potential use of digital computer groundwater models use of digital computer groundwater models...
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US Army Corps of Engineers Hydrologic Engineering Center
Potential Use of Digital Computer Groundwater Models April 1978 Approved for Public Release. Distribution Unlimited. TP-52
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4. TITLE AND SUBTITLE Potential Use of Digital Computer Groundwater Models
5c. PROGRAM ELEMENT NUMBER
5d. PROJECT NUMBER 5e. TASK NUMBER
6. AUTHOR(S) David L. Gundlach
5F. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US Army Corps of Engineers Institute for Water Resources Hydrologic Engineering Center (HEC) 609 Second Street Davis, CA 95616-4687
8. PERFORMING ORGANIZATION REPORT NUMBER TP-52
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12. DISTRIBUTION / AVAILABILITY STATEMENT Approved for public release; distribution is unlimited. 13. SUPPLEMENTARY NOTES From the preliminary report, Albuquerque Greater Urban Area Water Supply Study, prepared by the Hydrologic Engineering Center, Davis, California 14. ABSTRACT The discussion on the potential use of digital computer groundwater models was prepared for the Albuquerque District, Corps of Engineers, Albuquerque, New Mexico, as part of a water supply study of the Albuquerque Greater Urban Area (AGUA). Although the material presented was developed for the Albuquerque area, the concepts are applicable to the understanding of groundwater modeling generally. The discussion included both quantity and quality models and reasons why an agency may wish to undertake a modeling effort. Available computer programs were cited and the probable advantages and disadvantages of specific programs were given. Costs for prior modeling efforts of groundwater systems in other localities were also included as a guide to probable cost when considering the use of a digital computer groundwater model. 15. SUBJECT TERMS model studies, groundwater, aquifers, systems analysis, New Mexico, computer models, water quality, mathematical models, costs, groundwater movement, aquifer systems, aquifer characteristics, hydraulic conductivity, groundwater recharge, flow system, Albuquerque (NM), two-dimensional model, three-dimensional model 16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON a. REPORT U
b. ABSTRACT U
c. THIS PAGE U
17. LIMITATION OF ABSTRACT UU
18. NUMBER OF PAGES 46 19b. TELEPHONE NUMBER
Potential Use of Digital Computer Groundwater Models
April 1978 US Army Corps of Engineers Institute for Water Resources Hydrologic Engineering Center 609 Second Street Davis, CA 95616 (530) 756-1104 (530) 756-8250 FAX www.hec.usace.army.mil TP-52
Papers in this series have resulted from technical activities of the Hydrologic Engineering Center. Versions of some of these have been published in technical journals or in conference proceedings. The purpose of this series is to make the information available for use in the Center's training program and for distribution with the Corps of Engineers. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products.
POTENTIAL USE OF DIGITAL COXPUTER
GROUND WATER MODELS~
David L. Gundlach 2
PREFACE
The fol lowing d i scuss ion on t h e p o t e n t i a l u s e of d i g i t a l computer
ground water models w a s prepared f o r t h e Albuquerque D i s t r i c t , Corps of
Engineers, Albuquerque, New Mexico, as p a r t of a water supply s tudy of
t h e Albuquerque Grea ter Urban Area (AGUA). Although t h e m a t e r i a l pre-
sen ted h e r e i n was developed f o r t h e Albuquerque a r e a , t h e concepts a r e
a p p l i c a b l e t o t h e understanding of ground water modeling genera l ly . The
d i scuss ion inc ludes both quan t i t y and q u a l i t y models and reasons why an
agency may wish t o undertake a modeling e f f o r t . Avai lab le computer
programs a r e c i t e d and t h e probable advantages and disadvantages of
s p e c i f i c programs a r e given. Costs f o r p r i o r modeling e f f o r t s of ground
water systems i n o t h e r l o c a l i t i e s a r e a l s o included as a guide t o probable
c o s t s when cons ider ing t h e use of a d i g i t a l computer ground water model.
From t h e pre l iminary r e p o r t , Albuquerque Greater Urban Area Water Supply Study, prepared by The Hydrologic Engineering Center , U.S. Army Corps of Engineers, Davis, C a l i f o r n i a , 1978.
Hydraul ic Engineer, Planning Analysis Branch, The Hydrologic Engineering Center , Davis, C a l i f o r n i a , 95616.
SECTION 7
INTRODUCTION .
POTENTIAL USE OF DIGITAL COMPUTER
GROUND WATER MODELS
CONTENTS
P a g e
.................................. DLGLTAL COMPUTER MODELS 7 - 2
..... DLGITAL COMPUTERMODELS OF THE GROUND WATER FLOW SYSTEM 7 - 6
Two-Dimensional M o d e l o f the F l o w S y s t e m ............... 7 - 6
C a l i b r a t i o n o f a Two-Dimensional M o d e l o f the
......... F l o w S y s t e m 7-15
D a t a R e q u i r e d f o r a Two-Dimensional M o d e l of the
F l o w S y s t e m ......... 7-17
T h r e e - D i m e n s i o n a l Model o f the F l o w S y s t e m ............. 7-18
DLGLTAL COMPUTER MODELING OF WATER QUALITY .................. 7-21
....................... A DIGITAL COMPUTER MODEL FOR THE AGUA 7-26
................................... R e a s o n s f o r M o d e l i n g 7-27
C o s t s f o r D e v e l o p i n g a D i g i t a1 Compute r Mode1 .......... 7-28
.................................................. REFERENCES 7-33
SECTION 7
POTENTIAL USE OF DIGITAL COMPUTER GROUND WATER MODELS
In t roduc t ion
A model, i n t h e gene ra l sense, i.s a r e p r e s e n t a t i o n which a t tempts t o exp la in
t h e behavior of some a spec t of t h e pro to type system. It i s always less
complex than t h e r ea l , system i t rep resen t s , and l a r g e l y because of t h e com-
p l ex i n t e r d i s c i p l i n a r y i n t e r e s t s i n ground water, models d i f f e r markedly i n
purpose, information requirements , assumptions, u se fu lnes s , and i n t h e mathe-
m a t i c a l schemes incorporated.
The u s e of models t o a i d i n t h e a n a l y s i s of ground water systems has increased
s i g n i f i c a n t l y i n r ecen t yea r s (Konikow, 1970; Holcomb Research I n s t i t u t e , 1977).
Many i n v e s t i g a t o r s f i n d models u s e f u l inc luding t h e appl ied r e sea rche r
i n t e r e s t e d i n v e r i f y i n g t h e o r e t i c a l r e l a t i o n s h i p s , t h e hydro logis t i n t e r e s t e d
i n developing t h e c a p a b i l i t y t o p r e d i c t e f f e c t s of s t r e s s e s (such a s pumpage)
on a n a q u i f e r system, and planners i n t e r e s t e d i n t h e economic impact of t h e
development of ground water resources .
I n t e r d i s c i p l i n a r y modeling e f f o r t s a r e concerned w i t h t h e q u a n t i t a t i v e
d e s c r i p t i o n of t h e hydrogeologic p r o p e r t i e s and boundaries of a q u i f e r systems,
and wi th t h e response of a q u i f e r s t o development and management p r a c t i c e s .
The models a r e t o o l s used t o eva lua t e ground water resources and t o f o r e c a s t
t h e consequences of t h e u t i l i z a t i o n of a q u i f e r s . (Proper planning f o r t he
development of ground water resources r e q u i r e s t e s t i n g of a l l pos s ib l e schemes
of development and a p p r a i s a l of t h e r e l a t i v e m e r i t s of va r ious a l t e r n a t i v e s ) .
The modeling e f f o r t s a r e a l s o concerned wi th t h e economic consequences of
ground water development, w i th t h e p r a c t i c a l sus t a ined y i e l d s of w e l l s and
a q u i f e r s and w i t h t h e i n t e r r e l a t i o n between su r f ace water and ground water .
Objec t ives . The o b j e c t i v e of t h i s s e c t i o n i s t o po in t ou t p o t e n t i a l
uses of ground water computer models i n t h e management of t h e water resource
of t h e AGUA. This inc ludes models f o r both quan t i t y and q u a l i t y . Various
reasons a r e c i t e d a s t o when and why a n agency o r agencies should undertake
a d i g i t a l computer modeling e f f o r t and t h e d i f f e r e n t computer programs which
might be a p p l i c a b l e t o AGUA a r e d iscussed and t h e probable advantages of each
a r e given. Costs of t h e d i f f e r e n t modeling e f f o r t s a r e determined on t h e
b a s i s of s i m i l a r s t u d i e s done i n o t h e r a r e a s .
D i g i t a l Computer Models
I n t h e e a r l y 1950's r e s e r v o i r engineers looked t o numerical methods adapted
f o r d i g i t a l computers t o so lve l a r g e s c a l e flow problems. Ear ly numerical
r e s e r v o i r s imula t ions were seve re ly l i m i t e d by t h e s i z e and speed of t h e
d i g i t a l computers of t h e period. By t h e l a t e 1960's d i g i t a l computers could
compete w i t h t h e e l e c t r i c analog f o r t h e s o l u t i o n of t r a n s i e n t flow problems
involving a few thousand nodes (computation p o i n t s ) i n two space dimensions.
With today ' s d i g i t a l computers and powerful numerical techniques, three-
dimensional problems involving up t o 20,000 nodes can be solved.
Due l a r g e l y t o t h e widespread a v a i l a b i l i t y of t h e d i g i t a l computer, numerical
methods have replaced t h e e l e c t r i c analog i n most a p p l i c a t i o n s . However,
t h e e l e c t r i c analog model remains a very u s e f u l t o o l f o r problems involving
mul t i -aqui fe r hydrologic systems which must be s imulated wi th a l a r g e number
of nodes.
With the development of high-speed computers, i t has become f e a s i b l e t o
develop numerical models t h a t cons ider more r e a l i s t i c r e p r e s e n t a t i o n s of
complex hydrologic systems than was ever p o s s i b l e i n t h e p a s t .
Types of problems f o r which d i g i t a l models have been o r a r e being developed
inc lude , among o t h e r s (Appel, e t a l . , 1976):
(1) Flow i n water - tab le a q u i f e r s i n which r e l a t i v e l y l a r g e changes i n
s a t u r a t e d th ickness t ake p l ace
(2) Flow i n s a t u r a t e d o r p a r t i a l . 1 ~ unsa tura ted m a t e r i a l s
(3) Land subsidence r e s u l t i n g from ground water e x t r a c t i o n
(4) Flow i n coupled ground water l s t ream systems
(5) Coupling of r a in fa l l - runof f bas in models wi th s o i l moisture
accounting and aquifer-f low models
(6) I n t e r a c t i o n of economic and hydrologic cons ide ra t ions
(7) P r e d i c t i n g t h e t r a n s p o r t of contaminants i n an a q u i f e r , and
(8) Est imating t h e e f f e c t s of proposed development schemes f o r geo-
thermal systems.
Many of t h e s e types of problems r e q u i r e t h a t more than one equat ion be solved
s imultaneously. For example, gene ra l t r a n s p o r t problems r e q u i r e t h e coupling
and simultaneous s o l u t i o n of t h e p a r t i a l d i f f e r e n t i a l equat ions t h a t desc r ibe
two (o r more) components of a t r a n s i e n t flow system. Typica l ly , t hese would
inc lude , (1) an equat ion f o r p re s su re and (2 ) an equat ion f o r t h e concentra-
t i o n of each chemical c o n s t i t u e n t of i n t e r e s t .
A t a b u l a t i o n of t h e s t a t u s of U.S. Geological Survey techniques i n ground
water modeling is shown i n Table 7-1 (Appel, et a l . , 1976). If one contemplates
an ex tens ive modeling e f f o r t , then t h e documentation r e f e r r e d t o i n Table
should be reviewed. The techniques c o n s i s t of computer programs, a n a l y t i c a l
methods, and e l e c t r i c analog s o l u t i o n s which, wi th few except ions, a r e
a p p l i c a b l e t o t r a n s i e n t condi t ions . I n many cases more than one technique
has been app l i ed t o s i m i l a r ground water problems i n o rde r t h a t t h e compari-
t i v e s t r e n g t h s of d i f f e r e n t methods can be evaluated and used t o advantage.
Such eva lua t ions provide a r a t i o n a l b a s i s f o r determining t h e method l i k e l y
t o be most e f f i c i e n t f o r p a r t i c u l a r types of problems. To s t a t e t h a t a
technique i s i n t h e v e r i f i c a t i o n phase means t h a t t e s t s a r e being made t o
s e e i f model-derived s o l u t i o n s reasonably s imu la t e observed responses.
Techniques i n t h e o p e r a t i o n a l phase a r e being used t o eva lua t e f i e l d problems.
TA
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I n many cases , i n v e s t i g a t o r s o t h e r than those given i n Table 7-1 a r e , o r have
been, involved i n t h e l i s t e d a c t i v i t y . The i n v e s t i g a t o r s l i s t e d can be
contac ted through t h e U.S. Geological Survey f o r information regard ing t h e
s u b j e c t matter c i t e d .
D i g i t a l Computer Models of t h e Ground Water Flow System
D i g i t a l computer modeling of a n ex tens ive flow system t h e s i z e of t h e AGUA
demands a h ighly organized approach t o planning o r management. It involves
a r e l a t i v e l y h igh i n i t i a l c o s t and an i n t e n s i v e and coordinated d a t a co l l ec -
t i o n e f f o r t . However, i t enables s tudy of a much broader range of a l t e r n a -
t i v e s r e l a t i n g not on ly t o f low bu t t o q u a l i t y and economic cons ide ra t ions .
Two-Dimensional Model of t h e Flow System. There a r e s e v e r a l w e l l
documented two-dimensional. ground water. computer programs a v a i l a b l e f o r
s imu la t ing flow systems. Probably t h e one most commonly used is a two-
dimensional f i n i . t e d i f f e r e n c e model developed by Pinder (Pinder , 1970;
T resco t t , e t a l . , 1976).
The two-dimensional formulat ion of flow i n an a q u i f e r system conceptual . izes
t h e phys ics of t h e process a s being completely descr ibable by movement i n
t h e h o r i z o n t a l d i r e c t i o n s , gene ra l ly two orthogonal coord ina te d i r e c t i o n s
(f low i n p a r a l l e l h o r i z o n t a l p lanes being i d e n t i c a l ) . The movement (ve loc i ty )
of w a t e r i n a given d i r e c t i o n is i n propor t ion t o t h e nega t ive g rad ien t of
t h e water t a b l e o r piezometr ic s u r f a c e and t h e permeabi l i ty of t h e a q u i f e r
m a t e r i a l . Cont inui ty i s preserved by r e q u i r i n g volume accounting through
e i t h e r changes i n water s u r f a c e e l e v a t i o n s o r changes i n p iezometr ic head
and t h e compression and expansion of t h e water and of t h e porous framework
of t h e a q u i f e r . (The two-dimensional formula t ion does not s p e c i f d c a l l y
cons ider t h e v e r t i c a l flow process and thus does no t s imu la t e w e l l t hose
systems w i t h s i g n i f i c a n t v e r t i c a l components of flow and/or hydrau l i c con-
d u c t i v i t y ) . Solu t ion t o problems formulated i n two space dimensions proceeds
by d i s c r e t i z i n g t h e a q u i f e r system i n t o u n i t s , such a s g r i d s , and so lv ing
a t succes s ive t ime s t e p s t h e r e l a t i o n s h i p s f o r flow movement a t each
designated computational po in t .
I n o rde r t o g e t a f e e l i n g f o r what va r ious terms mean i t seems imperat ive
a t t h i s p o i n t t h a t a genera l d e s c r i p t i o n of t h e va r ious a s p e c t s of a two-
dimensional flow system be given. Since t h e ground water bas in of AGUA is
f o r t h e most p a r t an unconfined, (except f o r l o c a l i z e d a r e a s e x h i b i t i n g
a r t e s i a n c h a r a c t e r i s t i c s ) , heterogeneous, a n i s t r o p i c a q u i f e r , t h e fol lowing
continuous form i n two space dimensions is app l i cab le :
where x,y a r e t h e or thogonal d i r e c t i o n s (L), 2 -1 Txx i s t h e t r ansmis s iv i ty i n t h e x d i r e c t i o n (L T ), 2 -1 T is t h e t r ansmis s iv i ty i n t h e y d i r e c t i o n (L T ),
Y Y h i s t h e hydraul ic head (L),
S i s t h e s t o r a g e c o e f f i c i e n t (dimensionless) ,
W is t h e n e t r a t e of recharge o r d i scharge pe r u n i t a r e a (LT-'),
and t i s t i m e (T).
Equation 7-1 has been developed from t h e equat ion of con t inu i ty and Darcy's
Law. I n o rde r t o v i s u a l i z e t h e phys ica l s i g n i f i c a n c e of t h i s consider f o r
t h e moment a n i d e a l i z e d system a s shown i n F igure 7-1. The prism r e p r e s e n t s
a s m a l l . e lemental volume taken through a compressible, ho r i zon ta l , and con-
f i n e d a q u i f e r of uniform th ickness , b. Assuming t h a t flow t akes p l ace i n t h e
x -d i r ec t ion only then inf low minus outf low r e p r e s e n t s t h e r a t e of change i n
s to rage . This can be w r i t t e n a s
where V i s t h e volume of water contained i n t h e elemental prism a t a s p e c i f i c
Water level changing
Q1
Y
Figure 7-1
UNIDIRECTIONAL NON EQUILIBRIUM FLOW THROUGH AN ELEMENTAL PRISM OF A HORIZONTAL CONFINED AQUIFER. ( Bennett, G. D., Introduction to Ground-Water Hydraulics, U. S.Geological Survey ,i976)
p o i n t i n t i m e . Since t h e s t o r a g e c o e f f i c i e n t , S, is t h e volume of water
r e l ea sed from s t o r a g e i n a prism of u n i t a r e a extending through t h e f u l l
t h i ckness of t h e a q u i f e r i n response t o a u n i t d e c l i n e i n head, Equation
7-2 can be r e w r i t t e n as
Assuming a n i s o t r o p i c and homogeneous a q u i f e r and u t i l i z i n g Darcy7s Law,
8, - Q2 can be approximated a s shown below:
The term Kb, r e p r e s e n t s t h e hydraul ic conduct iv i ty of t h e a q u i f e r t imes i t s
th i ckness , and i s c a l l e d t r ansmias iv i ty o r t r a n s m i s s i b i l i t y , T. Now accord-
i ng t o t h e equat ion of c o n t i n u i t y , in f low minus outf low must equal t h e r a t e
of change of water i n s t o r a g e w i t h i n t h e prism of a q u i f e r such t h a t
Equation 7-6 d e s c r i b e s ground water movement under t h e si.mple cond i t i ons
which were assumed; t h a t i s , where t h e a q u i f e r i s confined, h o r i z o n t a l ,
homogeneous, and i s o t r o p i c , and t h e nioverfient i s i n one d i r e c t i o n . I f horizon-
t a l components of motion normal t o t h e x-axis were p re sen t , then inf low and
outf low through t h e o t h e r two f a c e s of t h e prism would have t o be considered;
t h a t is, t h e two f a c e s normal t o t h e y-axis . I n such a c a s e
The r e l a t i o n given above i s f o r two-dimensional ground water movement under t h e
assumed cons i t i ons . 7- 9
Although it is not important to understand the theory of partial differential
equations, it is important to understand the flow process in relation to
Figure 7-1. Later on in this section it will be shown how a two-dimensional
grid is developed in conjunction with a ground model of the flow system and
one should realize that each area of the grid system represents a prism of
the type shown in Figure 7-1.
A more detailed analysis similar to the preceding method_ology, for an uncon-
fined, heterogeneous and anistropic aquifer results in the approximation,
Equation 7-1. (It should be noted, however, that the calculation of the
rate of change in storage for confined and unconfined systems involve com-
pletely different processes. Withdrawal from or addition to unconfined
storage takes place at the water table whereas confined storage effects are
distributed throughout the vertical thickness of an aquifer. Confined - 5
storage coefficient values usually range from 10 to but unconfined
values range typically from 0.01 to 0.35). An additional component, W, has
been included to represent recharge to or discharge from the ground water
body. Examples of this are: recharge due to precipitation, discharge due
to pumpage, evapotranspiration, etc. Considering a prism, such as in
Figure 1, but of such size as to include a well, then the term W would
represent the rate of withdrawal from the prism due to pumpage.
As with ordinary differential equations, there will be an infinite number of
expressions which will satisfy a partial differential equation; the particu-
lar solution required for a given problem must satisfy, in addition, certain
conditions peculiar to that problem. These additional conditions, termed
boundary conditions, establish the starting points from which the changes
in h are determined.
Formal mathematical soluti.ons of Equation 7-1 are available only for a small
minority of field problems, representing simple boundary conditions. In
most cases, we are forced to seek approximate solutions, using methods other
than direct formal solution. One such method is the simulation of the above
d i f f e r e n t i a l equat ion by a f i n i t e - d i f f e r e n c e equat ion , which i n t u r n can
be solved a l g e b r a i c a l l y o r numerical ly . Another i s t h e f i n i t e element method
f o r so lv ing p a r t i a l d i f f e r e n t i a l equat ions (Appel, et a l . , 1976; P inder , 1974).
Although f i n i t e d i f f e r e n c e schemes a r e p re sen t ly t h e more widely used and
documented, t h e r e a r e d i s t i n c t advantages t o t h e f i n i t e element method as
mentioned l a t e r i n t h i s s e c t i o n .
Where va lues of recharge o r d i scharge , W, t r a n s m i s s i v i t y , T, s t o r a g e coef-
f i c i e n t , S, a r e known f o r t h e AGUA a q u i f e r system, then one can s o l v e f o r t h e
e l eva t ion of t h e water t a b l e . However, i f va lues of T and h a r e known and
a s t eady- s t a t e condi t ion e x i s t s (where s u r f a c e e l e v a t i o n s of t h e water t a b l e
remain e s s e n t i a l l y cons tan t f o r some period of t ime) , t h e t ime d e r i v a t i v e of
head equals zero, and the va lue of W can be found by us ing t h e remaining
terms of t h e equat ion. Thus under s t eady- s t a t e cond i t i ons , -= ah 0, and a t
The preceding methodology i s u t i l i z e d i n t h e computer program t o compute
e l eva t ions of t h e water t a b l e and/or e s t ima te va lues of recharge and d i scha rge
throughout t h e a q u i f e r system.
For t h e f i n i t e d i f f e r e n c e method, a two-dimensional g r i d network i s super-
imposed on a p lan view of t h e ground water r e s e r v o i r a s schemat ica l ly shown
i n F igure 7-2. The i n t e r s e c t i o n of any two l i n e s on t h i s g r i d i s considered
a node l o c a t i o n and va lues of t r a n s m i s s i v i t y , s t o r a g e c o e f f i c i e n t , and hydrau-
1i .c head a r e i npu t i n t o t h e model a t each node i n t h e network. Boundary
condi t ions and a r e a s of recharge and d ischarge a r e a l s o s t i p u l a t e d .
The two-dimensional computer programs a v a i l a b l e and u t i l i z i n g t h e f i n i t e
d i f f e r e n c e scheme, i n gene ra l , w i l l s imu la t e ground water flow i n a confined
( a r t e s i a n ) a q u i f e r , a n unconfined (water- table) a q u i f e r o r a combination of
t h e two. The a q u i f e r may be heterogeneous and a n i s t r o p i c and have i r r e g u l a r
Recharge Boundary
0 Nodes representing recharge
0 Nodes representing pumpage
e 5 060 Contours representing water table elevations
Figure 7-2. Two- Dimens~onal Variable Grid Network
boundaries. The source term i n t h e flow equat ion may inc lude recharge from
r i v e r s t o t h e a q u i f e r , d i scharge from t h e a q u i f e r t o r i v e r s , recharge from
i r r i g a t i o n r e t u r n and wastewater e f f l u e n t , d i scharge due t o evapotranspira-
t i o n o r pumping, recharge from a confined t o an unconfined a q u i f e r o r d i s -
charge from an unconfined t o a confined a q u i f e r .
Considerat ions i n designing t h e a q u i f e r model f o r t h e AGUA, are l i s t e d below:
(1) Boundary condi t ions
The phys i ca l boundaries of t h e a q u i f e r system should be included i n t h e
model i f f e a s i b l e i r r e g a r d l e s s of t h e p r o j e c t a r e a (AGUA). It appears
f e a s i b l e t h a t t h e e a s t e r n and western boundaries, a s they a r e now
de l inea t ed , can be incorporated i n t h e model. The no r the rn and southern
boundaries of t h e a q u i f e r a r e f a r removed from t h e p r o j e c t l i m i t s , such
t h a t they a r e imprac t i ca l t o inc lude . A r t i f i c i a l boundaries could be
designated a t t h e most nor thern and southern l i m i t s of t h e s tudy a r e a
if c o s t permi ts ( c o s t i s a func t ion of t h e number of nodes). I f t h e a r e a
of i n t e r e s t i s i n t h e immediate v i c i n i t y of t h e Ci ty of Albuquerque, t h e
boundaries of t h e model could be loca t ed j u s t f a r enough from t h e c i t y
a s t o have n e g l i g i b l e e f f e c t on t h e computed water l e v e l s i n t h a t a r e a
dur ing si.mul.ation. I f t h e a r e a of i n t e r e s t is t h e C i ty of Albuquerque
and a l l s i g n i f i c a n t i r r i g a t e d a r e a s w i th in AGUA t h e same c r i t e r i a would
apply. Where t h e nor thern and southern boundaries a r e loca ted depends
t o a l a r g e degree on what t h e ob jec t ives of t h e model s tudy a r e . Is one
i n t e r e s t e d only i n t h e impacts of pumpage on water t a b l e l e v e l s and Rio
Grande flows, o r t h e q u a l i t y of domestic water now and a t some l a t e r
da t e , or. t h e q u a l i t y of subsur face water a long the Rio Grande w i t h i n
AGUA? The c o s t of developing a two-dimensional model i s dependent, of
course, on t h e o b j e c t i v e s of t h e model s tudy .
I n gene ra l boundaries a r e t r e a t e d i n t h e va r ious computer programs a s
e i t h e r cons t an t head o r cons tan t f l u x ( inf low o r out f low) . I f t h e
e a s t e r n and western boundaries of t h e AGUA a r e taken a s t h e l i m i t s of
t h e a q u i f e r (impermeable boundaries) , then t h e cons tan t f l u x is zero .
For t h e nor thern and southern boundaries, constant-head o r f i n i t e - f l u x
va lues would be spec i f i ed .
(2) I n i t i a l condi t ions
I n t h e AGUA &he c a l i b r a t i o n of t h e model would probably begin from
s t eady- s t a t e condi t ions o r a t t h a t po in t i n t ime where i t i s reasonable
t o assume t h e change i n hydraul ic head wi th time is e s s e n t i a l l y zero
( see Equation 7-8). Since e s t ima te s of ground water l e v e l s (heads) a r e
a v a i l a b l e f o r 1936 and s i n c e manmade s t r e s s e s (pumpage, e t c . ) were r e l -
a t i v e l y n e g l i g i b l e a t t h a t t ime, a s t eady- s t a t e cond i t i on could be
assumed f o r 1936. S teady-s ta te condi t ions would permit e s t ima te s of
recharge o r d i scharge (such a s evaporat ion, recharge from p r e c i p i t a t i o n ,
recharge due t o s t reams, e t c . ) a t each node i n t h e system.
(3 ) Fin i t e -d i f f e r ence g r i d
A f i n i t e - d i f f e r e n c e g r i d , such a s shown i n F igure 7-2, can be v a r i a b l e
w i th in p a r t i c u l a r r e s t r a i n t s .
Nodes r ep re sen t ing pumping and observa t ion we l l s should b e c l o s e t o
t h e i r r e s p e c t i v e p o s i t i o n s t o f a c i l i t a t e c a l i b r a t i o n . I f s e v e r a l pump-
ing w e l l s a r e c l o s e toge ther , t h e i r d i scharge may be lumped and ass igned
t o one node s i n c e d ischarge and head is d i s t r i b u t e d over t h e a r e a of
a r ec t angu la r g r i d . I n t h e v i c i n i t y of t h e Ci ty of Albuquerque where
w e l l s i n some cases a r e l e s s than a mi l e a p a r t , t h e g r i d space could
be made f i n e r , probably down t o a mi l e o r l e s s depending on t h e a r e a
which w i l l be modeled, i n order t o adequately s imula te t h e s t r e s s due
t o pumpage on t h e system.
There a r e r e s t r i c t i o n s t o t h e t o t a l number of nodes which can be econ-
omical ly and phys i ca l ly incorporated i n a two-dimensional f i n i t e - d i f f e r -
ence model. Depending on t h e computer program and t h e computer f a c i l i t i e s
used f o r s imula t ion , i t could range from 10,000 t o 20,000 nodes. I f
a v a r i a b l e g r i d spacing i s incorporated ( a s would probably be t h e c a s e
f o r t h e AGUA), then t h e r e a r e r e s t r i c t i o n s a l s o t o t h e r e l a t i v e change i n
g r i d spac ing which can be accommodated ( t h e reader should check t h e
documentation of va r ious computer programs a v a i l a b l e ) . Nodes should
a l s o be placed c l o s e toge the r where t h e r e a r e s i g n i f i c a n t changes i n
t r a n s m i s s i v i t y ; and t h e a x i s of t h e g r i d o r i en t ed p a r a l l e l t o t h e
p r i n c i p a l d i r e c t i o n of t h e t r a n s m i s s i v i t y t enso r (vec to r ) .
A s mentioned previous ly , f in i te -e lement methods have been used t o
approximate t h e p a r t i a l d i f f e r e n t i a l equat ions r ep re sen t ing ground water
flow (Pinder , 1974). This method u t i l i z e s i r r e g u l a r elements ( t r i a n g l e s ,
r e c t a n g l e s which may be deformed i n a s p e c i f i c way, e t c . ) i n s t e a d of t h e
r e c t a n g l e s common t o t h e f i n i t e d i f f e r e n c e scheme. The r a t h e r a r b i t r a r y
arrangement of nodes is a d i s t i n c t advantage when modeling i r r e g u l a r
boundaries and r e l a t i v e l y l o c a l i z e d a r e a s of l a r g e s t r e s s e s .
C a l i b r a t i o n of a Two-Dimensional Model of t h e Flow System. The u l t i m a t e
purpose of a model s imula t ing t h e flow system is t o p r e d i c t changes i n water
l e v e l s i n t h e a q u i f e r caused by changes i n s t r e s s e s (pumpage, d i v e r s i o n s ,
r e s e r v o i r ope ra t ions , e t c . ) on t h e system. Before a model can be used f o r
p red ic t ion , i t must be c a l i b r a t e d ; t h a t i:; water l e v e l s s imulated by t h e
s t r e s s e d model must match m,?asured water l e v e l s a t any chosen time. I n t h e
AGUA t h i s would mean t h a t t h e ground t ra te r l e v e l s f o r 1936, 1960 and 1978,
a s determined i n t h i s s tudy and p r i o r s t u d i e s (Bjorklund, e t a l . , 1961; Reeder,
e t a l . , 1967; Nat iona l Resources Committee, 19.38), would be used i n t h e ca l -
i b r a t i s n process .
I n gene ra l t h e c a l i b r a t i o n process begins w i th t h e s t eady- s t a t e condi t ion .
(Although pumping w e l l s e x i s t e d i n t h e AGUA i n 1936, t h e i r impact on t h e
ground water l e v e l s has been considered n e g l i g i b l e ) . A msp of t r a n s m i s s i b i l i t y
va lues and a ground water l e v e l contour map would be requi red f o r t h i s
p a r t i c u l a r p o i n t i n t ime. S u b s t i t u t i n g map va lues of t r ansmis s iv i ty , T,
and hydraul ic head, h , i n t o equat ion 7-8, t h e computer program is used t o
compute recharge o r d i scharge (ne t f l u x ) , W, a t each nodal p o i n t i n t h e
system.
P l o t t i n g t h e proper s i g n (t, o r -) of W, y i e l d s a map t h a t i n d i c a t e s a r e a s
of recharge o r d i scharge . Also t h e va lues of W can be compared, and any
va lue of W t h a t i s cons iderably d i f f e r e n t from surrounding va lues is e a s i l y
not iced . Values of W t h a t are considerably d i f f e r e n t and obviously unreason-
a b l e can be ad jus t ed by modifying T . The modified va lue of T i s placed i n
t h e program and a computer run t h a t computes a new va lue of W is made. This
process is continued u n t i l a s e t of va lues f o r T, h and W is generated wherein
t h e va lues f o r T and h do n o t y i e l d va lues of W t h a t a r e judged t o be unreason-
a b l y l a r g e o r smal l . Also, ad jus t ed va lues of T o r h a r e checked f o r consis-
tency wi.th ad j acen t va lues of T and h. (Values of h could be ad jus t ed i n t h i s
process i f they were o r i g i n a l l y est imated i n an a r e a where very 1 . i t t l e o r no
observed d a t a was a v a i l a b l e ) .
The next s t e p i n t h e model a n a l y s i s gene ra l ly involves determining d i f f e r e n c e s
i n a l l recharge and d ischarge from t h e time of assumed s t eady- s t a t e con-
d i t i o n s (1936) t o 1960. These va lues a r e used t o s t r e s s t h e model i n
d i s c r e t e t ime s t e p s s o t h a t t h e model w i l l s o l v e f o r h ( f o r s p e c i f i e d va lues
of s t o r a g e c o e f f i c i e n t , S) i n 1960, according t o equat ion 7-1. The d i f f e r -
ences iL1 recharge o r d i scharge can only a r i s e i f t h e r e i s a phys i ca l change
t h a t has occurred i n t h e AGUA between 1936 and 1960 which a f f e c t s t h e water
resource . Examples of t h i s would inc lude new pumping w e l l s , a d d i t i o n a l
wastewater e f f l u e n t , new i r r i g a t i o n cana l s and ope ra t ions , changes i n stream
flow due t o r e s e r v o i r opera t ion , e t c .
A s i m i l a r a n a l y s i s would be requi red between 1960 and 1978 u n t i l model para-
meters s a t i s f a c t o r i l y reproduce t h e water - tab le l e v e l s f o r each of t h e
designated y e a r s a t each node i n t h e system.
Data Required for a Two-Dimensional Model of the Flow System. In the
AGUA the data that must be known or estimated for a two-dimensional ground
water model of the flow system (whether finite-difference or finite-element)
would include the following:
(1) A water-table level contour map for each of the years 1936, 1960 and
1978 for the area included in the ground water study.
(2) A map of transmissivity values for each of the years 1936, 1960, and
1975. (It could be that changes in saturated thickness due to pro-
gressive mining of the ground water body are insignificant when compared
to the total saturated thickness. If this is the case throughout the
aquifer system, then transmissivity values could be considered the same
for each year without significant error).
(3) A map of storage coefficient values. At present this coefficient for
the AGUA has been estimated as 0.20 but a more detailed analysis of
this parameter is appropriate to calibrate the model. An average value
of the storage coefficient can be obtained in the vicinity of a pumped
well by measuring in one or more observation wells the decline of head
with time under the influence of a constant pumping rate. Estimates
can be made when there are no observation wells and only measurements
of the drawdowns in the abstraction well are available. (Rushton, 1978)
In a two-dimensional ground water model developed for the Modesto,
California area the storage coefficient was estimated by using values
of specific yield associated with the size and distribution of granular
material (Page, 1977)
(4) Recharge from precipitation, wastewater and irrigation return.
(5) Pumpage and its distribution in time and space.
(6) Hydrologic parameters of any confining aquifer beds.
(7) Hydrologic parameters of river beds (particularly vertical hydraulic
conductivity) .
(8) Stages and flows in rivers and canals.
(9) Physical boundaries of aquifer system.
(10) Evapotranspiration rates from soils, agricultural crops, phreatophytes,
etc.
The above data are placed at nodes in a particular grid system which is used
for entering data in the flow equation. Additional data or better estimates
of existing data would depend upon a sensitivity analysis (assuming that the
model has been reasonably calibrated). A sensitivity analysis consists of
determining model response when varying the magnitude of the model parameters
by an amount proportional to the degree of uncertainty present in their
determination. The degree of uncertainty can be determined statistically for
some parameters and estimated for others.
Sensitivity testing consists of varying a given parameter in the model and
recording the changes in simulated head as a result of the change in
parameter. During a test, all other parameters are held at their adopted
value, If model results are highly sensitive to a particular parameter,
then a special effort should be made to determine that parameter as accurately
as possible in order to improve the predicting accuracy of the model.
Three-Dimensional Model of the Flow System. With a three-dimensional - model, the physics of the flow process is thought of as being completely
describable by movement in three directions, generally three orthogonal coor-
dinate directions. (In the two-dimensional system discussed previously, the
flow process was described utilizing the x and y-coordinate directions
as shown in Figure 7-1. For the three-dimensional simulation a vertical
Component is added). The equation of continuity now involves the determination
of inf low and outf low through s i x f a c e s of a prism ins t ead of f o u r a s used
i n t h e two-dimensional a n a l y s i s . The r a t e of change of water i n s t o r a g e
i s c a l c u l a t e d i n t h e same manner a s prev ious ly descr ibed .
For t h e three-dimensional s imula t ion , a g r i d network i s superimposed on t h e
a r e a under s tudy , and va lues of hydraul ic conduct iv i ty , hydraul ic head and
s p e c i f i c s t o r a g e a r e i npu t t o t h e model a t each node i n t h e network ( s e e
F igure 7-3). Boundary condi t ions , pumpage, recharge, e t c . must a l s o be
included.
V e r t i c a l flow and v a r i a t i o n i n permeabi l i ty wi th depth, f o r example, need no
s p e c i a l cons ide ra t ion , thus g iv ing t h e model added f l e x i b i l i t y over a two-
dimensional system.
Seve ra l f i n i t e - d i f f e r e n c e schemes f o r s imula t ion of three-dimensional ground
water flow systems have been documented (Tresco t t , 1976; T resco t t , e t a l . ,
1976). The porous medium t o be s imulated may be heterogeneous and a n i s t r o p i c
and have i r r e g u l a r boundaries. The uppermost hydrologic u n i t ( aqu i f e r system)
may have a f r e e su r f ace . S t r e s s on t h e system may be i n t h e form of we l l
d i scha rge ( o r recharge) , d i scharge due t o evaporat ion, recharge from p rec ip i -
t a t i o n , e t c . The model a l s o permits t h e use of v a r i a b l e g r i d spacing.
Boundary cond i t i ons , i n i t i a l condi t ions and t h e des ign of t h e f i n i t e -
d i f f e r e n c e g r i d system a r e q u i t e s i m i l a r t o t h a t f o r t he two-dimensional
systems descr ibed previous ly . A disadvantage of a three-dimensional s imula t ion
i s t h e s i z e requirement (core) of t h e computer f a c i l i t y and t h e computation
time involved. Both a r e p ropor t iona l t o t h e number of nodes r ep re sen t ing t h e
porous medium.
There have been succes s fu l a p p l i c a t i o n s of t h e three-dimensional ground water
model t o f low systems s i m i l a r t o AGUA, (U.S. Geological Survey, 1978) and
s e v e r a l s t u d i e s underway o r proposed.
Figure 7-3. Three- Dimensional Grid Network
P rec/bifation
Water Tbb/e
.
J
The calibration process and the data required are similar to that for the
two-dimensional system. The added dimension though requires that storage
and hydraulic conductivity be determined with respect to depth and that the
directional aspects of hydraulic conductivity be thoroughly analyzed.
Digital Computer Modeling of Water Quality
The quality of water, because of its significance relative to various uses,
has become of increasing importance. More intense efforts are now required
to protect water resources from contamination and to predict the effects of
man's activities on the chemical, physical and bacterial characteristics of
ground water.
The capability to predict the movement of various constituents in flowing
ground water can be of help in (Konikow, 1970)
(1) Planning and designing projects to minimize ground water contamination.
(2) Estimating spatial and temporal variations of concentrations of inorganic
constituents.
(3) Estimating the time of travel between a source of contamination and
a discharge point such as a stream, spring or well.
( 4 ) Designing an effective and efficient monitoring system.
(5) Evaluating the physical and economic feasibility of alternative
reclamation plans for removing contaminants from an aquifer and/or
preventing the contaminants from spreading.
The purpose of a digital computer quality model is to compute the concen-
tration of a dissolved constituent in an aquifer at any specified place and
t i m e . Since t h e movement of contaminants depends t o a l a r g e degree on t h e
v e l o c i t y of ground water flow, i t i s a necessary p r e r e q u i s i t e t h a t t h e flow
system be s imula ted . This , i n essence, r e q u i r e s t h a t a two o r three-dimen-
s i o n a l model of t h e flow system be c a l i b r a t e d be fo re a r e l i a b l e q u a l i t y model
can be developed.
A model which inc ludes q u a l i t y cons ide ra t ions must s o l v e two simultaneous
p a r t i a l d i f f e r e n t i a l equat ions. One i s t h e equat ion of flow (such a s
equat ion 7-I) , from which ground water v e l o c i t i e s a r e obta ined , and t h e
second is t h e so lu t e - t r anspor t equat ion, desc r ib ing t h e concent ra t ion of a
d i s so lved c o n s t i t u e n t i n t h e ground water (Konikow, 1970). It i s important
t o n o t e t h a t t h e f i n i t e - d i f f e r e n c e and f in i te -e lement approximations of t h e
f low equat ions do no t d i r e c t l y y i e l d ground water v e l o c i t i e s . The v e l o c i t i e s
c a l c u l a t e d by t h e s e methods a r e apparent v e l o c i t i e s of t h e flow regime. Con-
s i d e r t h e d ischarge , Q2, through t h e c ros s - sec t iona l a r e a , 2, of F igure 7-1.
The apparent v e l o c i t y is t h e d ischarge , Q divided by t h e c ros s - sec t iona l 2'
a r e a , 2. The average seepage v e l o c i t i e s ( v e l o c i t i e s of flow through t h e pore
spaces of t h e a q u i f e r m a t e r i a l ) necessary i n q u a l i t y s imula t ions a r e deter-,
mined by t ak ing i n t o account t h e e f f e c t i v e p o r o s i t y ( t h e f r a c t i o n of t h e
g r o s s c ros s - sec t iona l a r e a of t h e s a t u r a t e d e a r t h m a t e r i a l r ep re sen t ing t h e
p o r t i o n through which flow occurs) according t o
- 2 where V,. i s t h e seepage v e l o c i t y i n t h e < -d i r ec t ion (LT ' )
X I . i s t h e hydrau l i c conduct iv i ty t enso r (LT-I) Z J
n i s t h e e f f e c t i v e p o r o s i t y (dimensionless)
Although i t i s not necessary t o f u l l y understand equat ion 7-9, what i s
important i s t h a t an a d d i t i o n a l phys i ca l c h a r a c t e r i s t i c of t h e a q u i f e r ,
e f f e c t i v e po ros i ty , must be determined a t each node i n t h e system when in-
c lud ing q u a l i t y of ground water i n t h e s imula t ion .
The so lu t e - t r anspor t equat ion, gene ra l ly used t o desc r ibe t r a n s p o r t
and d i spe r s ion of a given d isso lved chemical c o n s t i t u e n t i n flowing ground
water , involves t h e fol lowing ccns ide ra t ions :
(1) Dispersion c h a r a c t e r i s t i c s of t h e porous medium
(2) E f f e c t s of convect ive t r a n s p o r t ( func t ion of t h e seepage v e l o c i t y )
(3) Concentrat ion of d i sso lved chemicals a t a p a r t i c u l a r source of recharge
o r d i scharge (such a s we l l s , r i v e r s , cana ls , e t c . )
( 4 ) A l l chemical r e a c t i o n s a f f e c t i n g t h e chemical c o n s t i t u e n t s of i n t e r e s t
I tem 4 above may be e l imina ted from cons ide ra t ion i n t h e c a s e of a con-
s e r v a t i v e , nonreact ing c o n s t i t u e n t . (Conservative c o n s t i t u e n t s a r e t hose
considered t o have l i t t l e o r no r e a c t i o n t o t h e i r p resent environment.
Nonconservative c o n s t i t u e n t s , on t h e o the r hand, a r e those t h a t r e a c t t o some
degree w i t h t h e chemical composition of t h e rocks w i t h which they have been
i n con tac t , t h e temperature, t h e pressure , t h e du ra t ion of con tac t , t h e
m a t e r i a l s a l r eady i n s o l u t i o n , e t c . ) From t h e above d i scuss ion , i t is
apparent t h a t a s i g n i f i c a n t amount of a d d i t i o n a l d a t a i s r equ i r ed when q u a l i t y
cons ide ra t ions a r e included i n t h e modeling e f f o r t .
Coupled computer programs a r e a v a i l a b l e t o model both t h e flow system and
t r a n s p o r t of chemical c o n s t i t u e n t s . They a r e a p p l i c a b l e t o unconfined, he t e r -
ogenous and a n i s t r i p i c a q u i f e r s e i t h e r i n two o r t h r e e space dimensions.
Although t h e r e have been s e v e r a l succes s fu l a p p l i c a t i o n s involv ing q u a l i t y ,
a t t h e p re sen t they a r e r a t h e r l imi t ed i n scope and s t i l l , i n many r e s p e c t s ,
i n a developmental s t a t e (Konikow, 1970; Konikow, e t a l . , 1974).
With r e spec t t o t h e AGUA, it would appear t h a t only a few p o s s i b i l i t i e s e x i s t
i n regard t o q u a l i t y modeling based on t h e succes s fu l a p p l i c a t i o n s f o r
somewhat s i m i l a r bas ins . (This is not t o s ay t h a t succes s fu l s imula t ions of
o t h e r chemical c o n s t i t u e n t s a r e no t poss ib l e a t p re sen t bu t t h a t they have
not been succes s fu l ly appl ied t o a degree t h a t would warrant p r a c t i c a l
cons ide ra t ion ) . Of those succes s fu l a p p l i c a t i o n s (mostly two-dimensional
systems), t h e assumption was made t h a t no chemical r e a c t i o n s occurred
between t h e chemical c o n s t i t u e n t of i n t e r e s t and t h e a q u i f e r o r s o i l m a t e r i a l s
t h a t would a f f e c t t h e concent ra t ion . The so lu t e - t r anspor t equat ion i n t h i s
ca se reduces t o a cons ide ra t ion of d i spe r s ion , convec t ive t r a n s p o r t and t h e
concent ra t ion of d i sso lved chemicals f o r va r ious sources of recharge o r
d i scharge . Although t h e above assumption l i m i t s t h e q u a l i t y a n a l y s i s t o
r e l a t i v e l y conserva t ive (nonreact ing) chemical c o n s t i t u e n t s , reasonable sim-
u l a t i o n s have been made f o r low-level r a d i o a c t i v e wastes and d isso lved s o l i d
concent ra t ion v a r i a t i o n s (Konikow, 1970; Konikow, e t a l . , 1974). Of t h e
l a t t e r , an a n a l y s i s of d i sso lved s o l i d concent ra t ions o r s a l i n i t y i n c r e a s e s
of t h e ground water resource due t o i r r i g a t i o n p r a c t i c e s could be s imulated.
I n summary a coupled ground water f low q u a l i t y model a s a p p l i c a b l e t o AGUA
would c a l c u l a t e t h e head d i s t r i b u t i o n i n t h e a q u i f e r a t t h e end of each
computation per iod (time s t e p ) . The hydrau l i c g r a d i e n t s determined from
t h e new water t a b l e e l e v a t i o n s would then be used t o compute seepage velo-
c i t i e s through t h e a q u i f e r . The changes i n concen t r a t ion due t o d i s p e r s i o n
and convect ive t r a n s p o r t of t h e chemical c o n s t i t u e n t s during t h e t ime s t e p
would be computed next based on ground water v e l o c i t i e s and t h e concen t r a t ion
g rad ien t s i n t h e a q u i f e r a t t h e beginning of t h e s imula t ion per iod .
S ince two-dimensional flow and q u a l i t y models appear reasonable f o r AGUA,
t h e fol.lowing remarks a r e a p p l i c a b l e t o a coupled two-dimensional flow-
q u a l i t y s imu la t ion (assuming conserva t ive chemical c o n s t i t u e n t s ) . I n addi-
t i o n t o t h a t d i scuss ion made previous ly f o r modeling flow systems, and which
a r e a p p l i c a b l e now, q u a l i t y s imula t ion involves cons ide ra t ion of many o t h e r
condi . t ions. Constant concent ra t ion boundaries and t h e concen t r a t ion a t each
node i n t h e model must be s p e c i f i e d f o r those t ime per iods u t i l i z e d i n t h e
c a l i b r a t i o n process . The f i n i t e - g r i d system ( i f used) developed must be
based on both quan t i t y and q u a l i t y cons ide ra t ions . C a l i b r a t i o n of t h e model
now inc ludes matching concen t r a t ion changes over t ime and space; and t h e d a t a
requirements f o r i n c l u s i o n of q u a l i t y a r e , i n genera l , noted below:
(1) A map of e f f e c t i v e po ros i ty va lues f o r t h e a r e a included i n t h e ground
water s tudy
( 2 ) A map of t h e d i s p e r s i v i t y c h a r a c t e r i s t i c s of t h e porous medium
(3) Concentrat ions of t h e chemical c o n s t i t u e n t s of i n t e r e s t i n t h e a q u i f e r
f o r each time per iod used i n t h e c a l i b r a t i o n process
(4) Concentrat ions of t h e chemical c o n s t i t u e n t s of i n t e r e s t of a l l app l i ed
water ( p r e c i p i t a t i o n , i r r i g a t i o n water , s u r f a c e water , wastewater
e f f l u e n t , e t c . )
Seve ra l p o i n t s should b e emphasized a t t h i s t ime i n regard t o t h e computer
programs a v a i l a b l e f o r ground water modeling and which might be considered
f o r t h e AGUA.
The two-dimensional computer programs cons ider flow i n t h e h o r i z o n t a l p l ane
only. V e r t i c a l flow o r t h e v e r t i c a l component of flow cannot be handled
d i r e c t l y . Various modi f ica t ions have been incorpora ted i n t h e two-dimen-
s i o n a l systems t o handle v e r t i c a l components, bu t t h e added complicat ions
make i.t d i f f i c u l t t o apply i n t h e r e a l sense. A t p r e sen t i t would appear
t h a t a two-dimensional model could adequately s imula te t h e ground water f low
system of t h e AGUA. The one problem which might a r i s e and which could
in t roduce s i g n i f i c a n t e r r o r s i n t h e c a l i b r a t i o n process , i s t h e p o s s i b i l i t y
t h a t t h e major t r a n s m i s s i v i t y t enso r (vec tor ) is i n c l i n e d t o t h e p lane con-
t a i n i n g t h e g r i d o r element system. This s i t u a t i o n could occur i f s t r a t i f i e d
l a y e r s of v a l l e y - f i l l m a t e r i a l e x i s t and i f they s l o p e away from t h e land
s u r f a c e r a t h e r s i g n i f i c a n t l y . I n t h i s ca se t h e va lue of t r ansmis s iv i ty i n
t h e two-dimensional system w i l l have t o be ad jus t ed t o compensate f o r t h e
v e r t i c a l component and t h e ad jus t ed va lues w i l l no longer r e f l e c t t h e r e a l
system. I f t h e adjustment is extreme then c a l i b r a t i o n of t h e model may be
u n a t t a i n a b l e .
Although f in i te -e lement methods o f f e r d i s t i n c t advantages over f i n i t e -
d i f f e r e n c e methods, they a r e a t p resent no t w e l l documented nor have they
been widely appl ied t o ground water systems s i m i l a r t o t h e AGUA. The U.S.
Geological Survey i n t h e i r ground water modeling e f f o r t s f o r t h e San
Bernardino Valley Municipal Water D i s t r i c t , w i l l u t i l i z e both methods and
compare t h e r e s u l t s .
I n e i t h e r t h e two o r t h r e e di.mensiona1 system t h e drawdown i n an ind iv idua l
well i s n o t computed d i r e c t l y . The models compute a hydrau l i c head t h a t
r ep re sen t s t h e average head over an elemental a r e a . Various a n a l y t i c a l
techniques can be used t o compute t h e approximate drawdown i n a we l l based
on t h e average hydraul ic head (Tresco t t , e t a l . , 1976).
I f t h e o b j e c t i v e of a modeling e f f o r t i n t h e AGUA i s t o s imu la t e t h e ground
water flow system; then a t p re sen t a f i n i t e - d i f f e r e n c e two-dimensional model
would appear t o be t h e s imples t model t h a t w i l l y i e l d adequate r e s u l t s . I f
q u a l i t y i s an ob jec t ive , then i t must be remembered t h a t t h e f low system be
reasonably s imulated before a r e l i a b l e q u a l i t y model can be developed.
A D i g i t a l Computer Model f o r t h e AGUA
Discussions i n t h i s s e c t i o n support t h e conclusion t h a t a two o r t h r e e
dimensional d i g i t a l model of t h e AGUA ground water flow system could be
developed succes s fu l ly . Although the a r e a of t h e ground water bas in t o be
s imulated would depend upon t h e s p e c i f i c o b j e c t i v e s of a p a r t i c u l a r s tudy ,
i t appears t h a t adequate d a t a could be assembled ( r ega rd l e s s of t h e s i z e of
t he a r e a w i t h i n AGUA) t o adequately c a l i b r a t e a flow model.. I n t h e c a s e of
a coupled f low-qual i ty model, i t ' s devel.opment i s l e s s c e r t a i n because of
l i m i t e d a v a i l a b i l i t y of documented computer programs, t h e i n a b i l i t y a t p resent
t o s imu la t e r e a c t i v e chemical c o n s t i t u e n t s , and only a smal l number of p r a c t i -
c a l s i t u a t i o n s t h a t have been adequately s imulated. It should be emphasized
t h a t be fo re a r e l i a b l e so lu t e - t r anspor t model could be developed, a model of
t h e flow-system must be c a l i b r a t e d . This l a t t e r f a c t sugges ts t h a t a f low
model could be undertaken be fo re i nco rpora t ing q u a l i t y a spec t s . I n t h e
t i m e t h a t i t might t ake t o c a l i b r a t e t h e flow model, advances i n t h e f i e l d
of q u a l i t y s imula t ion may be such a s t o warrant i ts cons ide ra t ion a t a f u t u r e
d a t e . With t h i s i n mind a computer program should be s e l e c t e d t h a t is adap-
t a b l e t o q u a l i t y a s w e l l a s flow cons ide ra t ions .
Reasons f o r Modeling. Severa l reasons f o r u t i l i z i n g a d i g i t a l computer
model i n t h e AGUA a r e discussed below and provide t h e b a s i s f o r judging t h e
u t i l i t y of undertaking a modeling e f f o r t .
(1) Determine q u a n t i t a t i v e l y and s p a t i a l l y recharge due t o i r r i g a t i o n cana l s ,
wastewater t rea tment f a c i l i t i e s , s t reams, e t c .
(2) Evaluate e f f e c t i v e n e s s of bas in management p l ans on t h e water r e sou rce
both q u a n t i t a t i v e l y and q u a l i . t a t i v e l y
(3) I n v e s t i g a t e impacts of wastewater d i scharges on t h e system
(4) Study e f f e c t i v e n e s s of replenishment programs
(5) Evaluate pumping programs
a. Economic optimums
b. Hydraulic impacts
( 6 ) Determine s e n s i t i v i t y of assumptions i n both modeling techniques and
inpu t d a t a
(7) Help design monitor ing and s u r v e i l l a n c e programs
(8) Learn more about t h e behavior of t h e ground water bas in , and
(9) Encourage a b u s i n e s s l i k e approach t o development and management of water
resource d a t a .
I n ana lyz ing reasons f o r cons ider ing a d i g i t a l computer model, i t should
be noted t h a t t h e d i g i t a l model has t h e c a p a b i l i t y of desc r ib ing t h e
t o t a l system i n q u a n t i t a t i v e terms; and i n t e r r e l a t i o n s h i p s between components
of t h e system and s t r e s s e s on t h e system can be considered s imultaneously.
The r e a l p o t e n t i a l of a model of t h i s type a r i s e s when a ground water f low
system has been reasonably c a l i b r a t e d and v e r i f i e d . A t t h i s po in t i n t ime
t h e model can be u t i l i z e d f o r r a p i d eva lua t ion of m u l t i p l e a l t e r n a t i v e s and
poss ib ly coupled w i t h q u a l i t y , economic and r a in fa l l - runof f models.
Costs f o r Developing a D i g i t a l Computer Model. S ince t h e o b j e c t i v e s of
any p a r t i c u l a r modeling e f f o r t f o r t h e AGUA a r e , i n gene ra l , no t known,
d e f i n i t i v e c o s t e s t ima te s a r e n o t poss ib l e . It is poss ib l e , though, t o
r e l a t e c o s t s of o t h e r ground water modeling e f f o r t s i n s i m i l a r bas ins t o
those t h a t might be contemplated f o r t h e AGUA.
A ground water modeling e f f o r t ( t o p r e d i c t ground water l e v e l s ) developed
by t h e Kern County Water Agency i n coopera t ion wi th t h e C a l i f o r n i a Department
of Water Resources began i n A p r i l of 1967 (Kern County Water Agency, 1974,
1974 and 1977). The maximum o b l i g a t i o n of t h e water agency under t h e i n i t i a l
f i v e year agreement was $250,000. Included w i t h i n t h e o b l i g a t i o n was t h e
s t i p u l a t i o n t o provide personnel necessary t o a c q u i r e and t a b u l a t e d a t a
r e l a t i v e t o land and w a t e r use dur ing h i s t o r i c t imes (approximately 115 man-,
months) and t o provide computer s e r v i c e s . The model (a modi f ica t ion of a
two-dimensional link-node computer program developed by t h e C a l i f o r n i a
Department of Water Resources) s imulated a f low system c o n s i s t i n g of confined
and unconfined a q u i f e r s covering approximately 2000 square mi les . Each
elemental a r e a of t h e polygonal g r i d system contained approximately 9 square
m i l e s .
The C i ty of Modesto i n a 50-50 c o s t sha r ing e f f o r t w i th t h e U.S. Geological
Survey con t r ac t ed t o develop a two-dimensional ( f i n i t e - d i f f e r e n c e ) ground
water model of t h e unconfined a q u i f e r i n and near t h e Ci ty of Modesto,
C a l i f o r n i a (Page, 1977). The model encompasses about 542 square m i l e s u t i l -
i z i n g a v a r i a b l e r ec t angu la r g r i d system. The C i ty ' s es t imated c o s t t o d a t e
i s approximately $200,000 which inc ludes personnel necessary f o r t h e d a t a
c o l l e c t i o n e f f o r t . The model i s expected t o be a v a i l a b l e a s a management
t o o l around 1979-1980 a f t e r a d d i t i o n a l d a t a c o l l e c t i o n and ref inements t o t h e
e x i s t i n g model a r e made. (The e f f o r t w i l l t ake about seven yea r s w i th a t o t a l
c o s t t o t h e c i t y of about $250,000).
The San Francisco D i s t r i c t , U.S. Army Corps of Engineers, con t r ac t ed w i t h t h e
U.S. Geological Survey t o develop a ground water model f o r t h e S a l i n a s Valley
a r e a of C a l i f o r n i a (U.S. Geological Survey, 1978). The a r e a of i n t e r e s t was
approximately 600 square m i l e s and c o n s i s t s of confined and unconfined con-
d i t i o n s w i t h i n t h e a q u i f e r system. Fini te-element techniques a r e used t o
model t h e a q u i f e r i n both two and t h r e e space dimensions. The c o n t r a c t a l s o
included t h e development of a ground water q u a l i t y model ( a coupled flow-
q u a l i t y model) t o s imu la t e t h e t r a n s p o r t of conserva t ive chemical c o n s t i t u e n t s
and t e s t s of f u t u r e a l t e r n a t i v e s involv ing both flow and q u a l i t y . The time
involved w a s es t imated a s t h r e e yea r s w i th a t o t a l c o s t t o t h e San Francisco
D i s t r i c t of $300,000.
Although t h e a r e a t h a t a ground water model might encompass i n t h e AGUA i s
not known i t would probably be much l e s s than t h e s tudy l i m i t s . I f one
extends t h e i d e a l i z e d boundaries of t h e a q u i f e r a s def ined i n prev ious s t u d i e s
(Reeder, 1967) t h e a r e a would probably be about 1400 square mi l e s . Then
depending on t h e i n t e r e s t s of a p a r t i c u l a r modeling e f f o r t (whether t o de t e r -
mine t h e e f f e c t s of pumping on Rio Grande flows, q u a l i t y of water i n t h e
immediate v i c i n i t y of t h e Rio Grande, e t c . ) , t h e a r e a covered would s t i l l be
s i g n i f i c a n t l y l e s s than t h a t .
An a n a l y s i s of t h e c o s t s of s i m i l a r s t u d i e s inc luding those previous ly c i t e d ,
i n d i c a t e s t h a t t h e c o s t of d a t a c o l l e c t i o n , a n a l y s i s and i n t e r p r e t a t i o n i s
about 40 percent of t h e c o s t a s soc i a t ed wi th t h e development of t h e ground
water flow model. (Of course, the data collection effort is dependent on
the difficulties involved in calibration and on the foll.owing sensitivity
analyses). A summary of estimated costs and times (which might be over-
lapping) associated with a ground water mdoeling effort in the AGUA is given
below:
Time (year) Cost
(1) Data collection, analysis and interpretation
(2) Development of ground water flow model
Two-dimensional (Finite-difference or finite-element) 2-4 100,000
$140,000
The total cost of $140,000 represents the cost of developing a flow model
adequate for general planning purposes (assuming a comphter program can be
acquired from some agency or organization). It is expected that continued
data collecti.on and refinement of the model will be necessary as various sen-
siti.vity tests are made and new data becomes available.
If water quality is a consideration, then the total cost of a model is expected
to increase significantly. A summary of the estimated total cost and time
associated with a coupled ground water flow and quality model are indicated -- below :
Time (year) - Cost
(I) Data collection, analysis and interpretation
(2) Development of a ground water flow and quality model (conservative chemical constituents)
Two-dimensional (Finite-difference or finite-element)
~ l t h o u g h t h e c o s t s should be viewed as pre l iminary i n na tu re , t h e r e is one
cons ide ra t ion t h a t i s important t o note . The U.S. Geological Survey can
e n t e r i n t o coopera t ive (50-50 c o s t sha r ing ) agreements wi th l o c a l agencies
(such a s c i t i e s , water d i s t r i c t s , e t c . ) t o model t h e ground water b a s i n s of
i n t e r e s t . For an agency contemplat ing modeling of t h e AGUA a q u i f e r system,
t h e coopera t ive e f f o r t should be considered no t on ly i n regard t o funding
bu t a l s o i n regard t o t h e t e c h n i c a l c a p a b i l i t i e s of t h e U.S. Geological
Survey i n t h e f i e l d of ground water modeling.
Guide l ines f o r t h e Development of a Ground Water Model. The fol lowing
a r e important cons ide ra t ions f o r determining when a d i g i t a l computer model-
ing e f f o r t should be i n i t i a t e d .
(1) Evidence of t h e need f o r e f f e c t i v e ground water management. It is
advantageous t o begin d a t a c o l l e c t i o n and model development be fo re
c r i t i c a l problems develop s o t h a t information provided by a model can
a s s i s t i n prevent ing such problems. A proper ly c a l i b r a t e d and v e r i f i e d
model can be an important t o o l i n e f f e c t i v e ground water management.
I n s i t u a t i o n s where problems have a l r e a d y developed a model can be
e f f e c t i v e i n ana lyz ing t h e problems, explor ing a l t e r n a t i v e s o l u t i o n s ,
and i n minimizing t h e s e v e r i t y of such problems.
(2) An i n t e r e s t e d , capable, r e spons ib l e pub l i c agency and s t a f f . A good
example of t h i s i s t h e San Bernardino Valley Minic ipa l Water D i s t r i c t
(San Bernardino, C a l i f o r n i a ) . Although t h i s agency was one of s e v e r a l
agencies ope ra t ing w i t h i n t h e b a s i n and without complete l e g a l j u r i s -
d i c t i o n over t h e a c t i v i t i e s of t h e o t h e r agencies , they f e l t i t was
s t i l l i n t h e i r b e s t i n t e r e s t s and i n t h e b e s t s i n t e r e s t s of a l l con-
cerned t o develop a ground water model and t o dev i se a d a t a c o l l e c t i o n
and management system f o r t h e e n t i r e bas in .
(3) An adequate budget and t i m e schedule.
An i n v e s t i g a t i o n of numerous ground water model s t u d i e s involving
unconfined a q u i f e r systems somewhat comparable i n s i z e t o t h e AGUA,
sugges ts a range of c o s t s between $1.50,000 t o $400,000 depending on
t h e complexity of t h e model and t h e d a t a a v a i l a b l e . I n most of those
s t u d i e s a n i n t e n s i v e d a t a c o l l e c t i o n e f f o r t spanned two t o f o u r yea r s .
(4) A v a i l a b i l i t y and use of t h e proper technology
Computer programs a r e a v a i l a b l e f o r modeling ground water svstems.
For two and t h r e e space dimensions ground water f low systems have been
modeled wi th c o n s i s t e n t l y s a t i s f a c t o r y r e s u l t s over t h e l a s t decade
(P inder , e t a l . , 1968; Kern County Water Agency, 1977; Konikow, e t a l . ,
1974). The a b i l i t y t o model q u a l i t y of ground water ( t h e capac i ty t o
p r e d i c t t h e movement and concent ra t ion of d i sso lved chemicals) is s t i l l
i n a t r a n s i t i o n a l s t age . Although t h e r e have been numerous s t u d i e s i n
which t h e movement and concent ra t ion of conserva t ive chemicals (non-
r e a c t i n g ) , p a r t i c u l a r l y d isso lved s o l i d s , have been s a t i s f a c t o r i l y
s imula ted (Konikow, e t a l . , 1974) t h e c a p a b i l i t y t o model t h e movement
of organic o r nonconservat ive ( r e a ~ t ~ ~ e ) chemicals is s t i l l v e r y much
i n t h e developmental s t a g e (Konikow, 1970). I n t h e c a s e of combined
models, such as coupled ground water/economic systems and coupled
ground water I ra infa l l - runoff models, they a r e s t i l l i n t h e developmental and
v e r i f i c a t i o n s t a g e s .
(5) S u f f i c i e n t d a t a and information
Ground water modeling e f f o r t s t o d a t e involve a n a n a l y s i s ( c o l l e c t i o n
and i n t e r p r e t a t i o n ) of e x i s t i n g d a t a , t h e c o l l e c t i o n of new d a t a , and
d a t a management programs. The same procedure i s expected f o r t h e AGUA.
( I t should be noted t h a t one of t h e o b j e c t i v e s of developing a model is
t o p inpo in t a r e a s where a d d i t i o n a l information is requi red and based on
a s e n s i t i v i t y a n a l y s i s , t o determine which d a t a needs t o be determined
more a c c u r a t e l y ) .
REFERENCES
Appel, C.A. and Bredehoeft , J . D . , 1976, S t a t u s of Ground Water Modeling i n t h e U.S. Geologi.ca1 Survey: Geological Survey C i r c u l a r 737, 9 p.
Bennet t , G . D . , 1976, In t roduc t ion t o Ground Water Hydraul ics: U.S. Geological Survey, Washington, D . C . , 172 p.
Bjorklund, L.J. and Maxwell, B.W., 1961, A v a i l a b i l i t y of Ground Water i n t h e Albuquerque Area, B e r n a l i l l o and Sandoval Counties , New Mexico: New Mexico S t a t e Engineer Technical Report 2 1 , 117 p .
Holcomb Research I n s t i t u t e , June, 1977, The Use and U t i l i t y of Numerical Models i n Ground Water Related Water Resource Management: B u t l e r Univer s i t y .
Kern County Water Agency , C a l i f o r n i a , December, 1974, Kern County, C a l i f o r n i a Ground Water Basin Model Summary Report: 1 3 p .
Kern County Water Agency, December, 1974, Kern County, C a l i f o r n i a Ground Water Basin Model. a Review: 24 p.
Kern County Water Agency, C a l i f o r n i a and t h e Department of Water Resources, S t a t e of C a l i f o r n i a , March, 1977, Kern County Ground Water Model: 138 p.
Konikow, L.K., 1970, App l i ca t ion of Solu te-Transpor t Models t o Ground Water Qua l i t y Problems: I n t e r n a t i o n a l Conference on Ground Water Q u a l i t y , Measurements, P r e d i c t i o n and P r o t e c t i o n , Water Research Centre , Reading, England, 22 p.
Konikow, L.K. and Bredehoeft , J . D . , June, 1974, Modeling Flow and Chemical Qua l i t y Changes i n a n I r r i g a t e d Stream-Aquifer System: Water Resources Research, Vol. 10 , No. 3, pp. 546-562.
Nat iona l Resources Committee, February 1938, Regional Planning P a r t V I - The Rio Grande J o i n t I n v e s t i g a t i o n i n t h e Upper Rio Grande Basin i n Colorado, New Mexico, and Texas 1936-1937.
Page, R.W., February, 1977, Guide f o r Data C o l l e c t i o n t o C a l i b r a t e a Predic- t i v e D i g i t a l Ground Water Model of t h e Unconfined Aqui fer i n and nea r t h e C i t y of Modesto, C a l i f o r n i a : PB-265 602, Water Resources D iv i s ion , U.S. Geologica l Survey, Menlo Park, C a l i f o r n i a , 46 p .
P inder , G.F., 1970, A D i g i t a l Model f o r Aquifer Eva lua t ion , Book 7, Chapter C1: U.S. Geologica l Survey, Washington, D.C. , 1 8 p.
Pinder , G.F., 1974, A Ga le rk in -F in i t e Element Model f o r Aquifer Evaluat ion: U.S. Geologica l Survey, Washington, D.C. , 28 p.
P inder , G.F. and Bredehoeft , J . D . , October, 1968, App l i ca t ion of t h e D i g i t a l Computer f o r Aquifer Evaluat ion: Water Resources Research, Vol. 4 , No. 5, pp. 1069-1093.
Reeder, H.O. , Bjorklund, L.J. and Dinwiddie, G.A., 1967, Q u a n t i t a t i v e Analysis of Water Resources i n t h e Albuquerque Area, New Mexico: New Mexico S t a t e Engineer Technical Report 33, 34 p .
Rushton, K.R. , March-April, 1978, Es t imat ing Transmiss iv i ty and Storage C o e f f i c i e n t from Abs t r ac t ion Well Data: J o u r n a l of t h e Ground Water Technology Divis ion , NWWA, pp. 81-85.
T r e s c o t t , P.C., September, 1975, Documentation of F in i t e -Di f f e rence Model f o r S imula t ion of Three-Dimensional Ground Water Flow: U.S. Geological Survey, Washington, D.C. , 32 p .
T r e s c o t t , P.C. and Larson, S.P., August, 1976, Documentation of F i n i t e - D i f f e rence Model f o r S imula t ion of Three-Dimensional Ground Water Flow: U.S. Geologica l Survey, Washington, D.C. , 21 p.
T r e s c o t t , P.C., P inde r , G.F. and Larson, S.P., 1976, F in i te -Dif fe rence Model f o r Aqui fer S imula t ion i n Two Dimensions w i t h R e s u l t s of Numerical R e s u l t s , Book 7, Chapter C1: U.S. Geologica l Survey, Washington, D.C. 116 p.
U.S. Geologica l Survey, 1978, Development and Use of 2-D and 3-D D i g i t a l Models f o r t h e S a l i n a s Valley GW Basin, C a l i f o r n i a - P a r t 1, DE' elopment of GW Flow Model, Pre l im. r e p o r t under review f o r pub l i ca t ion : U.S. Geologica l Survey, Water Resources D iv i s ion , Menlo Park, C a l i f o r n i a .
Technical Paper Series TP-1 Use of Interrelated Records to Simulate Streamflow TP-2 Optimization Techniques for Hydrologic
Engineering TP-3 Methods of Determination of Safe Yield and
Compensation Water from Storage Reservoirs TP-4 Functional Evaluation of a Water Resources System TP-5 Streamflow Synthesis for Ungaged Rivers TP-6 Simulation of Daily Streamflow TP-7 Pilot Study for Storage Requirements for Low Flow
Augmentation TP-8 Worth of Streamflow Data for Project Design - A
Pilot Study TP-9 Economic Evaluation of Reservoir System
Accomplishments TP-10 Hydrologic Simulation in Water-Yield Analysis TP-11 Survey of Programs for Water Surface Profiles TP-12 Hypothetical Flood Computation for a Stream
System TP-13 Maximum Utilization of Scarce Data in Hydrologic
Design TP-14 Techniques for Evaluating Long-Tem Reservoir
Yields TP-15 Hydrostatistics - Principles of Application TP-16 A Hydrologic Water Resource System Modeling
Techniques TP-17 Hydrologic Engineering Techniques for Regional
Water Resources Planning TP-18 Estimating Monthly Streamflows Within a Region TP-19 Suspended Sediment Discharge in Streams TP-20 Computer Determination of Flow Through Bridges TP-21 An Approach to Reservoir Temperature Analysis TP-22 A Finite Difference Methods of Analyzing Liquid
Flow in Variably Saturated Porous Media TP-23 Uses of Simulation in River Basin Planning TP-24 Hydroelectric Power Analysis in Reservoir Systems TP-25 Status of Water Resource System Analysis TP-26 System Relationships for Panama Canal Water
Supply TP-27 System Analysis of the Panama Canal Water
Supply TP-28 Digital Simulation of an Existing Water Resources
System TP-29 Computer Application in Continuing Education TP-30 Drought Severity and Water Supply Dependability TP-31 Development of System Operation Rules for an
Existing System by Simulation TP-32 Alternative Approaches to Water Resources System
Simulation TP-33 System Simulation of Integrated Use of
Hydroelectric and Thermal Power Generation TP-34 Optimizing flood Control Allocation for a
Multipurpose Reservoir TP-35 Computer Models for Rainfall-Runoff and River
Hydraulic Analysis TP-36 Evaluation of Drought Effects at Lake Atitlan TP-37 Downstream Effects of the Levee Overtopping at
Wilkes-Barre, PA, During Tropical Storm Agnes TP-38 Water Quality Evaluation of Aquatic Systems
TP-39 A Method for Analyzing Effects of Dam Failures in Design Studies
TP-40 Storm Drainage and Urban Region Flood Control Planning
TP-41 HEC-5C, A Simulation Model for System Formulation and Evaluation
TP-42 Optimal Sizing of Urban Flood Control Systems TP-43 Hydrologic and Economic Simulation of Flood
Control Aspects of Water Resources Systems TP-44 Sizing Flood Control Reservoir Systems by System
Analysis TP-45 Techniques for Real-Time Operation of Flood
Control Reservoirs in the Merrimack River Basin TP-46 Spatial Data Analysis of Nonstructural Measures TP-47 Comprehensive Flood Plain Studies Using Spatial
Data Management Techniques TP-48 Direct Runoff Hydrograph Parameters Versus
Urbanization TP-49 Experience of HEC in Disseminating Information
on Hydrological Models TP-50 Effects of Dam Removal: An Approach to
Sedimentation TP-51 Design of Flood Control Improvements by Systems
Analysis: A Case Study TP-52 Potential Use of Digital Computer Ground Water
Models TP-53 Development of Generalized Free Surface Flow
Models Using Finite Element Techniques TP-54 Adjustment of Peak Discharge Rates for
Urbanization TP-55 The Development and Servicing of Spatial Data
Management Techniques in the Corps of Engineers TP-56 Experiences of the Hydrologic Engineering Center
in Maintaining Widely Used Hydrologic and Water Resource Computer Models
TP-57 Flood Damage Assessments Using Spatial Data Management Techniques
TP-58 A Model for Evaluating Runoff-Quality in Metropolitan Master Planning
TP-59 Testing of Several Runoff Models on an Urban Watershed
TP-60 Operational Simulation of a Reservoir System with Pumped Storage
TP-61 Technical Factors in Small Hydropower Planning TP-62 Flood Hydrograph and Peak Flow Frequency
Analysis TP-63 HEC Contribution to Reservoir System Operation TP-64 Determining Peak-Discharge Frequencies in an
Urbanizing Watershed: A Case Study TP-65 Feasibility Analysis in Small Hydropower Planning TP-66 Reservoir Storage Determination by Computer
Simulation of Flood Control and Conservation Systems
TP-67 Hydrologic Land Use Classification Using LANDSAT
TP-68 Interactive Nonstructural Flood-Control Planning TP-69 Critical Water Surface by Minimum Specific
Energy Using the Parabolic Method
TP-70 Corps of Engineers Experience with Automatic Calibration of a Precipitation-Runoff Model
TP-71 Determination of Land Use from Satellite Imagery for Input to Hydrologic Models
TP-72 Application of the Finite Element Method to Vertically Stratified Hydrodynamic Flow and Water Quality
TP-73 Flood Mitigation Planning Using HEC-SAM TP-74 Hydrographs by Single Linear Reservoir Model TP-75 HEC Activities in Reservoir Analysis TP-76 Institutional Support of Water Resource Models TP-77 Investigation of Soil Conservation Service Urban
Hydrology Techniques TP-78 Potential for Increasing the Output of Existing
Hydroelectric Plants TP-79 Potential Energy and Capacity Gains from Flood
Control Storage Reallocation at Existing U.S. Hydropower Reservoirs
TP-80 Use of Non-Sequential Techniques in the Analysis of Power Potential at Storage Projects
TP-81 Data Management Systems of Water Resources Planning
TP-82 The New HEC-1 Flood Hydrograph Package TP-83 River and Reservoir Systems Water Quality
Modeling Capability TP-84 Generalized Real-Time Flood Control System
Model TP-85 Operation Policy Analysis: Sam Rayburn
Reservoir TP-86 Training the Practitioner: The Hydrologic
Engineering Center Program TP-87 Documentation Needs for Water Resources Models TP-88 Reservoir System Regulation for Water Quality
Control TP-89 A Software System to Aid in Making Real-Time
Water Control Decisions TP-90 Calibration, Verification and Application of a Two-
Dimensional Flow Model TP-91 HEC Software Development and Support TP-92 Hydrologic Engineering Center Planning Models TP-93 Flood Routing Through a Flat, Complex Flood
Plain Using a One-Dimensional Unsteady Flow Computer Program
TP-94 Dredged-Material Disposal Management Model TP-95 Infiltration and Soil Moisture Redistribution in
HEC-1 TP-96 The Hydrologic Engineering Center Experience in
Nonstructural Planning TP-97 Prediction of the Effects of a Flood Control Project
on a Meandering Stream TP-98 Evolution in Computer Programs Causes Evolution
in Training Needs: The Hydrologic Engineering Center Experience
TP-99 Reservoir System Analysis for Water Quality TP-100 Probable Maximum Flood Estimation - Eastern
United States TP-101 Use of Computer Program HEC-5 for Water Supply
Analysis TP-102 Role of Calibration in the Application of HEC-6 TP-103 Engineering and Economic Considerations in
Formulating TP-104 Modeling Water Resources Systems for Water
Quality
TP-105 Use of a Two-Dimensional Flow Model to Quantify Aquatic Habitat
TP-106 Flood-Runoff Forecasting with HEC-1F TP-107 Dredged-Material Disposal System Capacity
Expansion TP-108 Role of Small Computers in Two-Dimensional
Flow Modeling TP-109 One-Dimensional Model for Mud Flows TP-110 Subdivision Froude Number TP-111 HEC-5Q: System Water Quality Modeling TP-112 New Developments in HEC Programs for Flood
Control TP-113 Modeling and Managing Water Resource Systems
for Water Quality TP-114 Accuracy of Computer Water Surface Profiles -
Executive Summary TP-115 Application of Spatial-Data Management
Techniques in Corps Planning TP-116 The HEC's Activities in Watershed Modeling TP-117 HEC-1 and HEC-2 Applications on the
Microcomputer TP-118 Real-Time Snow Simulation Model for the
Monongahela River Basin TP-119 Multi-Purpose, Multi-Reservoir Simulation on a PC TP-120 Technology Transfer of Corps' Hydrologic Models TP-121 Development, Calibration and Application of
Runoff Forecasting Models for the Allegheny River Basin
TP-122 The Estimation of Rainfall for Flood Forecasting Using Radar and Rain Gage Data
TP-123 Developing and Managing a Comprehensive Reservoir Analysis Model
TP-124 Review of U.S. Army corps of Engineering Involvement With Alluvial Fan Flooding Problems
TP-125 An Integrated Software Package for Flood Damage Analysis
TP-126 The Value and Depreciation of Existing Facilities: The Case of Reservoirs
TP-127 Floodplain-Management Plan Enumeration TP-128 Two-Dimensional Floodplain Modeling TP-129 Status and New Capabilities of Computer Program
HEC-6: "Scour and Deposition in Rivers and Reservoirs"
TP-130 Estimating Sediment Delivery and Yield on Alluvial Fans
TP-131 Hydrologic Aspects of Flood Warning - Preparedness Programs
TP-132 Twenty-five Years of Developing, Distributing, and Supporting Hydrologic Engineering Computer Programs
TP-133 Predicting Deposition Patterns in Small Basins TP-134 Annual Extreme Lake Elevations by Total
Probability Theorem TP-135 A Muskingum-Cunge Channel Flow Routing
Method for Drainage Networks TP-136 Prescriptive Reservoir System Analysis Model -
Missouri River System Application TP-137 A Generalized Simulation Model for Reservoir
System Analysis TP-138 The HEC NexGen Software Development Project TP-139 Issues for Applications Developers TP-140 HEC-2 Water Surface Profiles Program TP-141 HEC Models for Urban Hydrologic Analysis
TP-142 Systems Analysis Applications at the Hydrologic Engineering Center
TP-143 Runoff Prediction Uncertainty for Ungauged Agricultural Watersheds
TP-144 Review of GIS Applications in Hydrologic Modeling
TP-145 Application of Rainfall-Runoff Simulation for Flood Forecasting
TP-146 Application of the HEC Prescriptive Reservoir Model in the Columbia River Systems
TP-147 HEC River Analysis System (HEC-RAS) TP-148 HEC-6: Reservoir Sediment Control Applications TP-149 The Hydrologic Modeling System (HEC-HMS):
Design and Development Issues TP-150 The HEC Hydrologic Modeling System TP-151 Bridge Hydraulic Analysis with HEC-RAS TP-152 Use of Land Surface Erosion Techniques with
Stream Channel Sediment Models
TP-153 Risk-Based Analysis for Corps Flood Project Studies - A Status Report
TP-154 Modeling Water-Resource Systems for Water Quality Management
TP-155 Runoff simulation Using Radar Rainfall Data TP-156 Status of HEC Next Generation Software
Development TP-157 Unsteady Flow Model for Forecasting Missouri and
Mississippi Rivers TP-158 Corps Water Management System (CWMS) TP-159 Some History and Hydrology of the Panama Canal TP-160 Application of Risk-Based Analysis to Planning
Reservoir and Levee Flood Damage Reduction Systems
TP-161 Corps Water Management System - Capabilities and Implementation Status
