b a s e d on e s t i m a t e d
n e t i r r i g a t i o n r e q u i r e m e n t s , and
h i s t o r i c a l l y observed cropping p a tt e r n s .
However,
i t is
n o t p o s s i b l e t o s e p a r a t e n e t s t r e a m a u g m e n t a t i o n s and
r e t u r n f l o w s i n t o t h e i r r e s p e c t i v e m a g n i t u d e s u n l e s s one or
t h e o t h e r i s known.
In t h i s c ase , n e t stream augm entation
w a s t r e a t e d a s a n u n k n o w n v a r i a b l e t o be e s t i m a t e d a s a
r e s i d u a l when t h e r e t u r n f l o w p a t t e r n was s p e c i f i e d .
The
r e t u r n f l o w c o e f f i c i e n t s w e r e b a s e d on r e t u r n f l o w p a t t e r n s
estim ate d a t otner lo c a tio n s.
I n some o f t h e s u b - b a s i n s , s u c h a s t h e U p p e r Y e l l o w ­
s t o n e and t h e C l a r k s F o r k , i t a p p e a r s t h a t n e t s t r e a m
a u g m e n t a t i o n i s p o s i t i v e and s i g n i f i c a n t i n t h e summer.
In
t h e l o w e r p o r t i o n o f t h e b a s i n h o w e v e r , n e t s t r e a m augmen­
t a t i o n may be e i t h e r p o s i t i v e , n e g a t i v e or n e a r l y z e r o
d u r i n g t h e summer m o n t h s .
The c a l i b r a t i o n p r o c e s s makes an
e s tim a te of n e t stream augm entation during th e c a l i b r a t i o n
p h a s e , and t h e r e a f t e r i t i s t a c i t l y a ssu m e d t h a t n e t s t r e a m
augm entation s ta y s c o n s ta n t throughout a l l of th e sc e n a rio s
87
e x c e p t th e d ry y e a r s c e n a r i o s where n e t s tre a m a u g m e n ta tio n
i s a d j u s t e d downward p r o p o r t i o n a t e l y w i t h r i v e r f l o w s .
The LP model was c a l i b r a t e d t o a v e r a g e l e v e l s o f r i v e r
flo w f o r t h e p e r i o d 1963-1977.
th e f o l l o w i n g were s p e c i f i e d ?
I n c a l i b r a t i n g t h e m o d e l,
th e r e t u r n flow p a t t e r n ,
the
n e t i r r i g a t i o n re q u ire m e n ts fo r c ro p s, th e l e v e l s of con­
v e y a n c e and f i e l d e f f i c i e n c i e s and a c r o p p i n g p a t t e r n
(an
a v e r a g e c r o p p i n g p a t t e r n f o r t h e y e a r s 1 9 5 9 -1 9 7 8 was u s e d
for c a lib ra tio n ).
Then e s t i m a t e s o f n e t s t r e a m a u g m e n t a ­
t i o n w e r e a d j u s t e d so t h a t t h e m o d el g e n e r a t e d r i v e r f l o w s
which c o rre sp o n d e d t o th e a v erag e m easured flo w s of th e
r i v e r f o r t h e 1 9 6 3 —1977 p e r i o d .
C a l i b r a t i o n was b a s e d on
USGS m e a s u r e m e n t s o f r i v e r f l o w s a t t h r e e c h e c k p o i n t s on
th e m ainstem ; B i l l i n g s ,
M i l e s C i t y , and S i d n e y .
The a v e r ­
a g e a n n u a l f l o w o f t h e r i v e r a t S i d n e y f o r t h i s p e r i o d was
10.2 mmaf.
The c a l i b r a t i o n p r o c e s s a c c o m p l i s h e d tw o p u r ­
poses? f i r s t , i t was u se d t o a d j u s t t h e m odel t o a c c o u n t
f o r n e t s t r e a m a u g m e n t a t i o n and s e c o n d ,
i t was u s e d t o
im p r o v e t h e i n t e r n a l c o n s i s t e n c y o f t h e m o d el.
R e s u l t s o f t h e c a l i b r a t i o n r u n a r e r e a s o n a b l e when
c o m p a r e d t o v a l u e s a p p r o x i m a t e d by t h e SCS-USDA (1978) i n
th e Y ellow stone Basin.
For e x am p le ? t h e a v e r a g e d i v e r s i o n
p e r a c r e o f t h e c a l i b r a t e d model i s 6.63 a c r e - f e e t p e r a c r e
( a f / a c r e ) , a b o u t 92 p e r c e n t o f t h e SCS v a l u e o f 7.22
af/acre?
c r o p i r r i g a t i o n r e q u i r e m e n t s a r e a b o u t 1.29
af/acre,
a b o u t 88 p e r c e n t o f t h e SCS v a l u e o f 1.46 a f / a c r e ?
88
and r e t u r n f l o w s f o r t h e May t o S e p t e m b e r i n t e r v a l a r e
a b o u t 3.23 a f / a c r e ,
c o m p a r e d t o t h e SCS v a l u e o f 3.94
af/acre.
C e rta in p a ra m eters s p e c if ie d during th e c a l i b r a t i o n
p r o c e s s w e r e m o d i f i e d i n o r d e r t o r u n t h e b a s i c model and
the subsequent scen ario s.
The c r o p p i n g p a t t e r n was
r e l e a s e d i n o r d e r t o a l l o w t h e LP m o d e l t o s e l e c t t h e c r o p
r o t a t i o n t h a t w o u ld m a x i m i z e r e t u r n s t o a g r i c u l t u r e
according to the o b je c tiv e fu n c tio n .
I r r ig a te d acreage
c o n s t r a i n t s were changed from t h e h i s t o r i c a l l e v e l s used in
the c a l i b r a t i o n p ro cess to c u rre n t values.
minimum i n s t r e a m f l o w r e s t r i c t i o n s ,
In a d d itio n ,
which were n o t in p la c e
d u r i n g t h e h i s t o r i c a l c a l i b r a t i o n p e r i o d , w e r e im p o s ed on
t h e model.
R e s u l t s o f t h e B a s i c Model
The r e s u l t s o f t h e b a s i c m o d e l and t h e s c e n a r i o s a r e
p r e s e n te d in a s e r i e s o f t a b l e s which are l i s t e d below .
Table
7.
B a s i n - w i d e Summary o f t h e B a s i c Model
Table
8.
T o t a l D i v e r s i o n s and R e t u r n F lo w s .
T able
9.
D i v e r s i o n s by S u b - b a s i n .
T able 10.
R e t u r n Flows by S u b - b a s i n .
T ab le 11.
B asin-w ide Cropping P a t t e r n s .
T able 12.
R eturns to A g r ic u ltu r e .
T ab le 13.
Shadow P r i c e s o f W a t e r .
T a b l e 14 .
Shadow P r i c e s o f I r r i g a t e d A c r e s .
89
A summary o f t h e b a s i n - w i d e r e s u l t s o f t h e b a s i c m odel
a r e p r e s e n t e d i n T a b l e 7.
D i v e r s i o n s and r e t u r n f l o w s f o r
t h e i n d i v i d u a l s u b - b a s i n s a r e p r e s e n t e d i n T a b l e s 9 and 10.
R eturns to a g r i c u l t u r e fo r the in d iv id u a l s u b -b a sin s in the
b a s i c m o d e l a r e p r e s e n t e d i n t h e f i r s t c o lu m n o f T a b l e 12.
To t h e e x t e n t t h a t w a t e r i s s c a r c e i n t h e b a s i n , t h e m o d e l
w i l l r e f l e c t e c o n o m ic s c a r c i t y a s a n o n z e r o shadow p r i c e .
The s h a d o w p r i c e s f o r w a t e r i n t h e b a s i c m o d e l , by t i m e
i n t e r v a l and s u b - b a s i n , a r e l i s t e d
T a b l e 13.
i n t h e f i r s t c o lu m n o f
T h u s, t h e m odel d e t e c t s e c o n o m ic s c a r c i t y o f
w a t e r i n A u g u s t ( t i m e i n t e r v a l 3) i n s u b - b a s i n s I ,
and 8.
2 , 3,
The v a l u e o f t h e shadow p r i c e s r e p r e s e n t t h e v a l u e
o f an a d d i t i o n a l a c r e - f o o t o f w a t e r a t t h e m a r g i n ,
L e.,
w h a t on e a d d i t i o n a l a c r e - f o o t o f w a t e r w o u ld c o n t r i b u t e t o
th e value of th e o b je c tiv e fu n c tio n .
Table 7.
B a s i n - w i d e Summary o f t h e B a s i c Model ( B i ) .
T otal
P e r A cre
D iversion
(ac-ft)
4,119,824
'S b
CM
R e t u r n Flow
(ac-ft)
1,976,081
3.47
111,640,157
196.17
R eturns to A g ric u ltu re
Table 8.
Total Diversions and Return Flows (May to September in Acre-feet).
B asic
M odel
BI
Increased Ir rig a tio n
E ffic ie n cy
S c e n ario s
E2
El
D ry Y e a r
S c e n ario s
E3
Dl
D2
Al
Increased I r r ig a tio n
A creage
S c e n ario s
A2
A3
D iv ersio n s
4 ,1 1 9 ,8 2 4
2 ,9 5 9 ,9 4 0
2 ,2 2 6 ,4 7 8
1 ,7 1 3 ,7 2 7
4 ,4 2 3 ,7 0 1
3 ,3 9 1 ,6 7 0
4 ,6 0 8 ,2 9 6
5 ,0 9 6 ,0 7 6
5 ,7 5 8 ,7 1 7
R e tu rn Flow s
1 ,9 7 6 ,0 8 1
1 ,2 5 6 ,9 2 6
818,641
5 1 8 ,4 9 6
2 ,1 4 1 ,6 9 3
1 ,6 1 8 ,5 1 4
2 ,2 1 7 ,4 3 3
2 ,4 5 9 ,4 2 7
2 ,7 8 8 ,1 8 7
Table 9.
S u b -b asin
Diversions by Sub-basin
B asic
M odel
BI
El
(May to September in Acre-feet).
Increased Ir rig a tio n
E ffic ie n cy
S c e n ario s
E2
D ry Y e ar
S c e n ario s
E3
Dl
D2
Al
Increased I r r ig a tio n
A creage
S c e n ario s
A2
A3
i
1 ,2 4 8 ,4 6 4
815 ,8 6 4
5 8 4 ,7 9 3
4 3 4 ,6 0 0
1 ,4 1 1 ,1 9 5
947 ,9 5 8
1 ,4 2 1 ,9 7 4
1 ,5 9 5 ,4 6 0
1 ,8 3 1 ,2 3 7
2
678,0 7 4
539,701
363,675
254,8 6 0
691,5 2 3
104,1 9 8
6 9 3 ,5 4 2
7 7 5 ,4 8 5
886 ,8 4 9
3
648,6 0 9
47 2 ,5 0 1
3 9 8 ,8 7 7
3 2 2 ,9 0 1
577,0 7 8
5 8 3 ,8 4 4
739 ,6 7 7
7 6 3 ,6 2 7
7 9 6 ,1 7 7
4
4 6 3 ,8 8 7
343,984
265,2 9 5
210,8 5 8
5 2 4 ,3 5 1
561 ,2 5 9
529 ,2 2 7
594,560
683,350
5
340,4 0 3
2 5 9 ,6 2 9
2 0 8 ,5 8 0
168,5 9 1
3 8 4 ,7 5 5
4 1 2 ,0 2 1
3 8 6,065
4 3 1 ,7 1 6
493 ,4 8 5
6
6 5 ,155
4 9 ,6 9 5
3 9 ,9 2 4
3 2 ,269
7 3 ,638
7 8 ,861
74 ,4 6 4
8 3 ,777
9 6 ,4 2 8
7
1 0 0 ,4 3 9
7 3 ,5 9 8
5 7 ,9 9 7
4 5 ,6 6 4
1 1 3 ,5 2 7
121,5 7 3
1 14,131
1 2 7,819
146,423
8
5 5 ,2 2 0
4 1 ,3 5 6
3 2 ,0 3 0
2 5 ,216
6 0 ,2 4 4
6 2 ,3 8 3
61,7 3 7
6 8 ,2 5 3
77 ,1 1 2
9
519,5 7 3
3 6 3 ,6 1 2
275,3 0 7
2 1 8 .7 6 8
5 8 7 ,3 9 0
5 1 9 ,5 7 3
5 87,479
655,3 7 9
747,656
Table 10.
S u b -b asin
Return Flows by Sub-basin (May to Septernber in Acre-feet).
B asic
M odel
BI
El
In creased Ir rig a tio n
E ffic ie n cy
S cen ario s
E2
D ry Y e ar
S cen ario s
E3
Dl
D2
Al
Increased Ir rig a tio n
A creage
S cen ario s
A2
A3
i
6 1 4 ,7 6 7
3 5 7 ,7 1 1
2 2 0 ,1 7 7
1 3 0 ,8 0 2
6 9 4 ,8 1 7
5 1 2 ,1 9 2
700,2 3 8
7 85,697
901 ,8 4 1
2
3 6 0 ,7 2 4
232 ,9 6 1
127,504
6 2 ,9 7 1
3 7 7 ,2 6 8
5 0 ,3 9 1
3 7 9 ,2 0 2
4 2 4 ,7 4 0
4 8 6 ,6 2 9
3
2 9 4 ,8 7 9
196,299
1 4 7 ,0 4 2
1 0 2 ,5 7 0
271,9 5 8
253,9 4 1
3 3 6 ,6 8 8
3 5 2,097
373 ,0 3 8
4
2 1 6 ,5 9 8
145,693
9 9 ,198
6 7 ,0 5 2
244,854
262,0 6 6
247 ,3 0 1
2 7 8 ,0 0 0
319 ,7 2 4
5
1 4 8 ,7 5 9
103 ,2 0 6
7 4 ,4 1 2
5 1 ,8 7 6
168,160
1 8 0 ,0 3 7
168,694
1 8 8 ,6 2 7
2 1 5 ,5 9 5
6
2 8 ,4 4 8
2 1 ,0 7 6
1 4 ,2 3 2
9 ,9 2 0
3 2 ,1 5 4
3 4 ,4 2 6
3 2 ,511
36 ,5 7 7
4 2 ,1 0 0
7
4 2 ,1 6 3
2 7 ,035
1 8 ,245
1 1 ,2 9 7
4 7 ,6 6 3
5 1 ,030
4 7 ,9 1 0
5 3 ,6 5 5
6 1 ,4 6 4
8
2 3 ,8 0 2
1 5 ,2 4 2
1 0 ,0 7 4
6,237
2 6 ,7 4 4
2 8 ,4 9 0
2 6 ,9 2 8
30 ,0 5 5
3 4 ,3 0 5
9
2 4 5 ,9 4 1
157 ,7 0 3
1 07,757
7 5 ,7 7 1
278,075
245,9 4 1
277,9 6 1
3 0 9,979
3 5 3 ,4 9 1
Table 11.
Basin-wide Cropping Patterns
C rop
B asic
M odel
0
B arley
A lfa lfa
H ay
O t h e r Hay
P astu re
2 9 2 ,9 6 3
Increased Ir rig a tio n
E ffic ie n cy
S cen ario s
El
E 2 .E 3
0
3 8 4 ,1 5 6
0
3 5 8 ,7 6 9
(acres).
D2
A d d itio n al Ir r ig a te d
A creage
S cen ario s
Al
A2
A3
0
0
0
0
0
227,3 3 9
6 0 ,5 8 4
317 ,1 9 9
3 3 5 ,4 8 2
3 60,330
D ry
Y ear
S c e n ario s
Dl
6 5 ,8 0 6
0
0
8 3 ,2 4 4
133,0 9 7
9 6 ,226
109,207
1 2 6 ,8 4 9
0
0
0
0
0
0
0
0
Suqar B eets
5 7 ,9 7 5
5 7 ,9 7 5
5 7 ,975
5 7 ,9 7 5
5 7 ,9 7 5
5 7 ,9 7 5
5 7 ,975
5 7 ,9 7 5
C orn S i l a g e
138,2 6 4
1 3 9 ,8 7 8
139,8 7 8
1 3 5 ,9 9 3
210,135
160 ,9 8 5
1 8 3 ,7 0 3
214,5 2 7
1 2 ,4 7 8
1 2 ,4 7 8
1 2 ,4 7 8
1 2 ,4 7 8
1 2 ,478
1 2 ,4 7 8
1 2 ,4 7 8
1 2 ,4 7 8
1 ,614
1 0 ,6 1 3
5 2 ,0 7 1
5 ,997
3 ,398
2 8 ,567
6 2 ,7 7 3
T otal Irrig a te d
A creage
569 ,1 0 0
569,1 0 0
5 6 9 ,1 0 0
4 8 0 ,2 6 6
6 4 8 ,2 6 1
7 2 7,412
8 3 4 ,9 3 2
B eans
C orn
S la c k
0
5 6 9 ,1 0 0
8 8 ,8 3 4
Table 12.
S u b -b asin
Returns to Agriculture (dollars).
B asic
Model
BI
In c re a s e d I r r i g a t i o n
E f f ic ie n c y
S e c e n a rio s
El
E2,E3
Dry Y ear
S c e n a rio s
Dl
D2
Al
In c re a se d I r r i g a t i o n
A creage
S c e n a rio s
A2
A3
In c re a se d A g r ic u ltu r a l
P r ic e s
S c e n a rio s
Pl
P2 •
I
31 ,0 2 2 ,8 4 0
31,022,840
3 1 ,022,840
31,022,840
13,186,888
35,318,921
39,614,376
45,452,137
55,220,744
2
12,110,118
2 0 ,351,661
20,351,661
9 ,9 2 6 ,1 8 3
2 ,9 7 6 ,1 4 1
11,010,050
12,093,834
13,566,764
21.555,877
28,337,937
3
2 1 ,132,004
19,967,652
21,132,004
1 5 ,845,518
18,825,321
23,817,986
23,937,981
2 4 ,101,125
37,615,017
49,449,038
72,593,712
4
1 3 ,425,043
13,425,043
13,425,043
1 3 ,425,043
13,425,043
15,192,986
16,960,720
19,363,203
23,896,609
31,414,700
5
11 ,3 7 9 ,7 6 5
11,379,765
11,379,765
11,379,765
11,379,765
12,835,091
14,290,060
16,258,694
20,255,761
26,628,493
4,859,241
6
2 ,0 7 6 ,6 1 5
2 ,0 7 6 ,6 1 5
2 ,0 7 6 ,6 1 5
2 ,0 7 6 ,6 1 5
2,07 6 ,6 1 5
2,373,249
2,670,061
3,073,247
3,696,323
7
3 ,7 8 5 ,6 1 9
3 ,7 85,619
3,785,619
3 ,7 8 5 ,6 1 9
3,785,619
4,280,187
4,77 4 ,5 7 7
5,446,554
6,738,329
8,85 8 ,2 9 7
8
1 ,9 0 0 ,1 7 5
2 ,0 2 8 ,4 2 3
2,02 8 ,4 2 3
1,719,721
1,551,902
2,068,092
2,236,009
2,46 4 ,1 5 1
3,382,295
4,446,386
9
14 ,8 0 7 ,9 7 8
14,807,978
14,807,978
14,807,978
14,807,978
16,574,038
18,339,919
20,739,761
26,357,984
34.650,520
111,640,157
118,845,596
120,009,948
103,989,282
82,105,272
123,470,600
134,917,537
150,465,536
198,718,939
261.238,324
94
Table 13.
Sub­
b a s in
i
Time
In te rv a l
May
June
J u ly
Auqust
Septem ber
Shadow Prices of Water
In c re a se d
Irrig a tio n
E f f ic ie n c y
S c e n a rio s*
Cl
B asic
Model
BI
p ry
Year
S c e n a rio s
Dl
J u ly
A ugust
Septem ber
J u ly
A ugust
‘Septem ber
59.50
9 4 .9 8
62.26
May
June
J u ly
A ugust
Septem ber
6
May
June
J u ly
A ugust
Septem ber
In c re a se d
A g r ic u ltu r a l
P r ic e s
S c e n a rio s
Pl
p;
1 .0 0
57.58
1.00
71.68
71.68
71.53
1.00
114.24
153.54
114.24
153.54
114.24
153.54
1 .0 0
69.82
1.00
59 .5 0
9 4 .9 8
62.26
57.88
62.26
1.00
69.82
1.00
57.88
5 9 .5 0
9 4 .9 0
J u ly
August
Septem ber
5
A3
1 .00
May
4
Al
1.00
May
3
D2
A d d itio n a l
Irrig a te d
A creage
S c e n a rio s
A2
69.82
May
2
(dollars).
1.00
71.68
71.68
71.53
1.00
71.68
1.00
71.53
71.68
1.00
1.00
1 .0 0
1.00
1 .0 0
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1 .0 0
1.00
1.00
1.00
1 .0 0
1 .0 0
1 .0 0
May
7
J u ly
August .
Septem ber
May
8
J u ly
A uqust
Septem ber
5 7 .3 7
.
50.40
1.00
46.72
1.00
57.37
57.37
57.30
May
9
June
J u ly
August
Septem ber
1.00
•E2 and E3 scenarios were not included in this table because all shadow prices were zero
1 .0 0
1.00
104.61
138.54
Table 14.
S u b -b asin
Shadow Prices of Irrigated Acres
B asic
M odel
BI
Increased I r r ig a tio n
E ffic ie n cy
S c e n ario s
El
E2
E3
(dollars).
D ry Y e ar
S c e n ario s
Dl
D2
A d d itio n al Ir r ig a te d
A creage
S c e n ario s
Al
A2
A3
Increased
A g ric u ltu ra l P rice s
S cen ario s
Pl
Pq
i
1 0 3 .7 4
107 .4 2
1 8 8 .9 9
1 9 4 .0 6
8 6 .6 9
—0 —
9 0 .8 8
9 0 .8 8
8 8 .7 8
2 0 8 .7 3
2 8 4 .1 1
2
8 4 .8 2
1 0 0 .6 2
1 8 8 .9 1
1 9 4 .8 4
8 6 .7 2
—0 —
9 1 .5 5
9 1 .5 5
8 8 .7 8
1 8 0.21
2 4 8.69
3
9 5 .4 2
82.78
1 8 7 .0 7
1 9 1 .2 0
7 6 .5 7
2 0 .1 4
7 9 .4 4
7 9.44
7 8.02
1 8 6.38
2 5 1.69
4
1 7 0 .1 6
1 8 0 .1 3
1 8 6.67
1 9 1.20
1 6 5 .1 3
1 5 7.12
1 7 0.16
1 7 0 .1 6
1 6 6 .0 7
332 .9 7
4 4 9 .8 6
5
1 5 0 .4 8
1 5 7 .1 2
1 6 1.32
1 6 4 .6 1
1 4 6.84
1 4 2 .7 6
1 5 0.48
1 5 0.48
1 4 7 .7 7
2 8 9 .6 9
3 8 9 .6 4
6
1 5 0 .4 8
15 7 .1 2
1 6 1.32
1 6 4 .6 1
1 4 6.84
1 4 1 .3 1
1 5 0.48
1 5 0.48
14 7 .7 7
2 8 9 .6 9
3 8 9 .6 4
7
1 5 3.77
1 6 0 .3 8
1 6 4 .2 1
1 6 7 .2 5
1 5 0 .5 6
1 4 7.07
1 5 3.77
1 5 3.77
1 5 1 .4 4
2 9 2 .9 8
3 9 2 .9 3
8
8 9 .9 6
1 6 0.06
1 6 4 .2 1
1 6 7 .2 5
8 7 .1 7
8 4 .0 3
8 9 .9 6
8 9 .9 6
8 8 .7 9
1 7 7 .0 5
2 3 9 .5 5
9
1 4 4 .1 7
1 5 4 .4 7
1 6 0 .3 0
1 6 4 .0 3
1 3 9 .6 9
1 4 1 .5 3
1 4 4.17
1 4 4 .1 7
1 3 8 .9 0
2 8 3.38
3 8 3 .3 3
96
The shadow p r i c e s f o r i r r i g a t e d a c r e s i n t h e b a s i c
mod el a r e p r e s e n t e d i n t h e f i r s t
column o f T a b l e 14.
T hes e
v a l u e s i n d i c a t e w h a t an a d d i t i o n a l a c r e o f i r r i g a t e d l a n d
would c o n t r i b u t e t o t h e v a lu e of th e o b j e c t i v e f u n c t i o n .
The r e s u l t s o f t h e b a s i c m o d e l a r e t h e b e n c h m a r k by
w h i c h t h e r e s u l t s o f t h e s c e n a r i o s w i l l be com pare d.
the
Thus,
s c e n a r i o s become a s e r i e s o f njW h a t - I f " q u e s t i o n s ,
i.e .,
g iv e n th e r e s u l t s of th e b a s i c m o d el, what i f a p a r t ic u l a r
c om p on en t c h a n g e s ?
R esu lts of Increased I r r ig a tio n
E ffic ie n c y S cenarios
One o f t h e p r i m a r y o b j e c t i v e s o f t h i s s t u d y w a s t o
e v a l u a t e t h e e c o n o m i c and h y d r o l o g i c i m p l i c a t i o n s o f r i v e r
m an a g em en t p o l i c i e s w h i c h a r e a i m e d a t i n c r e a s i n g i r r i g a ­
tio n
efficien cies.
H y d r o lo g ic Impacts
As t h e l e v e l o f i r r i g a t i o n e f f i c i e n c y i n c r e a s e s ,
the
q u a n t i t i e s o f d i v e r s i o n s and r e t u r n f l o w s d e c r e a s e and t h e
d i s t r i b u t i o n of r i v e r flow throughout the year i s a lte r e d .
I n t h e El s c e n a r i o ,
d i v e r s i o n i s r e d u c e d by 28 p e r c e n t and
r e t u r n f l o w s f o r t h e May t o S e p t e m b e r i n t e r v a l a r e r e d u c e d
by 36.4 p e r c e n t .
I n t h e E2 s c e n a r i o ,
d i v e r s i o n s and r e t u r n
f l o w s f o r t h e May t o S e p t e m b e r i n t e r v a l a r e r e d u c e d by 46
and 58.6 p e r c e n t r e s p e c t i v e l y fr o m t h e b a s i c m o d e l.
E3 s c e n a r i o ,
In th e
d i v e r s i o n s and r e t u r n f l o w s f o r t h e May t o
S e p t e m b e r i n t e r v a l a r e r e d u c e d by 58.4 and 73.8 p e r c e n t
97
r e s p e c t i v e l y f r o m t h e b a s i c m o d el.
B asin-w ide q u a n t i t i e s
f o r d i v e r s i o n s and May t o S e p t e m b e r r e t u r n f l o w s f o r t h e
b a s i c m odel and t h e s c e n a r i o s a r e l i s t e d i n Table. 8 and
d i v e r s i o n s and r e t u r n f l o w s f o r t h e i n d i v i d u a l s u b - b a s i n s
a r e l i s t e d i n T a b l e s 9 and 10 r e s p e c t i v e l y .
B asin-w ide
c r o p p i n g p a t t e r n s f o r t h e E l , E2 f and ES s c e n a r i o s a r e
l i s t e d i n T a b l e 11.
sub-basins are l i s t e d
Cropping p a t t e r n s f o r th e i n d i v i d u a l
i n A p p en d ix C.
Economic I m p a c t s
R e t u r n s t o a g r i c u l t u r e f o r t h e E l , E2, and ES s c e n a ­
r i o s a r e l i s t e d i n T a b l e 12.
The c r o p p i n g p a t t e r n i s t h e
sa m e i n s c e n a r i o s E2 a n d ES a n d t h e r e f o r e t h e r e t u r n s t o
a g r i c u l t u r e does not change.
The r e t u r n s t o a g r i c u l t u r e
not include d iv e rsio n c o sts.
T h u s,
do
th e value of th e o b jec ­
t i v e f u n c t i o n i s g r e a t e r f o r t h e ES s c e n a r i o t h a n f o r t h e
E2 s c e n a r i o s i n c e l e s s w a t e r h a s b e e n d i v e r t e d .
T otal
r e t u r n s t o a g r i c u l t u r e f o r t h e e n t i r e b a s i n i n c r e a s e d 6.5
p e r c e n t o v e r t h e b a s i c m od el i n t h e El s c e n a r i o .
T otal
r e t u r n s t o a g r i c u l t u r e b a s i n - w i d e i n c r e a s e d 7=5 p e r c e n t
o v e r t h e b a s i c m o d el i n t h e E2 and ES s c e n a r i o s .
The shadow p r i c e f o r w a t e r i n s u b - b a s i n s I , 2, and 3
for
t h e month o f A u g u s t i n c r e a s e d f r o m $59.50 t o $94.98 and
t h e shadow p r i c e o f w a t e r i n s u b - b a s i n 8 f o r t h e m onth of
A u g u s t d e c r e a s e d f r o m $57.37 t o 0 i n t h e El s c e n a r i o (shown
i n T a b l e 1 3 ).
Shadow p r i c e s f o r w a t e r i n a l l o t h e r m o n th s
and s u b - b a s i n s w e r e 0 i n t h e E l s c e n a r i o .
The E2 and ES
98
s c e n a r i o s had shadow p r i c e s o f w a t e r t h a t w e re 0 i n a l l
m o n th s and s u o - b a s i n s and c o n s e q u e n t l y w e r e n o t i n c l u d e d i n
T a b l e 13.
The shadow p r i c e s o f i r r i g a t e d a c r e s a r e p r e ­
sented for
e a c h s u b - b a s i n i n T a b l e 14.
R e s u l t s o f t h e Dry Year S c e n a r i o s
I n t n e Dl s c e n a r i o ,
w h i c h r e p r e s e n t s an a n n u a l f l o w a t
S i d n e y o f 8.87 mmaf, d i v e r s i o n s i n c r e a s e d by 7.3 p e r c e n t
o v e r t h e b a s i c m o d el and r e t u r n f l o w s i n c r e a s e d by 8.4
percent.
I n t h e D2 s c e n a r i o ,
w h i c h r e p r e s e n t s an a v e r a g e
a n n u a l f l o w a t S i d n e y o f 6.9 mmaf, d i v e r s i o n s d e c r e a s e d by
2.5 p e r c e n t and r e t u r n f l o w s d e c r e a s e d by 2.9 p e r c e n t fr o m
t h e b a s i c m o d el l e v e l s .
T o t a l d i v e r s i o n s and r e t u r n f l o w s
a r e l i s t e d i n T a b l e 8 , w h i l e d i v e r s i o n s a n d r e t u r n f l o w s by
s u b - b a s i n a r e l o c a t e d i n T a b l e s 9 and 10.
B asin-w ide
c r o p p i n g p a t t e r n s a r e p r e s e n t e d i n T a b l e 11 and c r o p p i n g
p a t t e r n s for th e in d iv id u a l su b -b a sin s a re l i s t e d in
A p p e n d ix
C.
I n t n e D2 s c e n a r i o ,
s u b - b a s i n s I and 2 h a d s l a c k or
i d l e i r r i g a t e d a c r e a g e o f 5 ,5 9 0 and 83,244 a c r e s r e s p e c ­
tiv ely .
the f i f t h
A l s o t h e Y e l l o w t a i l and Tongue r e s e r v o i r s ended
tim e i n t e r v a l ,
i.e.,
Septem ber, a t l e s s than f u l l
c a p a c i t y i n t h i s s c e n a r i o . The tw o r e s e r v o i r s w e r e l e f t a t
11 and 89 p e r c e n t l e s s t h a n c a p a c i t y r e s p e c t i v e l y .
tne i n a b i l i t y to f i l l
W h ile
t h e r e s e r v o i r s a t t h e end o f t h e
i r r i g a t i o n s e a s o n may or may n o t be a d e s i r e d r e s e r v o i r
m an ag em en t g o a l , t h e f a c t t h a t t h i s s c e n a r i o d e v i a t e s fro m
99
th e o t h e r s i s i n d i c a t i v e of th e s e v e r i t y of th e w a te r
shortage
in t h i s scenario.
B a s i n - w i d e r e t u r n s t o a g r i c u l t u r e d e c r e a s e d by 6.85
p e r c e n t and 26.5 p e r c e n t f ro m t h e b a s i c model i n t h e Dl and
D2 s c e n a r i o s r e s p e c t i v e l y .
l i s t e d i n T a b l e 12.
acres are lis te d
R eturns to a g r i c u lt u r e are
Shadow p r i c e s o f w a t e r and i r r i g a t e d
i n T a b l e s 13 and 14 r e s p e c t i v e l y .
R e su lts of Increased Ir r ig a te d
Acreage S c e n a r io s
T a k in g i n t o a c c o u n t t h e i n c r e a s e d a c r e a g e i n t h e A l ,
A2, and A3 s c e n a r i o s , d i v e r s i o n s on a p e r a c r e b a s i s w e r e
7.11,
7 .0 1 ,
and 6.90 a c r e - f e e t p e r a c r e
a c r e - f e e t per a c r e in t h e b a s i c model.
co m p a red t o 7.24
T his o ccu rs because
th e c ro p p in g p a t t e r n which accom panied th e a d d i t i o n a l a c r e s
included l e s s w ater in te n s iv e crops.
However, t h e a d d i ­
t i o n a l a c r e a g e r e s u l t e d in i n c r e a s e s in t o t a l d i v e r s i o n s of
12 p e r c e n t ,
23.7 p e r c e n t ,
and 39.8 p e r c e n t r e s p e c t i v e l y f o r
t h e A l, A2, and A3 s c e n a r i o s o v e r t h e l e v e l of t h e b a s i c
m odel
( s e e T a b l e 8).
R eturns to a g r i c u lt u r e
percent,
i n c r e a s e d by 10.6 p e r c e n t ,
20.9
and 34.8 p e r c e n t f o r t h e A l , A2, and A3 s c e n a r i o s
resp ectiv ely .
R etu rn s to a g r i c u l t u r e for each su b -b asin
a r e l i s t e d i n T a b l e 12 b u t s h o u l d n o t b e v i e w e d a s p r o j e c ­
t i o n s of p o t e n t i a l i r r i g a t e d a g r i c u l t u r a l developm ent in
th e i n d i v i d u a l s u b - b a s i n s a s t h e a d d i t i o n a l a c r e s were
d i s t r i b u t e d a c c o rd in g t o t h e d i s t r i b u t i o n of c u r r e n t l y
100
i r r i g a t e d a c r e s and n o t a c c o r d i n g t o any p r o j e c t i o n s o f
w h e r e d e v e l o p m e n t c o u l d be e x p e c t e d t o o c c u r .
Shadow
p r i c e s f o r w a t e r , by t i m e i n t e r v a l and s u b - b a s i n , and
i r r i g a t e d a c r e s by s u b - b a s i n a r e l i s t e d i n T a b l e s 13 and 14
resp ectiv ely .
R e su lts of the Increased A g r ic u ltu r a l
P r ic es Scenarios
S in ce t h e r e l a t i v e v a lu e of th e c ro p s w ere n o t changed
as a r e s u l t of i n c r e a s i n g th e l e v e l of r e t u r n s over v a r i ­
a b le c o s t , t h e c ro p p in g p a t t e r n d id n o t change from t h a t of
t h e b a s i c model a n d . c o n s e q u e n t l y n e i t h e r d i d d i v e r s i o n s or
re tu rn flow s.
The i n c r e a s e d l e v e l o f p r i c e s r e c e i v e d
r e s u l t e d i n i m p a c t s on o t h e r e c o n o m i c v a r i a b l e s . The
c h a n g e s i n r e t u r n s t o a g r i c u l t u r e a r e l i s t e d i n T a b l e 12.
T a b l e s 13 a n d 14 c o n t a i n t h e s h a d o w p r i c e s o f w a t e r , by
t i m e i n t e r v a l and s u b - b a s i n , and i r r i g a t e d a c r e a g e , by s u b ­
basin.
C a v e a t s and L i m i t a t i o n s o f T h i s S tud y
Any m o d e l, by d e f i n i t i o n , m u s t make c e r t a i n s i m p l i ­
f y i n g a ssu m p tio n s as a p art of th e m odeling p r o c e s s .
Th ese
a s s u m p t i o n s i n v a r i a b l y i n t r o d u c e some p o t e n t i a l f o r e r r o r
i n p a r a m e t e r v a l u e s u s e d i n t h e m o d e l.
I t i s im perative
t h a t t h e r e s u l t s o f an y m o d e l b e e v a l u a t e d i n l i g h t o f t h e
a s s u m p t i o n s t h a t w e r e i n c o r p o r a t e d i n t h e c o n s t r u c t i o n of.
t h e m o d e l.
101
One o f s e v e r a l i m p o r t a n t a s s u m p t i o n s o f t h i s model i s
t h a t i t i s l i m i t e d t o one i r r i g a t i o n scheme f o r e a c h c r o p .
In o t h e r w o rd s, t h e c r o p i s grown o n ly i f t h e r e i s enough
w a t e r t o m e e t one s e t o f n e t i r r i g a t i o n r e q u i r e m e n t s w h i c h
a re s p e c i f i e d fo r each tim e i n t e r v a l .
This te n d s to over­
e s t i m a t e th e economic im p a c ts a s s o c i a t e d w i t h w a te r
s c a r c i t y b e c a u s e i t d o e s n o t a l l o w t h e c r o p t o be grown
under a d im in is h e d w a te r regim e w ith a c o rre sp o n d in g reduc­
tio n in y ie ld .
T h u s,
i f w a t e r i s s c a r c e and t h e r e i s n o t
eno u g h w a t e r t o grow a l f a l f a h a y , f o r e x a m p le , a t t h e
s t a t e d i r r i g a t i o n r e q u i r e m e n t s t h e m odel m u s t r e v e r t t o
so m e o t h e r c r o p w h i c h u s e s l e s s w a t e r a n d m o s t l i k e l y h a s a
s u b s t a n t i a l l y low er o b j e c t i v e f u n c t i o n v a lu e .
A c c o m o d a ti o n
o f m u l t i p l e i r r i g a t i o n sc h e m e s i n t h e model i s s t r a i g h t ­
forw ard but th e req u ire d data i s p re s e n tly u n av ailab le.
I t i s i m p o r t a n t t o rem ember t h a t t h i s model u s e s
re tu rn s to a g ric u ltu re
in th e o b je c tiv e fu n c tio n ,
r e tu r n s over v a r ia b le c o s ts .
Thus,
i.e.,
the r e s u l t s presen ted
h e r e r e p r e s e n t a s h o r t run s o l u t i o n r a t h e r th a n a long run
so lu tio n .
More i m p o r t a n t l y ,
t h e u s e o f ROVCs o v e r e s t i ­
m a te s t h e economic v a l u e s in t h e r e s u l t s p r e s e n t e d in t h i s
chapter.
T h u s, t h e shadow p r i c e s a s s o c i a t e d w i t h w a t e r and
i r r i g a t e d a c r e s a r e o v e r s t a t e d due t o t h e u se o f ROVCs
be ca u se f i x e d c o s t s have not been c o n s id e re d .
I t s h o u l d be r e m e m b e r e d a l s o t h a t t h e b a s i c model was
c a l i b r a t e d t o a r e c e n t h i s t o r i c p e r i o d of t i m e when t h e
102
av erag e flo w s of th e Y ello w sto n e R iv er were h ig h e r th an th e
long run average.
T h u s7 t h e m odel would t e n d t o u n d e r s t a t e
t h e p h y s i c a l s c a r c i t i e s o f w a t e r t h a t w o u ld be p r e s e n t a t a
low er l e v e l of flow .
,
How ever7 t h e Dl s c e n a r i o r e p r e s e n t s a
I
f l o w much c l o s e r t o t h e t h e l o n g r u n a v e r a g e f l o w a n d
t h e r e f o r e c o r r e c t s t h i s s i t u a t i o n som ewhat.
S u g g e s t e d R e f i n e m e n t s o f T h i s Model
As w i t h any m o d e l , an a l m o s t i n f i n i t e number o f
r e f i n e m e n t s c o u l d b e i n c o r p o r a t e d and w o u ld be d e s i r a b l e i n
some s e n s e .
H o w ev er7 some r e f i n e m e n t s f o r t h i s p a r t i c u l a r
mod el c o u l d e a s i l y be made and w o u ld g r e a t l y i n c r e a s e t h e
flex ib ility
o f t h i s m o d el.
The use o f n e t r e t u r n s r a t h e r t h a n r e t u r n s o v e r
v a r i a b l e c o s t s as o b j e c ti v e f u n c tio n v a lu e s fo r th e a g r i ­
c u l t u r a l c r o p s w o u l d r e s u l t i n l o n g r u n s o l u t i o n s and w o u ld
s i m p l i f y i n t e r p r e t a t i o n o f t h e shadow p r i c e s a s s o c i a t e d
w ith the v a rio u s reso u rces.
The e x p a n s i o n o f t h i s
model f r o m f i v e m o n t h l y i n t e r v a l s t o one w h i c h w o u l d
i n c l u d e t h e e n t i r e y e a r w o u ld s i g n i f i c a n t l y i n c r e a s e t h e
v a lu e of t h e m odel.
I t w o u ld f a c i l i t a t e use of t h e model
i n s c e n a r i o s o f f u t u r e d e v e l o p m e n t and t h e i m p a c t o f r i v e r
m an ag em en t p o l i c i e s on f a c t o r s o t h e r t h a n i r r i g a t e d a g r i ­
c u ltu re,
s u c h a s f i s h and w i l d l i f e h a b i t a t , m u n i c i p a l u s e ,
and e n e r g y and o t h e r i n d u s t r i a l u s e s o f w a t e r w h i c h a r e n o t
l i m i t e d t o t h e summer m o n th s .
103
I t w o u l d be u s e f u l t o i n c o r p o r a t e o t h e r f a c t o r s
a s s o c i a t e d w i t h i r r i g a t e d a g r i c u l t u r a l p r o d u c t i o n more
rea listic ally
i n t o t h e m o d el.
T h i s w o u l d i n c l u d e su ch
p r o d u c tio n f a c t o r s as m u l t i p l e i r r i g a t i o n schemes,
d if­
f e r e n t d i s t r i b u t i o n and a p p l i c a t i o n s y s t e m s f o r i r r i g a t i o n ,
d i f f e r e n t f a r m i n g s y s t e m s , d i f f e r e n t l e v e l s o f m anagem ent
and p h y s i c a l f a c t o r s s u c h a s t h e v a r i e t y o f s o i l t y p e s
found i n t h e b a s in .
I
f
104
Chapter 6
C o n c l u s i o n s , P o l i c y I m p l i c a t i o n s and
S u g g estio n s f o r F u rth e r Research
T h is stu d y has been d ev o te d t o m odeling t h e Yellow­
s t o n e R i v e r B a s i n i n Montana so t h a t t h e e c o n o m ic and
h y d r o l o g i c i m p l i c a t i o n s o f a l t e r n a t i v e w a t e r man agem ent
p o l i c i e s c o u l d be e s t i m a t e d .
The i n i t i a l e m p h a s i s of t h i s
s t u d y was t o e v a l u a t e t h e i m p l i c a t i o n s o f i n c r e a s i n g t h e
t e c h n i c a l e f f i c i e n c y of w a ter used f o r i r r i g a t i o n .
study p ro g re sse d ,
As t h e
o p p o rtu n itie s to ev alu ate other a lte r n a ­
t i v e s c e n a r i o s w e r e r e c o g n i z e d and e x p l o i t e d .
The v a s t
c o m p l e x i t i e s o f t h e h y d r o l o g i c and e c o n o m ic s y s t e m s i n t h e
b a s i n a s w e l l . a s t h e maze o f l e g a l and o t h e r i n s t i t u t i o n a l
f a c t o r s w h i c h i n f l u e n c e w a t e r u s e a l l co m b in e t o s u g g e s t
t h a t a c o m p r e h e n s i v e u n d e r s t a n d i n g o f w a t e r m an agem en t
i m p l i c a t i o n s would be, a t t h e v e r y l e a s t , t a x i n g .
Not a l l
o f t h e i s s u e s a r e r e s o l v e d by t h i s s t u d y , b u t a f r a m e w o r k
was d e v e l o p e d w h e r e b y many o f t h e s e i s s u e s can be
i n v e s t i g a t e d i n f u t u r e work.
C o n c l u s i o n s and P o l i c y I m p l i c a t i o n s
The r e s u l t s o f t h e b a s i c model i n d i c a t e t h a t w h i l e
t h e r e i s an a b u n d an ce of w a te r i n m o st p l a c e s m o st of th e
tim e,
s i t e and t i m e s p e c i f i c s h o r t a g e s o f w a t e r do o c c u r i n
105
t h e Y e l l o w s t o n e B a s i n a s i n d i c a t e d by t h e n o n z e r o shadow
p r i c e s o f water in four of the n in e s u b -b a sin s .
le v e l of ir r ig a t io n e f f ic ie n c y
As t h e
in c r e a s e s in the i r r i g a t i o n
e f f i c i e n c y s c e n a r i o s , r e t u r n s t o a g r i c u l t u r e i n c r e a s e over
'
■
■
t h e l e v e l o f t h e b a s i c m o d e l i n E l a n d E2, w h i l e h o l d i n g
c o n s t a n t f r o m E2 t o E3.
This i n d i c a t e s t h a t t h e r e a re
g a i n s t o be made by i n c r e a s i n g t h e l e v e l of i r r i g a t i o n
efficien cy ,
a t l e a s t m a r g i n a l l y , above c u r r e n t l e v e l s .
How ever, a c l o s e r e x a m i n a t i o n o f t h e i n d i v i d u a l s u b ­
b a sin s in d ic a t e s t h a t m arginal in c re a s e s in i r r i g a t i o n
e f f i c i e n c y do r e s u l t i n d e t r i m e n t a l e c o n o m ic i m p a c t s t o
certain
irrig ato rs.
At t h e l e v e l o f i r r i g a t i o n e f f i c i e n c y
i m p l i e d by t h e E l s c e n a r i o , i f w a t e r i s u s e d o p t i m a l l y a s
d e t e r m i n e d i n t h e m o d e l , w a t e r b e co m es more s c a r c e i n s u b ­
basins I ,
2 , and 3 t h a n i s t r u e f o r t h e b a s i c m o d el. T h i s
i s i n d i c a t e d by t h e i n c r e a s e d shadow p r i c e o f w a t e r i n
those su b -b a sin s.
A co m p arisio n of th e r e t u r n s t o a g r i c u l ­
t u r e i n t h o s e s u b - b a s i n s b e t w e e n t h e b a s i c m o d el and t h e El
s c e n a r i o shows a s i g n i f i c a n t r e d i s t r i b u t i o n o f in co m e a s a
r e s u l t of th e in c r e a s e d i r r i g a t i o n e f f i c i e n c y .
R eturns to
a g r i c u l t u r e in s u b - b a s in 3 a re reduced w h ile th o se in sub­
basin 2 are increased.
The i n c r e a s e s i n s u b - b a s i n 2 a r e
more t h a n enou gh t o o f f s e t t h e d e c r e a s e s i n s u b - b a s i n 3, so
t h e r e s u l t i s an i n c r e a s e i n r e t u r n s t o t h e e n t i r e b a s i n .
In s u b - b a s i n 8 h o w e v e r ,
t h e shadow p r i c e o f w a t e r f a l l s t o
z e r o i n t h e El s c e n a r i o i n d i c a t i n g t h a t w a t e r s c a r c i t y has
106
b e e n e l i m i n a t e d by t h e i n c r e a s e i n i r r i g a t i o n e f f i c i e n c y
and a h i g h e r l e v e l o f r e t u r n s t o a g r i c u l t u r e i s a c h i e v e d a s
a resu lt.
A c h i e v i n g t h e l e v e l o f i r r i g a t i o n e f f i c e n c y i m p l i e d by
t h e E2 s c e n a r i o i n d i c a t e s t h a t a l l w a t e r s c a r c i t i e s h a v e
b e e n e l i m i n a t e d when t h e 196 3 -1 9 7 7 a v e r a g e f l o w o c c u r s .
T h u s , i n some s u b - b a s i n s , a s t h e l e v e l o f i r r i g a t i o n e f f i c ­
i e n c y i s i n c r e a s e d t h e r e s u l t w i l l be f i r s t an i n c r e a s i n g
and t h e n a d e c r e a s i n g l e v e l o f shadow p r i c e s o f w a t e r .
The e x p l a n a t i o n t o t h i s phenomenon i s f a i r l y s t r a i g h t ­
f o r w a r d though n o t i n i t i a l l y o b v io u s .
In th o se su b -b a sin s
w h e r e t h e b a s i c m o d el g e n e r a t e s n o n z e r o shadow p r i c e s ,
w a t e r i s a b i n d i n g c o n s t r a i n t on t h e l e v e l o f a g r i c u l t u r a l
production.
In itial
i n c r e a s e s in t h e l e v e l of i r r i g a t i o n
e f f i c ie n c y , w ith e v ery th in g e ls e c o n s ta n t, w i l l r e s u l t
e f f e c t i v e l y i n more w a t e r b e i n g made a v a i l a b l e due t o
decreased d iv e rs io n requirem ents.
However, i n t h o s e s u b ­
b a s i n s which a re i n i t i a l l y s h o r t of w a te r , t h e in c r e a s e d
w a t e r a v a i l a b i l i t y w i l l r e s u l t i n a move t o w a r d s a more,
o p tim al cropping p a tt e r n .
Thus, e i t h e r t h e i n c r e a s e d n e t
i r r i g a t i o n r e q u i r e m e n t s a s s o c i a t e d w i t h t h e new c r o p p i n g
p a t t e r n , which o c c u rs because t h e h i g h e s t v a lu e d c ro p s ten d
t o be t h e m o s t w a t e r i n t e n s i v e ,
o r t h e i n c r e a s e d e co n o m ic
v a l u e a s s o c i a t e d w i t h t h e new c r o p p i n g p a t t e r n o r a c o m b i­
n a tio n of b oth r e s u l t s in th e in c r e a s e d v alu e of w a te r as
reflected
i n h i g h e r shadow p r i c e s .
107
In c re a s e s in r e tu r n s to a g r i c u lt u r e w i l l continue
u n t i l enough w a t e r b e co m es a v a i l a b l e t o a l l o w t h e
c o n s t r a i n e d g l o b a l l y o p tim um c r o p p i n g p a t t e r n i m p l i e d i n
t h e m odel t o be a c h i e v e d .
The c o n s t r a i n e d g l o b a l l y optimum
c r o p p i n g p a t t e r n i s t h a t w h i c h i s a c h i e v e d when w a t e r i s
n o t a b i n d i n g c o n s t r a i n t i n an y s u b - b a s i n and t i m e i n t e r ­
val.
The g l o b a l l y o p tim u m c r o p p i n g h a s b e e n a c h i e v e d a t
th e p o i n t where i r r i g a t i o n e f f i c i e n c y i s in c r e a s e d t o th e
l e v e l o f t h e E2 s c e n a r i o .
The c r o p p i n g p a t t e r n s f o r t h e
i n d i v i d u a l s u b - b a s i n s w h i c h c o l l e c t i v e l y make up t h e
c o n s t r a i n e d g l o b a l l y o p tim u m c r o p p i n g p a t t e r n w e r e a c h i e v e d
i n some s u b - b a s i n s a t . t h e l e v e l o f i r r i g a t i o n e f f i c i e n c y i n
th e b a s i c model, in s u b - b a s i n 8 a t th e l e v e l of i r r i g a t i o n
e f f i c i e n c y in th e El sc e n a rio ,
and i n t h e r e s t o f t h e s u b ­
b a s i n s a t t h e l e v e l o f i r r i g a t i o n e f f i c i e n c y i n t h e E2
scenario.
I n c r e a s e d i r r i g a t i o n e f f i c i e n c y beyond t h e l e v e l o f E2
w ill not increase re tu rn s to a g ric u ltu re but w ill increase
th e v a lu e of o b j e c t i v e f u n c t i o n v a lu e as d i v e r s i o n c o s t s
continue to d ecrease.
This s u g g e s ts t h a t p o l i c i e s designed
t o i n c r e a s e t h e l e v e l o f i r r i g a t i o n e f f i c i e n c y m u st be
b a s e d o n , f i r s t , d e t e r m i n i n g t h e l e v e l of e f f i c i e n c y w h i c h
i s d e s i r e d a s a g o a l and d e t e r m i n i n g t h e p o t e n t i a l e c o n o m ic
im p a cts w i t h i n each s u b - b a s in of a c h ie v in g t h a t g o a l.
a n a l y s i s s h o u l d be c o m p l e t e d p r i o r t o i m p l e m e n t a t i o n of
these
p o licies.
Such
108
D e t e r m in a t io n of th e o p tim a l l e v e l of i r r i g a t i o n
efficien cy
i s i m p l i e d by t h e b e n e f i t / c o s t a n a l y s i s
p r e s e n t e d i n C h a p t e r 2.
The r e s u l t s o f t h i s w ork a r e
i n d i c a t i v e of th e im p a c ts of in c r e a s e s in i r r i g a t i o n e f f i c ­
i e n c y b u t do n o t s u g g e s t w h a t l e v e l o f e f f i c i e n c y i s
d esirab le.
W h il e t h i s s t u d y made no a t t e m p t t o d e t e r m i n e t h e
c o s t o f a c h i e v i n g and m a i n t a i n i n g a l t e r n a t i v e l e v e l s of
i r r i g a t i o n e f f i c i e n c y , an e x a m i n a t i o n o f t h e r e t u r n s t o
a g r i c u lt u r e a s s o c ia te d w ith the in cre ased i r r i g a t i o n e f f i c ­
ien cy s c e n a r i o s does s u g g e s t th e l i m i t s t o e c o n o m ic a lly
f e a s i b l e im provem ents.
The i n c r e a s e i n e f f i c i e n c y fro m t h e
b a s i c m o d el t o t h e E l s c e n a r i o r e s u l t s i n i n c r e a s e d r e t u r n s
t o a g r i c u l t u r e o f a b o u t $7.2 m i l l i o n or $12.66 p e r a c r e .
T h u s, t h e c o s t o f a c h i e v i n g t h e e f f i c i e n c y i n c r e a s e fr o m 19
t o 28 p e r c e n t i s e c o n o m i c a l l y f e a s i b l e o n l y i f i t c a n b e
a c c o m p l i s h e d a t a c o s t o f l e s s t h a n $12.66 p e r a c r e .
This
f i g u r e i s on an a n n u a l b a s i s and i s s t a t e d i n t h e a b s e n c e
o f p r e s e n t v a l u e c a l c u l a t i o n s w h i c h w o u ld r e d u c e t h e v a l u e
o f a n n u a l c o n t r i b u t i o n s i n f u t u r e y e a r s of t h e p l a n n i n g
horizon.
S u b t r a c t i n g f i x e d c o s t s from th e o b j e c t i v e fu n c ­
t i o n v a l u e s w o u ld a l s o r e d u c e . t h e v a l u e s s t a t e d h e r e .
The
d im inishing re tu rn s a sso c ia te d w ith increased i r r i g a t i o n
e f f i c i e n c y i s i l l u s t r a t e d by t h e f a c t t h a t e f f i c i e n c y
i n c r e a s e s f r o m t h e El t o E2 l e v e l s ,
i.e.,
28 t o 37 p e r c e n t ,
i s a c c o m p a n i e d by i n c r e a s e d r e t u r n s t o a g r i c u l t u r e of o n l y
109
$2.05 p e r a c r e .
increase
The i n c r e a s e f r o m E2 t o ES d o e s n o t
the r e tu r n s to a g ric u ltu r e .
T h e r e i s no a p r i o r i r e a s o n t o b e l i e v e t h a t t h e
o p t i m a l l e v e l o f i r r i g a t i o n e f f i c i e n c y w i l l n e c e s s a r i l y be
h ig h e r th a n th e l e v e l which overcom es th e r e d i s t r i b u t i v e
im pacts p re se n te d in th ese r e s u l t s in a p a r t i c u l a r subbasin.
The r e d i s t r i b u t i v e
i m p a c t s may be o n l y t r a n s i t o r y
i f t h e o p t i m a l i r r i g a t i o n e f f i c i e n c y l e v e l i s h i g h enough
b u t w i l l be p e r m a n e n t i f
i t i s not.
The s p e c i f i c l e v e l o f
t h e i m p a c t s w i l l be u n i q u e t o e a c h i n d i v i d u a l s u b - b a s i n .
Thus i t i s n o t c l e a r t h a t g e n e r a l or n o n s p e c i f i c p o l i c i e s
o f i n c r e a s e d i r r i g a t i o n e f f i c i e n c y can be a c c o m p l i s h e d
w i t h o u t s i g n i f i c a n t d e t r i m e n t a l e c o n o m ic i m p a c t s t o c e r t a i n
w ater u se rs.
T h ese i m p a c t s may be e i t h e r t e m p o r a r y or
p e r m a n e n t d e p e n d i n g on p a r t i c u l a r c i r c u m s t a n c e s .
There
a p p e a r s t o be a t e n d e n c y among w a t e r p l a n n i n g o f f i c i a l s t o
b e l i e v e t h a t w h a t e v e r l e v e l o f i r r i g a t i o n e f f i c i e n c y can be
a c h i e v e d above c u r r e n t l e v e l s w i l l be b e n e f i c i a l t o a l l
w ater u se rs.
th is
T h is b e l i e f i s c o n t r a r y t o th e r e s u l t s of
study.
The d r y y e a r s c e n a r i o s i n d i c a t e d , a s m i g h t be e x p e c ­
t e d , t h a t w a t e r s c a r c i t i e s a r e i n c r e a s e d i n lo w f l o w y e a r s .
The Dl s c e n a r i o i s b a s e d on a n n u a l r i v e r f l o w s a t S i d n e y o f
8.87 mmaf w h i c h i s o n l y s l i g h t l y b e lo w t h e 1 9 3 4 -1 9 8 0 a v e r ­
age o f 8.9 mmaf.
Thus, t h e Dl s c e n a r i o i s more n e a r l y t h e
long run av erag e l e v e l of r i v e r flow than t h a t used in th e
HO
b a s i c m o d e l , w h i c h was b a s e d on t h e a v e r a g e f l o w f o r t h e
y e a r s 1 9 6 3 -1 9 7 7 o f 10.2 mmaf.
p articu lar, illu s tra te
The d r y y e a r s c e n a r i o s ,
in
th e i m p l i c a t i o n s of h av in g or not
having sto ra g e f a c i l i t i e s
on t h e r i v e r .
The w i d e f l u c t u a t i o n s i n r e t u r n s t o a g r i c u l t u r e i n t h e
t h r e e u p p e r s u b - b a s i n s a r e i n d i c a t i v e o f t h e v a l u e of
s t o r a g e and a l s o o f th e d e c r e a s e s i n r i s k t o w a t e r u s e r s
a s s o c i a t e d w ith th e a v a i l a b i l i t y of s to ra g e f a c i l i t i e s .
D e p e n d in g on t h e i n s t i t u t i o n a l r e g i m e ,
th e upstream , u s e r s
may h a v e f i r s t u s e o f t h e w a t e r i n w h i c h c a s e w a t e r w o u l d
n o t be g o i n g t o t h e h i g h e s t v a l u e d u s e .
In t h a t s i t u a t i o n
t h e v a l u e o f s t o r a g e w o u ld be g r e a t e r t h a n t h a t i m p l i e d by
th e r e s u l t s of t h i s stu d y .
A com prehensive b e n e f i t / c o s t
a n a l y s i s w o u ld be n e c e s s a r y t o a c c u r a t e l y d e t e r m i n e t h e n e t
s o c i a l v a lu e of s t o r a g e in th e b a s in .
An e x a m i n a t i o n of
t h e shadow p r i c e s o f i r r i g a t e d a c r e a g e f o r t h e d r y y e a r
s c e n a r i o s i n d i c a t e s t h a t th e v a lu e of i r r i g a t e d lan d i s
v e r y d e p e n d a n t on a r e l i a b l e w a t e r s o u r c e t h r o u g h o u t t h e
irrig atio n
season.
I n t h e D2 and a l s o i n t h e A3 s c e n a r i o s , shadow p r i c e s
o f w a t e r o f $1.00 a p p e a r i n v a r i o u s t i m e i n t e r v a l s and s u b ­
basins.
T hes e r e s u l t fr o m t h e f a c t t h a t t h e r e s e r v o i r s a r e
n o t f i l l e d a t t h e e nd o f t h e i r r i g a t i o n s e a s o n i n t h e s e
scenarios.
The tw o r e s e r v o i r s , t h e Y e l l o w t a i l dam i n s u b ­
b a s i n 4 and t h e Tongue dam i n s u b - b a s i n 6, have! an a c t i v i t y
w h i c h p l a c e s a v a l u e on t h e c a r r y - o v e r o f w a t e r beyon d t h e
Ill
irrig a tio n
season.
T h i s a c t i v i t y was g i v e n a $1.00 p e r
a c r e - f o o t o b j e c t i v e f u n c t i o n v a l u e a s an i n c e n t i v e t o t h e
m o d el so t h a t i t w o u ld n o t d r a i n t h e r e s e r v o i r s a t t h e end
of th e i r r i g a t i o n season.
Thu s,
i n t h e D2 and A3
s c e n a r i o s , w h e r e w a t e r i s v e r y s c a r c e , t h e $1.00 b ecom es
t h e o p p o r t u n i t y c o s t o f n o t h a v i n g an a d d i t i o n a l a c r e - f o o t
of w ater to lea v e in th e r e s e r v o i r s .
I n t e r p r e t a t i o n of the r e s u l t s of the dry year
s c e n a r i o s m u s t be made i n l i g h t of t h e t a c i t a s s u m p t i o n of
a p r i o r i knowledge of d i m i n i s h e d r i v e r f lo w s .
The f a c t
t h a t t h e D2 s c e n a r i o r e s u l t s i n i r r i g a t e d a c r e s b e i n g t a k e n
o u t o f p r o d u c t i o n i n s u b - b a s i n s I and 2 s u g g e s t s t h e
s e r i o u s n e s s o f t h e p o t e n t i a l c o n f l i c t w h i c h may a r i s e i n
t h e Y e l l o w s t o n e B a s i n d u r i n g lo w f l o w y e a r s .
t h a t w a te r becomes v e r y s c a r c e ,
In the event
t h e a g r i c u l t u r a l demand f o r
w a t e r w i l l be i n c o n f l i c t w i t h t h e c u r r e n t minimum i n s t r e a m
r e s e r v a tio n s fo r the a v a ila b le w ater su p p lie s.
In r e a l i t y ,
u n l e s s t h e d i m i n i s h e d w a t e r s u p p l i e s w e r e known i n a d v an c e
w ith c e r t a i n t y ,
i r r i g a t e d a c r e s would n o t a c t u a l l y sta n d
i d l e b u t w o u ld be u t i l i z e d i n d i m i n i s h e d i r r i g a t e d p r o d u c ­
tio n .
However, t h e f a c t t h a t t h e model c a l l s f o r d e c r e a s e s
i n c r o p p e d a c r e a g e by o v e r 8 0 ,0 0 0 a c r e s i s i n d i c a t i v e of
t h e p o t e n t i a l c o n f l i c t i n v o l v e d and t h e p o t e n t i a l e c o n o m ic
im pacts.
The r e s u l t s o f t h e i n c r e a s e d p r i c e s and a d d i t i o n a l
ir r ig a t e d acreage sc e n a r io s as v a r ia t io n s of the b a sic
11 2
I
model d i d n o t p r e s e n t any u n e x p e c t e d r e s u l t s .
However? t h e
i n c r e a s e d a g r i c u l t u r a l p r i c e s s c e n a r i o s d i d i l l u s t r a t e an
obvious but o f t e n o v erlooked f a c t t h a t the va lu e of w ater
t o i r r i g a t e d a g r i c u l t u r e i s n o t s t a t i c b u t i s d e p e n d e n t on
th e v a lu e of th e a g r i c u l t u r a l p r o d u c ts produced.
The
i n c r e a s e d a g r i c u l t u r a l p r i c e s and i r r i g a t e d a c r e a g e
s c e n a r i o s a r e more s i g n i f i c a n t when c o n s i d e r e d i n j o i n t
occurrence w ith the oth er sc e n a rio s thereby exag g eratin g the
i m p l i c a t i o n s o f v a r i o u s w a t e r m an ag em en t p o l i c i e s .
S u g g estio n s fo r F u rth e r Research
The r e s u l t s o f t h e b a s i c m o d e l a n d t h e s c e n a r i o s a r e
a l l p r e s e n t e d i n t h e c o n t e x t o f a c e t e r i s p a r i b u s a ssu m p ­
tio n ,
i.e.?
each of th e s c e n a r i o s i s in th e fram ework of
w h a t i f on e v a r i a b l e c h a n g e s and e v e r y t h i n g e l s e r e m a i n s
constant?
The m o s t o b v i o u s e x t e n s i o n s o f t h e work p r e ­
s e n t e d i n t h i s s t u d y w o u ld be t o r e l a x t h e
c^J l^ x J-S
gai,lfcm.S
a s s u m p t i o n and i n v e s t i g a t e t h e i m p a c t s o f c o m b i n a t i o n s o f
f a c t o r s a f f e c t i n g r i v e r m anagem ent p o l i c i e s .
Such work
w o u ld r e s u l t i n t h e d e t e r m i n a t i o n o f p o t e n t i a l e c o n o m ic
im p a c ts of i n c r e a s e d i r r i g a t i o n e f f i c i e n c y over a wider
range of v a r i a b l e s .
Sim ultaneously?
i n v e s t i g a t i o n b a s e d on
t h e s t o c h a s t i c n a t u r e o f t h e o c c u r r e n c e and m a g n i t u d e of
p h y s i c a l and e c o n o m i c v a r i a b l e s b o t h i n d e p e n d e n t l y and
j o i n t l y would p ro v id e u s e f u l i n f o r m a t i o n t o p o l i c y makers.
I n a d d i t i o n , more d e t a i l e d a n a l y s i s o f t h e s i t e
s p e c i f i c f a c t o r s on t h e p o t e n t i a l e c o n o m ic i m p a c t s w o u ld
113
p r o v i d e i n f o r m a t i o n a b o u t t h e k i n d and e x t e n t o f w a t e r
m an a g em en t w h i c h can be a p p l i e d i n e a c h o f t h e s u b - b a s i n s .
T h i s , i n t u r n , may h a v e i m p l i c a t i o n s , f o r e x a m p l e , on t h e
s o c i a l l y d e s i r a b l e n a t u r e and e x t e n t o f f e d e r a l and s t a t e
su p p o rt f o r i r r i g a t i o n p r o j e c t developm ent.
In a d d itio n ,
b e n e f i t/ c o s t s tu d ie s r e la te d to in c re a se s in i r r i g a t i o n
e f f i c i e n c y a s w e l l a s s t o r a g e f a c i l i t i e s and o t h e r w a t e r
m an a g em en t a l t e r n a t i v e s a r e i n d i c a t e d by t h e r e s u l t s of
th is
study.
F u r t h e r work i n m o d e l i n g t h e h y d r o l o g y o f t h e b a s i n
w o u l d be d e s i r a b l e .
E m p i r i c a l d e t e r m i n a t i o n of r e t u r n flow
p a t t e r n s h a s p r o v e n t o be a v e r y d i f f i c u l t t a s k and a d d i ­
t i o n a l work t o d e f i n e r e t u r n f l o w p a t t e r n s a s w e l l a s
s e n s i t i v i t y a n a l y s i s of th e r e s u l t s p re s e n te d h e re w ith
r e g a r d t o a l t e r n a t i v e r e t u r n flo w p a t t e r n s would c o n t r i b u t e
much t o t h e p o s s i b i l i t y o f w e l l i n f o r m e d w a t e r m anagem ent
p o licies.
In a d d i t i o n ,
i s s u e s r e g a r d i n g w a te r q u a l i t y must
be a d d r e s s e d on a s i t e s p e c i f i c b a s i s a s a p a r t o f an
o v e r a l l w a t e r m an ag em en t p l a n .
The r e s u l t s p r e s e n t e d i n t h i s w o r k a r e d o n e i n t h e
a b s e n c e o f t h e l e g a l and i n s t i t u t i o n a l f r a m e w o r k i n t h e
basin.
For e x a m p l e , t h e income r e d i s t r i b u t i o n w h i c h o c c u r s
a s i r r i g a t i o n e f f i c i e n c y i n c r e a s e s may be e x a g g e r a t e d or
d i m i n i s h e d by t h e w a t e r r i g h t s r e g i m e and o t h e r i n s t i t u ­
tio n a l f a c to r s w ith in the basin.
F u r t h e r work i s n e c e s s a r y
. 114
t o e v a l u a t e t h e i m p a c t o f t h e i n s t i t u t i o n a l and l e g a l
m e c h a n i s m s on t h e r e s u l t s r e p o r t e d h e r e .
115
APPENDICES
116
APPENDIX A
BUDGETS
I
117
Table 15o
I r r i g a t e d A l f a l f a f o r S u b - b a s i n s I f 2 , 3 , and 4 .
RETURNS
(I)
$ 3 0 0 .0 0
F e r t i l i z e r and A p p l i c a t i o n
(2)
$ 1 1 .9 0
Crop C h e m i c a l s
(3)
3.60
I r r i g a t i o n Labor
(4)
6.00
M achinery: F u e l , O i l , R e p a irs
(5)
31.03
Pickup V a r ia b le C osts
(6)
5.00
M i s c e l l a n e o u s E x p en s e
(7)
7.17
Other
(8)
6.60
(9)
1.37
(10)
18.60
TOTAL VARIABLE COSTS
(11)
$ 9 1 .2 7
RETURN OVER VARIABLE COST
(12)
$ 2 0 8 .7 3
Y ield
(5 Tons x $ 6 0 .0 0 )
VARIABLE COSTS
(tw ine)
I n t e r e s t on O p e r a t i n g C a p i t a l
M a c h i n e r y Labor
( 4 . 6 5 h r . x $ 4 .0 0 )
B a s e d on d a t a f r o m F o g l e and L u f t
(1980).
118
T able 16.
I r r i g a t e d A l f a l f a f o r Sub- ■basins 5 and 7.
RETURNS
Cl)
$ 2 4 0 .0 0
Stand E s ta b lis h m e n t
(2)
$
F e r t i l i z e r and A p p l i c a t i o n
(3)
28.44
C ro p C h e m i c a l s
(4)
4.77
I r r i g a t i o n L ab o r.
(5)
4.50
M achinery: F u e l p O i l , R e p a irs
(6)
31.73
P ick u p V a r i a b l e Cost
(7)
3.50
M i s c e l l a n e o u s Expense
(8)
13.79
I n t e r e s t on O p e r a t i n g C a p i t a l
(9)
2.96
M a c h i n e r y Labor
(10)
1 5 .8 2
TOTAL VARIABLE COSTS
(11)
$ 1 1 5 .2 7
RETURNS OVER VARIABLE COST
(12)
$ 1 2 4 .7 3
Y ield
(4 t o n s x $ 6 0 .0 0 )
VARIABLE COSTS
B a s e d on d a t a f r o m G r i f f i t h , S c h a e f e r and L u f t
9.02
(1978)
119.
T able 17.
I r r i g a t e d A l f a l f a f o r S u b - b a s i n s 6 , 8 , and 9 .
RETURNS
(I)
$2 4 0 .0 0
Stand E s ta b lis h m e n t
(2)
$
F ertilizer
(3)
19.01
Crop C h e m i c a l s
(4)
4.47
Custom S t a c k
(5)
23.40
I r r i g a t i o n Labor
(6)
6.98
M achinery$ F u e l, O i l , R e p airs
(7)
12.23
Pickup V a r i a b l e Cost
(8)
5.59
M i s c e l l a n e o u s E x p en s e
(9 )
7.35
Twine
(10)
4.96
I n t e r e s t on O p e r a t i n g C a p i t a l
(11)
1.70
M a c h i n e r y Labor
(12)
7.62
TOTAL VARIABLE COSTS
(13)
$ 1 0 3 .1 5
RETURN OVER VARIABLE COST
(1 4 )
$ 1 3 6 .8 5
Y ield
(4 t o n s x $ 6 0 .0 0 )
VARIABLE COSTS
and A p p l i c a t i o n
B ased on d a t a fro m S c h a e f e r , G r i f f i t h and L u f t
9.84
(1978).
120
T a b l e 18. I r r i g a t e d Corn f o r G r a i n f o r A l l S u b - b a s i n s .
RETURNS
(I)
$325.00
S eed ( 1 6 . 7 l b . x $ 1 . 0 5 / l b . )
(2)
$ 17.53
F e r t i l i z e r and A p p l i c a t i o n
(3)
38.40
C ro p C h e m i c a l s
(4)
11.25
Custom H i r e
(5)
55.00
(6)
6.00
. (7)
47.59
Pickup V a r ia b l e C osts
(8)
5.00
M i s c e l l a n e o u s E x p en s e
(9)
13.19
I n t e r e s t bn O p e r a tin g C a p i t a l
(10)
7.22
M achinery Labor
(11)
24.80
TOTAL VARIABLE COSTS
(12)
$225.98
RETURN OVER VARIABLE COST
(1 3 )
$ 99.02
Y ield
(100 bu.
x $3.25)
VARIABLE COSTS
(Corn D r y i n g )
I r r i g a t i o n Labor
M achinery: F u e l, O i l , R e p a ir s
( 6 . 2 h r . x $ 4 .0 0 )
B a s e d on d a t a f r o m F o g l e and L u f t
(1980).
121
T a b l e 19 .
I r r i g a t e d F eed B a r l e y f o r A l l S u b - b a s i n s .
RETURNS
Y ield
(80 b u . x $ 2 . 0 0 )
(I)
$1 6 0 .0 0
(2)
$
VARIABLE COSTS
Seed (90 l b .
@ $4.50/bu.)
8.46
F e r t i l i z e r and A p p l i c a t i o n
(3)
24.50
Crop C h e m i c a l s
(4)
3.25
I r r i g a t i o n L ab o r
(5)
4.00
M achinery: F u e l, O i l , R e p a irs
(6)
26.07
Pickup V a r i a b l e Cost
(7)
5.00
M i s c e l l a n e o u s Expense
(8)
7.82
I n t e r e s t on O p e r a t i n g C a p i t a l
(9)
3.17
(10)
17.87
TOTAL VARIABLE COSTS
(11)
$1 0 0 .1 4
RETURN
(12)
$ 59.86
M a c h i n e r y Labor
(4.47 h r . x $4.00)
OVER VARIABLE COST
B a s e d on d a t a f r o m F o g l e and L u f t
(1980).
122
T able 20.
I r r i g a t e d B e an s f o r A l l S u b - b a s i n s .
RETURNS
(I)
$ 4 6 0 .0 0
Seed (50 l b . x $48 . 0 0 / c w t . )
(2)
$ 24.00
F e r t i l i z e r and A p p l i c a t i o n
(3)
11.10
Crop C hem icals
(4)
4.12
I r r i g a t i o n L ab o r
(5)
6.40
M achinery: F u e l , O i l , R e p a irs
(6)
60.09
Pickup V a r ia b le Cost
(7)
5.00
M i s c e l l a n e o u s Expense
(8)
1 0 .9 5
I n t e r e s t on O p e r a t i n g C a p i t a l
(9)
4.61
(10)
30.32
TOTAL VARIABLE COSTS
(11)
$ 1 5 6 .5 9
RETURN OVER VARIABLE COST
(12)
$303.41
Y ield
(20 cwto x $ 2 3 .0 0 )
VARIABLE COSTS
M a c h i n e r y Labor
(7.58 h r . x $4.00)
B a s e d on d a t a fr o m F o g l e and L u f t
(1980).
123
T able 21.
I r r i g a t e d Sugar B e e ts f o r A ll Sub- b a s i n s .
(I)
$ 5 7 6 .0 0
Seed ( 2 . 1 l b . x $ 9 . 5 0 / l b . )
(2)
$ 19.95
F e r t i l i z e r and A p p l i c a t i o n
(3)
58.25
C ro p C h e m i c a l s
(4)
9.45
Custom H i r e
(5)
to
RETURNS
I r r i g a t i o n Labor
(6)
11.40
M achinery: F u e l, O i l , R e p a ir s
(7)
93.42
Pickup V a r i a b l e Cost
(8)
5.00
M i s c e l l a n e o u s E x p en s e
(9 )
20.75
I n t e r e s t on O p e r a t i n g C a p i t a l
(10)
7.64
M achinery Labor
(11)
43.73
TOTAL VARIABLE COSTS
(12)
$293.59
RETURN OVER VARIABLE COST
(13)
$ 282.41
Y ield
(18 t o n x $ 3 2 .0 0 )
(Hbe B e e t s )
( 1 0 . 9 3 h r . x $ 4 .00)
B a s e d on d a t a f r o m F o g l e and L u f t
(1980)
O
O
VARIABLE COSTS
124
T able 22.
I r r i g a t e d Corn S i l a g e f o r A l l S u b - b a s i n s .
(I)
$ 3 6 0 .0 0
Seed ( 1 6 . 7 l b . x $ 1 . 0 5 / l b . )
(2)
$ 1 7 .5 3
F e r t i l i z e r and A p p l i c a t i o n
(3)
CO
CO
RETURNS
Crop C h e m i c a l s
(4 )
11.25
I r r i g a t i o n L ab o r
(5)
6.00
M achinery; F u e l f O i l , R ep airs
(6)
5 6 .0 5
Pickup V a r ia b le Cost
(7)
5.00
M i s c e l l a n e o u s E x p en se
(8)
1 2 .1 8
I n t e r e s t on O p e r a t i n g C a p i t a l
(9)
7.47
(10)
27.64
TOTAL VARIABLE COSTS
(11)
$ 1 8 1 .5 2
RETURN OVER VARIABLE COST
(12)
$1 7 8 .4 8
Y ield
(20 t o n x $ 1 8 .0 0 )
M a c h i n e r y Labor
( 6 . 9 1 h r . x $ 4 .0 0 )
B a s e d on d a t a f r o m F o g l e and L u f t
(1980).
O
=g&
VARIABLE COSTS
125
APPENDIX B
NET IRRIGATION REQUIREMENTS
126
Table 23.
C l i m a t i c . Zones f o r
th e Nine S u b - b a s in s .
C l i m a t i c Zone
S u b -b a sin s
1
T a b le 24.
Month
5 ,6 ,7
and 8
2
, 2 , 3, 4 and 9
3
. I
N et I r r i g a t i o n R e q u ir e m e n ts
in a c r e - f e e t ) .
A lfalfa
B e an s
(May t o Sep tem b er
S u g a r Corn Corn
B eets S i l a g e G rain P a s tu r e
B arley
C l i m a t i c Zone I
M
j
J
A
S
.23
.33
.57
.47
.23
.0 4
.06
.24
.54
.24
.19
.55
.56
.28
.03
.12
.47
.47
.17
.15
.38
.48
.04
.18
.25
.46
.40
.20
.32
.32
.12
.33
: 46
.05
.16
.22
.42
.36
.17
.28
.28
.04
.03
.14
.39
.35
.15
.25
.25
.04
„05
C l i m a t i c Zone 2
M
J
J
A
S
.20
.03
.29
.52
.43
.18
o21
.54
.27
.05
.16
.52
.52
.23
.02
.10
.43
.43
.14
C l i m a t i c Zone 3
M
J
J
A
S
.16
.27
.48
.39
.15
.04
.15
.47
.46
.19
127
APPENDIX C
CROPPING PATTERNS
Table
25.
C rops
Cropping Patterns
a nd the Pl and P2
I
2
3
1 4 7 ,0 2 2
1 7 ,438
5 2 ,2 4 9
by Sub - b a s i n for the
Scenarios (acres).
S u b -b asin s
5
4
6
Basic
Model
8
7
(Bi)
9
B arley
A lfa lfa
Hay
O t h e r H ay
6 5 ,8 0 6
P astu re
S ugar B ee ts
1 ,1 8 6
6 ,9 2 1
1 5 ,1 1 8
8 ,0 6 7
Corn
3,367
3 ,118
794
1 ,1 1 7
1 1 ,6 3 5
2 ,547
498
16 ,4 6 4
16,8 4 7
8 ,963
5 0 ,3 1 0
3 ,8 8 6
196
1,614
128
5 0 ,5 0 9
C orn S i l a g e
Beans
7 ,174
Table
26.
C rops
Cropping
Patterns
by
Sub-basin
S u b -b asin s
5
i
2
3
4
147,0 2 2
8 3 ,2 4 4
6 5 ,6 4 1
5 2 ,2 4 9
1 ,186
6 ,9 2 1
1 5 ,1 1 8
8 ,0 6 7
for t h e El S c e n a r i o
6
9
8
7
(acres).
B arley
A lfa lfa
H ay
O t h e r H ay
P astu re
Sugar B eets
Beans
C o rn
5 0 ,5 0 9
S ilag e
3 ,367
10,613
3 ,118
794
1 ,117
1 1 ,6 3 5
2 ,547
498
1 6 ,4 6 4
1 6 ,8 4 7
1 0 ,5 7 7
5 0 ,3 1 0
196
3 ,886
129
Com
7 ,174
27.
Table
C rops
C r o p p i n g P a t t e r n s by
Scenarios (acres).
I
2
Sub-basin
3
4
S u b -b asin s
5
for
the
6
E2 and E3
8
7
9
B arley
A lfa lfa
H ay
1 4 7 ,0 2 2
8 3 ,2 4 4
7 6 ,2 5 4
5 2 ,249
1 ,186
6 ,9 2 1
1 5 ,1 1 8
8 ,0 6 7
O t h e r Hay
P astu re
Sugar B eets
C orn
3 ,3 6 7
3 ,1 1 8
7 94
1 ,1 1 7
1 1 ,635
2 ,547
498
1 6 ,4 6 4
1 6 ,847
1 0 ,577
5 0 ,3 1 0
196
3 ,886
130
5 0 ,509
C orn S i l a g e
Beans
7 ,174
Table
28.
C rops
Cropping
I
Patterns
2
3
by
Sub-basin
S u b -b asin s
5
4
for t h e Dl S c e n a r i o
6
9
8
7
(acres).
B arley
A lfa lfa
Hay
1 4 7 ,0 2 2
2 8 ,0 6 8
5 2 ,2 4 9
1 5 ,1 1 8
8 ,067
8 3 ,2 4 4
O t h e r H ay
P astu re
Sugar B eets
1 ,1 8 6
6 ,9 2 1
C orn
3 ,367
3 ,1 1 8
4 8 ,1 8 6
794
1 ,1 1 7
1 1 ,6 3 5
2 ,547
498
1 6 ,464
16,8 4 7
6 ,692
5 0 ,3 1 0
3 ,8 8 6
196
3 ,885
131
5 0 ,5 0 9
C orn S i l a g e
B eans
7 ,1 7 4
Table
29.
Cropping Patterns
by
Sub-basin
for
th e D2
Scenario
(acres).
Sub-basins
Crops
I
2
3
5
4
6
8
7
9
Barley
Alfalfa Hay
Other Hay
5 2 ,2 4 9
8 ,3 3 5
1 3 3 ,0 9 7
Pasture
Sugar Beets
1 ,186
6 ,9 2 1
3,367
3 ,118
7 ,1 7 4
5 0 ,5 0 9
794
1 ,117
1 1 ,6 3 5
2 ,547
498
16,4 6 4
16 ,8 4 7
4 ,580
5 0 ,3 1 0
3 ,886
196
5 ,9 9 7
132
Corn
8 ,067
7 6 ,2 5 4
Corn Silage
Beans
1 5 ,118
Table
30.
C rops
Cropping Patterns
I
2
by
Sub-basin
S u b -b asin s
5
3
4
8 8 ,8 7 6
6 0 ,7 1 9
1 5 ,1 1 8
8 ,0 6 7
for
the Al S cenario
6
8
7
(acres).
9
Barley
Alfalfa Hay
167,6 0 4
O t h e r Hay
9 6 ,2 2 6
P a stu re
S ugar B ee ts
1,186
6 ,921
C orn
3 ,367
3 ,118
519
794
1 ,117
1 3 ,2 9 7
2 ,547
498
1 6 ,4 6 4
19,6 1 8
9 ,2 0 2
6 0 ,2 0 5
196
3 ,8 8 6
2 ,8 7 9
133
5 8 ,6 6 3
C orn S i l a g e
Beans
7 ,174
Table
C rops
31.
Cropping
I
2
Patterns
3
by
Sub-basin
S u b -b asin s
5
4
for t h e A 2
6
Scenario
9
8
7
(acres).
B arley
A lfa lfa
Hay
1 8 8 ,1 8 3
7 8 ,1 1 1
6 9 ,1 8 8
1 5 ,1 1 8
8 ,0 6 7
1 0 9 ,2 0 7
O t h e r Hay
P a stu re
Sugar B eets
1 ,186
6 ,9 2 1
6 6 ,8 1 5
C orn S i l a g e
C orn
3 ,367
3 ,1 1 8
2 4 ,4 2 3
794
1 ,1 1 7
1 4 ,9 6 0
2 ,547
498
1 6 ,4 6 4
2 2 ,3 8 8
9 ,4 4 1
7 0 ,0 9 9
3,886
196
4 ,1 4 4
134
Beans
7 ,1 7 4
Table
32.
C rops
Cropping Patterns
i
2
3
by
Sub-basin
S u b -b asin s
5
4
for t h e A 3
6
Scenario
9
8
7
(acres).
B arley
A lfa lfa
Hay
216,1 5 1
6 3 ,4 8 1
8 0 ,6 9 8
1 5 ,1 1 8
8 ,0 6 7
126,8 4 9
O t h e r Hay
P astu re
Sugar B eets
Beans
C orn
6 ,9 2 1
7 ,174
7 7 ,8 4 5
S ilag e
3,367
3 ,118
5 6 ,9 0 9
794
1 ,117
1 7 ,219
2 ,547
498
1 6 ,4 6 4
2 6 ,1 5 3
9 ,765
8 3 ,545
3 ,8 8 6
196
5 ,8 6 4
135
Com
1 ,186
REFERENCES. CITED
137
R e fe r e n c e s C ited
A n d e r so n , Raymond L. "The E f f e c t s o f S t r e a m f l o w V a r i a t i o n
on P r o d u c t i o n and Income o f I r r i g a t e d Fa rm s O p e r a t i n g
Under t h e D o c t r i n e o f P r i o r A p p r o p r i a t i o n " , ffflfcfiE
R e s o u r c e s R e s e a r c h , V o l , 11, NOi I^ F e b r u a r y 1975, pp,
15-22.
Boone, S h e l d o n ,G.
" E n v i r o n m e n t a l A s p e c t s o f I r r i g a t i o n and
D rainage."
P r o c e e d i n g s Q l a S p e c i a l t y CpnfePAhSS
s p o n s o r e d by t h e I r r i g a t i o n and D r a i n a g e P a v i SAQR
t h e A m e ri c a n S o c i e t y M C i v i l EnglnQQRS EEt a l l .
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MaiQR JELLshiS
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in te g ra te d A n aly sis. B altim o re;
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F u t u r e , I n c . > J o h n s H o p k in s U n i v e r s i t y P r e s s , 1 9 8 0 .
Bowman, C.C., and W.W. L e s s l e y .
Montana S u r f a c e W a t e r Law,
M easurement-and s t r u c t u r e .
Montana A g r i c u l t u r e
E x p e r i m e n t S t a t i o n , Montana S t a t e U n i v e r s i t y , Bozeman,
B u l l e t i n 6 2 0 , A p r i l 19 6 8 .
Boyd, D o n a ld W i l l i a m . S i m u l a t i o n V i a T i m e - p a r t i t i o n e d
L in e a r Programming;
A Ground and S u r f a c e W a te r
A l l o c a t i o n Model f o r t h e G a l l a t i n V a l l e y o f Montana.
U n p u b l i s h e d d o c t o r a l t h e s i s , J u n e 1968.
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