Title: Basin Yield -Safe Yield and Optimal Yield of a Groundwater Basin
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Title: Basin Yield -Safe Yield and Optimal Yield of a Groundwater Basin
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Language: English
Spatial Coverage: North America -- United States of America -- Florida
Abstract: Basin Yield -Safe Yield and Optimal Yield of a Groundwater Basin From: Groundwater Resources Evaluation
General Note: Box 9, Folder 7 ( SF-Safe Yield - 1956-1995 ), Item 13
Funding: Digitized by the Legal Technology Institute in the Levin College of Law at the University of Florida.
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364 Groundwater Resouce Evaluation / Ch. e

Fact that the variables of the system under study are represented by analogous
physical quantities and pieces of equipment is extremely valuable for the purposes
of teaching or display, but the cost in time is large. The network, once built,
describes only one specific aquifer. In digital modeling, on the other hand, once a '1
general computer program has been prepared, data decks representing a wide vari- 1
ety of aquifers and aquifer conditions can be run with the same program. The
effort involved in designing and keypunching a new data deck is much less than
that involved in designing and building a new resistance-capacitance network.
This flexibility is equally important during the calibration phase of aquifer
The advantages of digital simulation weigh heavily in its favor, and with the
advent of easy accessibility to large computers, the method is rapidly becoming
the standard tool for aquifer management. However, analog simulation will
undoubtedly continue to play a role for some time, especially in developing coun-
tries where computer capacities are not yet large.

8.10 Basin Yield

Safe Yield and Optimal Yield
of a Groundwater Basin
Groundwater yield is best viewed in the context of the full three-dimensional
hydrogeologic system that constitutes a groundwater basin. On this scale of study
we can turn to the well-established concept of safe yield or to the more rigorous
|: concept of optimalyield.
z Todd (1959) defines the safe yield of a groundwater basin as the amount of
water that can be withdrawn from it annually without producing an undesired
result. Any withdrawal in excess of safe yield is an overdraft. Domenico (1972)
and Kazmann (1972) review the evolution of the term. Domenico notes that the
j "undesired results" mentioned in the definition are now recognized to include
Snot only the depletion of the groundwater reserves, but also the intrusion of water
I" of undesirable quality, the contravention of existing water rights, and the dete-
rioration of the economic advantages of pumping. One might also include excessive
depletion of streamflow by induced infiltration and land subsidence.
i Although the concept of safe yield has been widely used in groundwater
resource evaluation, there has always been widespread dissatisfaction with it
(Thomas, 1951; Kazmann, 1956). Most suggestions for improvement have encour-
aged consideration of the yield concept in a socioeconomic sense within the overall
framework of optimization theory. Domenico (1972) reviews the development
of this approach, citing the contributions of Bear and Levin (1967), Buras (1966),
Burt (1967), Domenico et al. (1968), and others. From an optimization viewpoint,
groundwater has value only by virtue of its use, and the optimal yield must be
i; determined by the selection of the optimal groundwater management scheme from
Sj a set of possible alternative schemes. The optimal scheme is the one that best meets

1 ru d ae a au nyb iteo isue n h pi a il utb

SCh. 8 365 Groundwater Resource Evaluation / Ch. 8
a / Ch. 8
logos a set of economic and/or social objectives associated with the uses to which the
water is to be put. In some cases and at some points in time, consideration of the
e buit, present and future costs and benefits may lead to optimal yields that involve mining
1, once a groundwater, perhaps even to depletion. In other situations, optimal yields may
ide vari- reflect the need for complete conservation. Most often, the optimal groundwater
ide van- development lies somewhere between these extremes.
es thn The graphical and mathematical methods of optimization, as they relate to
network. groundwater development, are reviewed by Domenico (1972).
' aquifer
Sa Transient Hydrologic Budgets and Basin Yield
with the In Section 6.2 we examined the role of the average annual groundwater recharge,
becoming R, as a component in the steady-state hydrologic budget for a watershed. The value
ion will of R was determined from a quantitative interpretation of the steady-state, regional,
ng coun- groundwater flow net. Some authors have suggested that the safe yield of a ground-
water basin be defined as the annual extraction of water that does not exceed the
average annual groundwater recharge. This concept is not correct. As pointed out
by Bredehoeft and Young (1970), major groundwater development may signif-
icantly change the recharge-discharge regime as a function of time. Clearly, the
basin yield depends both on the manner in which the effects of withdrawal are
transmitted through the aquifers and on the changes in rates of groundwater
recharge and discharge induced by the withdrawals. In the form of a transient
iensional hydrologic budget for the saturated portion of a groundwater basin,
of study
rigorous Q(t) = R(t) D(t) + dS (8.72)

nount of i:i
mdesird where Q(t) = total rate of groundwater withdrawal
desired) = total rate of groundwater recharge to the basin i
o (1972)R(t) = total rate of groundwater recharge to the basin
that the D(t) = total rate of groundwater discharge from the basin
include dS/dt = rate of change of storage in the saturated zone of the basin.
of water
the dete- Freeze (1971a) examined the response of R(t) and D(t) to an increase in Q(t)
excessive in a hypothetical basin in a humid climate where water tables are near the surface. ii
e i- The response was simulated with the aid of a three-dimensional transient analysis
ndwater -of a complete saturated-unsaturated system such as that of Figure 6.10 with a
I with it pumping well added. Figure 8.32 is a schematic representation of his findings.
The diagrams show the time-dependent changes that might be expected in the
ie overall various terms of Eq. (8.72) under increased pumpage. Let us first look at the case
shown in Figure 8.32(a), in which withdrawals increase with time but do not
Selopmen, become excessive. The initial condition at time to is a steady-state flow system in
Ls (1966),
1iewpont, which the recharge, R,,equals the discharge, Do. At times t1, t2, t3, and t,, new
'must be wells begin to tap the system and the pumping rate Q undergoes a set of stepped
from increases. Each increase is initially balanced by a change in storage, which in an
est meets unconfined aquifer takes the form of an immediate water-table decline. At the
*est meets

Groundwater Resource Evluation / Ch. 8


decline t--

--~- Recharge rote,R
----- Discharge rote,D
.--. Rate of thonge of storage, dS/dt

os Do


0 t11

.12 'It" \to

Ma --i i411M*
Maximum stobt
bosin yield

Water" Stoable-.4Unstoble
table / Water table
Water table depth depth below
below which maximum which notable
groundwater recharge rate rechn ate
can no longer be sustained sustained


Figure 8.32 Schematic diagram of transient relationships between recharge
rates, discharge rates, and withdrawal rates (after Freeze. 1971 a).

same time, the basin strives to set up a new equilibrium under conditions of
increased recharge, R. The unsaturated zone will now be induced to deliver greater
flow rates to the water table under the influence of higher gradients in the satu-
rated zone. Concurrently, the increased pumpage may lead to decreased discharge
rates, D. In Figure 8.32(a), after time 14, all natural discharge ceases and the
discharge curve rises above the horizontal axis, implying the presence of induced
recharge from a stream that had previously been accepting its baseflow component
from the groundwater system. At time tr, the withdrawal Q is being fed by the
recharge, R, and the induced recharge, D; and there has been a significant decline
in the water table. Note that the recharge rate attains a maximum between t3 and
t,. At this rate, the groundwater body is accepting all the infiltration that is avail-
able from the unsaturated zone under the lowered water-table conditions.
In Figure 8.32(a), steady-state equilibrium conditions are reached prior to
each new increase in withdrawal rate. Figure 8.32(b) shows the same sequence of
events under conditions of continuously increasing groundwater development
over several years. This diagram also shows that if pumping rates are allowed
to increase indefinitely, an unstable situation may arise where the declining water
table reaches a depth below which the maximum rate of groundwater recharge R
can no longer be sustained. After this point in time the same annual precipitation
rate no longer provides the same percentage of infiltration to the water table.
Evapotranspiration during soil-mnoisture-redistribution periods now takes more
of the infiltrated rainfall before it has a chance to percolate down to the ground-
water zone. At t, in Figure 8.32(b), the water table reaches a depth below which
no stable recharge rate can be maintained. At t, the maximum available rate of
induced recharge is attained. From time t, on, it is impossible for the basin to supply
increased rates of withdrawal. The only source lies in an increased rate of change of
storage that manifests itself in rapidly declining water tables. Pumping rates can


b .


81: 1~

Groundwetar Resource Evaluation / Ch. 8

stion / Ch. 8


- Water table
depth below
which notable
recharge rote
can be

no longer be maintained at their original levels. Freeze (1971a) defines the value
of Q at which instability occurs as the maximum stable basin yield. To develop a
basin to its limit of stability would, of course, be foolhardy. One dry year might
cause an irrecoverable water-table drop. Production rates must allow for a factor
of safety and must therefore be somewhat less than the maximum stable basin
The discussion above emphasizes once again the important interrelationships
between groundwater flow and surface runoff. If a groundwater basin were devel-
oped up to its maximum yield, the potential yields of surface-water components
of the hydrologic cycle in the basin would be reduced. It is now widely recognized
that optimal development of the water resources of a watershed depend on the
conjunctive use of surface water and groundwater. The subject has provided a
fertile field for the application of optimization techniques (Maddock, 1974; Yu
and Haimes, 1974). Young and Bredehoeft (1972) describe the application of digital
computer simulations of the type described in Section 8.8 to the solution of manage-
ment problems involving conjunctive groundwater and surface-water systems.

8.11 Artificial Recharge and Induced Infiltration

In recent years, particularly in the more populated areas of North America where
water resource development has approached or exceeded available yield, there
has been considerable effort placed on the management of water resource systems.
Optimal development usually involves the conjunctive use of groundwater and
surface water and the reclamation and reuse of some portion of the available water
resources. In many cases, it involves the importation of surface water from areas
of plenty to areas of scarcity, or the conservation of surface water in times of plenty
for use in times of scarcity. These two approaches require storage facilities, and
there is often advantage to storing water underground where evaporation losses
are minimized. Underground storage may also serve to replenish groundwater
resources in areas of overdraft.
Any process by which man fosters the transfer of surface water into the
groundwater system can be classified as artificial recharge. The most common
method involves infiltration from spreading basins into high-permeability, uncon-
fined, alluvial aquifers. In many cases, the spreading basins are formed by the
construction of dikes in natural channels. The recharge process involves the growth
of a groundwater mound beneath the spreading basin. The areal extent of the mound
and its rate of growth depend on the size and shape of the recharging basin, the
duration and rate of recharge, the stratigraphic configuration of subsurface forma-
tions, and the saturated and unsaturated hydraulic properties of the geologic
materials. Figure 8.33 shows two simple hydrogeological environments and the
type of groundwater mound that would be produced in each case beneath a circular
spreading basin. In Figure 8.33(a), recharge takes place into a horizontal uncon-
fined aquifer bounded at the base by an impermeable formation. In Figure 8.330,

editions of
ver greater
n the satu-
I discharge
es and the
of induced
fed by the
ant decline
veen t3 and
iat is avail-
Ad prior to
sequence of
re allowed
ning water
recharge R
ater table.
akes more
'ie ground-
.low which
ble rate of
a to supply
change of
J rates can

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