A Unified Approach t o Regional Groundwater Management Robert Willis Humboldt State University, Arcata, California 95521 Introduction The management of groundwater resources and the evaluation of the hydrologic and environmental impacts associated with groundwater development is commonly approached using simulation or optimization models of the aquifer system. Simulation models are predictive models of the hydraulic response of the groundwater system. In simulation modeling, a set of groundwater management policies is analyzed to determine a probable response of the aquifer system. From this information, a policy is then determined which best meets the objectives of the management problem. However, in simulation the policies are inherently nonoptimal. They are nonoptimal in an operational sense in that only a limited number of alternatives can usually be analyzed. Furthermore, the tradeoffs associated with the system's economic or hydrologic objectives are difficult to determine. In contrast, however, optimization modeling represents a unified approach t o groundwater management. Optimization modeling identifies the optimal planning, design, and operational policies and the tradeoffs in the system's objectives. Moreover, optimiza- tion modeling can also generate the set of noninferior solutions to multiobjective groundwater planning problems. The objective of this paper is to present an optimization method- ology for regional groundwater management. Specifically, it will be shown how the response equations for confined and unconfined aquifer systems can be incorporated within the framework of an optimal planning model. As a result, the hydraulic response of the Water Resources Monograph Groundwater Hydraulics Vol. 9 Copyright American Geophysical Union
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A Unified Approach t o Regional Groundwater Management
Robert Willis Humboldt S t a t e University, Arcata, Cal ifornia 95521
Introduction
The management of groundwater resources and t h e evaluation of the
hydrologic and environmental impacts associated with groundwater
development is commonly approached using simulation o r optimization
models of the aquifer system. Simulation models a r e predict ive
models of t he hydraul ic response of the groundwater system. In
simulation modeling, a s e t of groundwater management pol ic ies is
analyzed t o determine a probable response of t h e aquifer system.
From t h i s information, a policy is then determined which best meets
t he objectives of t he management problem. However, i n simulation
t h e pol ic ies a r e inherent ly nonoptimal. They a r e nonoptimal i n an
operational sense i n t h a t only a l imited number of a l te rna t ives can
usually be analyzed. Furthermore, t he t r a d e o f f s associated with
t he system's economic or hydrologic object ives a r e d i f f i c u l t t o
determine. In cont ras t , however, optimization modeling represents
a unif ied approach t o groundwater management. Optimization modeling
iden t i f i e s t he optimal planning, design, and operat ional po l ic ies
and t h e t r a d e o f f s i n t h e system's objectives. Moreover, optimiza-
t i on modeling can a l s o generate t he s e t of noninferior solut ions
t o multiobjective groundwater planning problems.
The object ive of t h i s paper is t o present an optimization method-
ology f o r regional groundwater management. Spec i f ica l ly , it w i l l
be shown how the response equations fo r confined and unconfined
aquifer systems can be incorporated within t he framework of an
optimal planning model. A s a r e s u l t , t h e hydraulic response of t h e
Water Resources Monograph Groundwater Hydraulics Vol. 9
Copyright American Geophysical Union
Unified Approach t o RegionaZ Groundwater Management 393
aqui fer system is an in t eg ra l par t of t he optimization model. I n
t h e optimization methodology, t he groundwater planning problem i s
formulated a s a multiobjective optimization model. The methodology
is applied t o t he Yun Lin Basin, Taiwan, t o determine the optimal
groundwater extract ion pat tern.
Response Equations
The response o r t r ans fe r equations of t he groundwater system a r e
those equations r e l a t i ng the s t a t ed variables of t he aqui fer and the
proposed planning o r management pol ic ies . A s has been discussed
by Maddock [1972],Willis and Dracup [1973], and Aguado and Remson
[1974], t h e technique transforms t h e p a r t i a l d i f f e r e n t i a l equation
of t he groundwater system via Green's functions, f i n i t e d i f fe rence
o r f i n i t e element methods. These r e su l t i ng equations may be imbed-
ded within t h e constraint region of t h e planning o r design problem,
o r equivalently, t he problem can be formulated a s a problem i n
optimal control [Wil l is and Newman, 19771.
Confined o r Leaky Aquifer System
We assume t h a t t he surface-groundwater system may be represented
by the v e r t i c a l l y averaged continui ty equation f o r a leaky aqui fer
[Cooley, 19741 :
where T is t h e t ransmissivi ty tensor (L'/T), h is the hydraul ic
head (L), S is the s torage coef f ic ien t , and S* is a source o r s ink
term, e.g., leakage. 0 is an index s e t defining the locat ion of
a l l wells i n t he basin and 6( ) is the Dirac de l t a function.
The boundary conditions of t h e aqui fer system may be expressed
88
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39 4 Groundwater HydrauZics
where u l and u2 def ine t h e boundary of t he basin, h* is t h e known
potent ia l , - n is t h e outward pointing uni t normal t o ~ 2 , and q* is
the given f lux. Generally, these equations a r e time-dependent
boundary conditions.
Equation (1) may be transformed i n t o a system of ordinary dif-
f e r e n t i a l equations with t h e Galerkin f i n i t e element method. The
transformed equations may be wr i t ten a s [Pinder and Frind, 19721
where h now represents t h e f i n i t e element approximation t o t h e
hydraulic head; 10 a r e t he i n i t i a l conditions f o r the problem.
The C and H coef f ic ien t matrices contain t h e s torage coef f ic ien ts
and t ransmiss iv i t ies , respect ively. The f vector contains t h e
Dir ich le t and Newmann boundary conditions and importantly, t he
planning pol ic ies [Wil l is , 1976bl. Equation (2) can a l so be
e x p l i c i t l y wr i t ten a s a system of ordinary d i f f e r e n t i a l equations
i n time a s
h = A h + g - - - (3
where A = 4-1 H and g = -c-1 - f .
Unconfined Aquifer System
Assuming Dupuit assumptions a r e va l id f o r unconfined ground-
water, t h e ve r t i ca l l y averaged Boussinesqu equation can be expressed
a s [Cooley, 19741
where _k - t he hydraulic conductivity tensor [LIT], Sy is the spe-
c i f i c y ie ld , and R[L/T] i a t he recharge occurring i n t he aquifer.
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Unified Approach t o Regional Groundwater Management 395
Equation (3) is, however, a nonlinear function of t h e hydraul ic
head. Boundary and i n i t i a l conditions f o r t he problem a r e again
sunnnarized i n (1). F i n i t e d i f fe rence o r f i n i t e element methods
may be used t o transform t h e p a r t i a l d i f f e r e n t i a l equation i n t o
a system of nonlinear ordinary d i f f e r e n t i a l equations. These
transformed equations may be expressed a s
where t h e coef f ic ien t matrices D and E contain t h e s p e c i f i c y i e ld
and conductivity. Planning or operat ional po l ic ies , t h e recharge,
and boundary conditions a r e contained i n t h e L vector. Again, 5 represents t h e vector of t h e hydraul ic head a t a l l nodal points
i n t h e system.
Simplifying (5) , we have
where now A= - D - ~ E and & = -D-lr. - A s w i l l be discussed, we choose
t o l i n e a r i z e these equations using quas i l inear iza t ion [Bellman and
Kalaba, 19651. Assuming a t r i a l so lu t ion t o ( 6 ) , hk, and expanding
about t he solut ion using a generalized Taylor s e r i e s , we have
where H~ is a diagonal matrix containing hk; t h a t is EIllk=hlk,
~ ~ ~ = h ~ ~ , etc . Simplifying, we have the l i n e a r system of ordinary
d i f f e r e n t i a l equations,
where ~k = and gk = - gk - ~ h ~ , ~ . -
Solution of t he Response Equations
The response equations of t he groundwater system a r e usual ly
solved using conventional f i n i t e d i f fe rence approximations. Here,
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396 Groundwater Hydraulics
however, (3 ) o r (7) w i l l be solved ana ly t i ca l l y by using the matrix
calculus. The general so lu t ion of these equations is [Bellman,
Assuming tha t t he planning o r management pol ic ies and the system's
boundary conditions a r e constant over a period T,
The matrix exponential eAt can be evaluated by A=RQR-l. The matrix
R contains the eigenvectors of A, and Q is a diagonal matrix contain-
ing the eigenvalues of A. A s a r e su l t e ~ t = e ~ ~ R - l t is simply R~R-I ,
where 4 is again a diagonal matrix; however, t h e elements a r e now
eAit, where h i is the i t h eigenvalue of t he system. Simplifying,
we have
here,
Al(t) = RQR-l and A2(t) = A'-'(I-RGR-')c-'
For a s e r i e s of planning periods t l , t 2 , t m of equal length T, t h e
equations may be expressed a s
or , funct ional ly,
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Unified Approach t o Regional Groundwater Management 397
The Planning Model
We consider a groundwater system loca ted i n an a g r i c u l t u r a l r i v e r
basin . The planning problem is t o determine t h e optimal groundwater
pumping p a t t e r n t o s a t i s f y t h e a g r i c u l t u r a l water demands of t h e
basin . Assuming t h a t t h e planning hor izon c o n s i s t s of m opera t ing
per iods , t h e pol icy va r iab les of t h e model a r e t h e groundwater
e x t r a c t i o n r a t e s f o r each wel l s i t e i n t h e basin . Recognizing
t h a t t h e ob jec t ives of t h e system may r e f l e c t economic, hydrologic ,
and environmental cons ide ra t ions , t h e o b j e c t i v e func t ion of t h e mo-
d e l may be expressed a s
m man r= r G z hpfp ( z n , ~ n ) n n- 1 P
where f p i s t h e p th o b j e c t i v e and hp i s t h e weight o r p re fe rence
assoc ia ted with o b j e c t i v e p [Cohon and Marks, 19751. Qn is t h e
t o t a l groundwater discharge dur ing period n; a n is t h e discount
f a c t o r . The pol icy v a r i a b l e s - hn and Qn a r e constra ined t o s a t i s f y
(1 ) t h e water demand i n each i r r i g a t e d a r e a R., o r
(where Dt represen t s t h e demand i n i r r i g a t i o n system g i n per iod
n demand l e s s e f f e c t i v e p r e c i p i t a t i o n and s u r f a c e water a v a i l a b i l -
i t y ) , ( 2 ) t h e balance c o n s t r a i n t s ,
(3) t h e response equations (equat ions (10d)) and, poss ib ly , lower
bounds o r head g rad ien t c o n s t r a i n t s t o minimize subsidence o r sea-
water in t rus ion . These c o n s t r a i n t s may be w r i t t e n a s compactly a s
where X is an index s e t de f in ing t h e l o c a t i o n of t h e c o n t r o l p o i n t s
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398 Groundwater HydrauZics
i n t h e bas in and h* a r e t h e des i red bounds on t h e head. j
We a l s o have t h e w e l l capac i ty r e s t r i c t i o n ,
where Qi,,,, is t h e maximum pumping r a t e a t w e l l s i t e 1. F i n a l l y ,
t h e nonnegat ivi ty r e s t r i c t i o n s of t h e dec i s ion v a r i a b l e s ,
The planning-optimization model has s e v e r a l important a t t r i b u t e s .
F i r s t , t h e c o n s t r a i n t s e t is a convex s e t . This was e s s e n t i a l l y
t h e r a t i o n a l f o r l i n e a r i z i n g t h e unconfined flow equat ions . Second,
i f t h e ob jec t ives a r e separab le concave ( o r convex i f minimizing)
func t ions of t h e dec i s ion v a r i a b l e s , then g l o b a l l y optimal s o l u t i o n s
w i l l be obtained t o t h e planning problem. Third, f o r t h e l i n e a r i z e d
unconfined flow problem, a s e r i e s of opt imizat ion problems w i l l be
solved. The head d i s t r i b u t i o n from one s o l u t i o n i s then t h e b a s i s
f o r updating t h e response equat ions i n t h e next s o l u t i o n of t h e
planning model. This convergence and t h e o r e t i c a l p r o p e r t i e s of t h e
a lgor i thm a r e presented by Rosen [I9661 and Meyer [1970]. An appl i -
c a t i o n of t h e procedure t o parameter es t imat ion problems is d i s -
cussed by Willis [1976a].
Model Appl icat ion
Over t h e pas t 2 yea rs , a s p a r t of an i n t e r n a t i o n a l cooperat ive
research program, t h e mult l o b j e c t i v e planning model has been appl ied
t o t h e water resources problems of t h e Yun Lin Basin, Taiwan. The
over r id ing ob jec t ives of t h e resea rch program a r e t o develop (1)
planning and opera t iona l p o l i c i e s a l l o c a t i n g s u r f a c e and groundwater
resources t o a g r i c u l t u r a l water demands wi th in t h e basin , (2) t o
determine t h e t rade-offs a s s o c i a t e d with a d d i t i o n a l groundwater
development and a g r i c u l t u r a l water demands, and (3 ) t o minimize
t h e p o t e n t i a l impacts of s a l t w a t e r i n t r u s i o n . We consider he re ,
Water Resources Monograph Groundwater Hydraulics Vol. 9
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Unified Approach t o RegionaZ Groundwater Management 399
--- IRRIGATION SYSTEM
Fig. 1. The Yun Lin groundwater basin.
however, one pa r t i cu l a r applicat ion of t h e planning model involving
t h e determination of t h e optimal pumping pa t te rn f o r two d i f f e r en t
scenarios regarding groundwater development. In t h e f i r s t , ground-
water extract ions a r e determined assuming a well capacity r e s t r i c -
t i o n of 15,000 m3/d ( the current maximum). In t h e second case,
t h i s bound is increased t o 50,000 m3/d t o r e f l e c t t he poten t ia l
f o r addit ional groundwater development. Other uses of t he model
a r e presented by Willis [I9811 and Willis and Liu [1981].
The Yun Lin groundwater system is e s sen t i a l l y a semiconfined
aquifer . The aquifer , which is located i n t h e Cho Shui a l l u v i a l fan,
i s composed primarily of unconsolidated sand and gravel materials .
The aquifer depth ranges from 40 m i n t h e eastern portion of t h e
basin t o more than 1000 m i n t he Peikang area. Approximately 76% of
t h e t o t a l groundwater recharge occurs v i a i n f i l t r a t i o n of precipi-
t a t i o n and seepage from the numerous streams i n t h e basin [Water
Resources Planning Commission (WRPC), 19761. The Cho Shui River,
which forms t h e northern boundary of t h e study area , is t h e princi-
pa l recharge boundary of t he system. The Peikang River i n t h e
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Groundwater Hydraulics
Fig. 2. F i n i t e element g r i d : Yun Lin groundwater bas i n .
south, does not however i n t e r a c t wi th t h e Yun Lin a q u i f e r system
(Figure 1).
Water resources i n t h e bas in a r e d i s t r i b u t e d v i a four i r r i g a t i o n
systems: t h e Cho Shui, Fu Wei, S i Lo, and Tou Liu systems. Each
i r r i g a t i o n d i s t r i c t is administered by t h e Yun Lin I r r i g a t i o n
Association. The a s s o c i a t i o n c o n t r o l s t h e a l l o c a t i o n of s u r f a c e
water , o r i g i n a t i n g from t h e Cho Shui River, and groundwater from
t h e 500 assoc ia t ion we l l s i n t h e basin. Current ly , t h e t o t a l
i r r i g a t e d a r e a i n t h e basin is approximately 43,260 ha.
The hydrology of t h e bas in i s charac te r i zed by d i s t i n c t r a iny and
d ry seasons. The ra iny per iod, which extends from May through
October, is dominated by typhoon-producing thunderstorms. Seventy
s i x percent of t h e t o t a l r a i n f a l l occurs during t h i s period [Water
Resources Planning Commission, 19801. During t h e dry season, north-
e a s t monsoons produce t h e major i ty of t h e p r e c i p i t a t i o n . However,
streamflow i n t h e dry season is i n s u f f i c i e n t t o supply t h e a g r i -
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Unified Approach to Regional Groundwater Management 401
TABLE 1. Recharge Parameters f o r t h e Yun Lin Basin
Recharge Rates . Recharge x 1?i4 m/d ~
Zone November December January February March Apr i l
c u l t u r a l water demands of t h e basin. Typical ly , groundwater extrac-
t i o n s account f o r more than 90% of t h e t o t a l water usage during
t h e dry season. A s a r e s u l t , it is during t h e d ry season t h a t t h e
groundwater system i s most highly s t r e s s e d . For t h i s reason, t h e
groundwater pumping p a t t e r n is determined during t h i s period.
A Galerkin f i n i t e element s imulat ion model was developed t o
p red ic t t h e hydrau l ic head d i s t r i b u t i o n i n t h e Yun Lin system
and t o generate t h e response equations f o r t h e opt imizat ion a n a l y s i s
[Tsao e t a l . , 19801. The system was d i s c r e t i z e d i n t o 78 (4 by 4 km)
l i n e a r q u a d r i l a t e r a l elements; t h e system has 101 nodal points. The
f i n i t e element g r i d f o r t h e basin is d e t a i l e d i n Figure 2.
The va l ida t ion and c a l i b r a t i o n of t h e model is discussed by
W i l l i s [1981], and Tsao et a l . [1980]. The model's groundwater and
hydrologic parameters a r e summarized i n Tables 1, 2 , and 3. The
TABLE 2. Mean Dry Season Hydrology
Mean Mean I r r i g a t i o n P r e c i p i t a t i o n , Surface Water,* Water Target,*
System mm m3/dry season m3 /dry season
Cho Shui 194. S i Lo 232. Fu Wei 212. Tou Liu 355.
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Groundwater HydrauZics
TABLE 3. Hydraulic Parameters of t h e Yun Lin Basin
Transmiss ivi ty , Storage Mate r ia l Zone m2/d Coef f i c ien t
demand d a t a , which represen t a v a r i e t y of cropping p a t t e r n s i n t h e
Yun Lin Basin, was obtained from t h e Yun Lin I r r i g a t i o n Associa t ion
[KO, personal communication, 19811.
Model P r e l i m i n a r i e s
I n i t i a l l y , t h e dynamic response equat ions of t h e a q u i f e r system
a r e generated using a s e r i e s of Matr ix Eigensystem Routines [1976].
The response equat ions analyzed t h e hydrau l i c response of t h e aqui-
f e r system during t h e November through Apr i l dry season. The res-
ponse equat ions incorporated t h e time-dependent boundary cond i t ions ;
t h e s e condi t ions were expressed a s piecewise l i n e a r func t ions of
t ime over t h e 180-day planning period.
Two ob jec t ives were considered i n t h e ana lys i s : (1) maximize
t h e sum of t h e hydrau l i c heads over a l l t h e planning per iod and
(2) minimize t h e t o t a l water d e f i c i t f o r a l l i r r i g a t i o n systems.
The f i r s t o b j e c t i v e is a l i n e a r s u r r o g a t e f o r minimizing t h e ground-
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Unified Approach to Regional Groundwater Management 403
TABLE 4. Pumping Rates
Well S i t e (Node Number)
22 5 0 58 6 6 8 4 9 2 9 5
Jan .-Feb.
15000 15000 2821. 6837. 2804. 14739 869.
March-April
15000 15000 7630. 15000 14842. 15000 3333.
Constant Pumping
15000 12270. 1834. 5594. 3383. 15000. 716.
water ex t rac t ion c o s t s ; t h e l a t t e r o b j e c t i v e r e f l e c t s t h e l o s s e s
from decreased a g r i c u l t u r a l production. I n t h i s prel iminary analy-
sis t h e o b j e c t i v e weights were both s e t t o one, i n d i c a t i n g equal
preference f o r t h e ob jec t ives . The hydrau l i c head was a l s o bounded
a t -20 m t o r e f l e c t cu r ren t groundwater condi t ions .
A g r i c u l t u r a l Production
The r e s u l t i n g l i n e a r opt imizat ion model has 225 c o n s t r a i n t s and
438 dec i s ion v a r i a b l e s (no t including upper and lower bounds on t h e
head values and pumping r a t e s ) . The APEX-111 la rge-sca le optimiza-
t i o n package was used t o s o l v e t h e model [Control Data Corporation,
19801. Typical s o l u t i o n t imes averaged 800 CPU seconds; c e n t r a l
memory requirements a r e approximately 200K ( o c t a l ) .
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404 Groundwater HydrauZics
TABLE 6 . I r r i g a t i o n D e f i c i t s
Constant Pumping Nov.-Dec. Jan.-Feb. March-April
Cho Shui 3761255. 3761255. 3723352. 3648026. S i Lo 2943389. 2943389. 2943389. 2943389. Fu Wei 739575. 789575. 789575. 789575. Tou Liu 5414156. 5414156. 5411427. 5411427.
Tot a 1 12908375. 12908375. 12872743. 12792417.
Model Resu l t s
The r e s u l t s of t h e opt imizat ion analyses f o r t h e two d i f f e r e n t
combinat ions of pumping upper bounds a r e summarized, f o r s e l e c t e d
w e l l s and s i t e s i n Tables 4 and 5 . Several th ings a r e apparent from
t h e t a b l e s . F i r s t , given t h e opportuni ty t o pump more, t h e model
increased pumpage i n those regions which a r e more h igh ly permeable.
A s a r e s u l t , ex t rac t ions a r e increased i n c e r t a i n a reas , whi le they
a r e reduced i n t h e l e s s permeable regions of t h e aqu i fe r . For ex-
ample, consider node 92. The pumping r a t e has been increased i n
t h e f i r s t and t h i r d per iods wi th a minimal change i n t h e pumping
occurr ing during t h e second planning period. This is with t h e
i d e n t i c a l lower bound r e s t r i c t i o n on t h e head values.
Second, t h e a b i l i t y t o shu t o f f t h e pumps t o a l low recovery of
t h e head l e v e l s , a l s o is e f f e c t i v e i n inc reas ing t h e y i e l d of t h e
aqu i fe r . This, i n conjunction with increased pumping from t h e
more permeable regions of t h e a q u i f e r , has t h e e f f e c t of inc reas ing
t h e groundwater y i e l d without v i o l a t i n g t h e minimum head r e s t r i c -
t i o n s i n t h e basin.
Third , i n comparison with a constant dry season pumping p a t t e r n ,
t h e groundwater y i e l d can be s i g n i f i c a n t l y increased. For example,
Tables 4 and 5 show t h e optimal constant pumping schedule [Wi l l i e
and Liu, 19811. The corresponding water d e f i c i t s , f o r a l l p o s s i b l e
cropping p a t t e r n s , a r e represented i n Tables 6 and 7 . I n comparison
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Unified Approach t o Regional Grounduater Management 405
TABLE 7. I r r i ga t ion Def ic i t s
Constant Pumping Nov.-Dec. Jan.-Feb. March-April
Cho Shui 3691368. 3699342. 3621014. 3495427. S i LO 2663389. 2663389. 2663389. 2663389. Fu Wei 613735. 607227. 582389. 579575. Tou Liu 4994501. 4989748. 4994958. 4999813.
Tot a1 11962993. 11959756 11861750. 11738204.
with t he constant pumping pat tern, t he t rans ien t schedule reduces
t h e overal l d e f i c i t i n t he second and th i rd operat ional periods by
36,000 and 116,000 d i d . The s i t ua t ion is more dramatic when t h e
pumping upper bound is increased t o 50,000 m3/d. The water d e f i c i t
i s reduced i n each operational period. In t he f i r s t period, t h e
d e f i c i t decreases by 3200 m3/d (Tou Liu and Fe Wei regions).
This is balanced by an increase i n t h e d e f i c i t i n t he Cho Shui
area. The poten t ia l d e f i c i t i n t he second period, however, is
reduced by over 100,000 d / d . Pumping has increased i n t he Cho
Shui and Fe Wei i r r i g a t i o n d i s t r i c t s f i n a l l y during the t h i r d
period. The d e f i c i t has been decreased by 224,000 m3/d, again
primarily from increased extract ions i n Cho Shui and Fe Wei. The
s igni f icant r e su l t is t h e increased y ie ld does not degrade t h e
aqui fer below the current groundwater conditions, even with t h e
increased well capacity of t h e system.
Conclusions
This paper has presented a unif ied approach t o groundwater
management using an optimization methodology. The optimal planning
models a r e predicated on the response equations of t h e aqui fer
system. These same equations, which normally would be used i n a
simulation approach, can be incorporated d i r e c t l y within t h e frame-
work of optimization modeling. In contrast t o simulation modeling,
Water Resources Monograph Groundwater Hydraulics Vol. 9
Copyright American Geophysical Union
t h e optimization approach i d e n t i f i e s t h e optimal planning o r opera-
t i o n a l pol icies . In conjunction with mult iobject ive programming
techniques, t h e system trade-offs and t h e s e t of noninf e r i o r solu-
t i ons can a l s o be iden t i f ied . The methodology has been appl ied t o
Yun Lin Basin, Taiwan. Groundwater ex t rac t ion r a t e s were determined
f o r two scenarios , r e f l ec t i ng a l t e r n a t i v e groundwater development
scenarios. The r e s u l t s demonstrate t he u t i l i t y of optimization
modeling i n ident i fying t h e po t en t i a l s a f e y ie ld of regional
groundwater systems.
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