8.3. Groundwater Quality Management Models
289
subject to constraints:
Z2(q+, q-) ~ li,
o ~ q+ ~ Q+, 0 ~ q- ~ Q-,
(8.3.40)
(8.3.41 )
where li is the limited remediation budget, Q+ and Q- are the upper limits
of q+ and q-, respectively, which are determined by the capabilities of the
equipment and limitations of hydraulic conditions.
The alternative formulation of minimizing the cost subject to residual
contaminant standards may be stated as
subject to constraints:
Zl(q+,q-) ~ C,
o ~ q+ ~ Q+, 0 ~ q- ~ Q-,
(8.3.42)
(8.3.43)
(8.3.44)
where C is the maximum allowable contaminant concentration in the wh oie
aquifer when the remediation is completed. Equation (8.3.43) mayaiso be
transformed into
(8.3.45)
where C k is the concentration of the kth subdomain and C k is the given
standard of water quality in the subdomain.
Both formulations for the optimal remediation of aquifers are classified
as nonlinear programming problems. Zl(q+,q-) and C k in Eq. (8.3.45) can be
computed by an established water quality model. During the process of
.
.
.
OZl
OZl (
oCk OCk )
solvmg the nonlmear programmmg, oq+ and oq- or oq+' oq- also need
to be calculated, wh ich can be obtained with the aid of the water quality
model and using finite difference or variational methods (see Section 7.3.2).
Gorelick et al. (1984) combined a contaminant transport model with a
non-linear programming technique to solve the aquifer reclamation problem.
Ahlfeld et al. (1988a, b) gave a detailed introduction to the numerical solutions for the above two types of problems, as weIl as some examples.
8.3.6 The Reliability of Management Models
The solution of a management model depends on the established water
flow and water quality models. In the simulation models, however, there are
always uncertainties associated with model structure and model parameters.
We should estimate the effects of these uncertainties on the optimal management decision so as to determine the reliability of the management model.
The Monte-Carlo method provides the most general way for solving
this kind of problem. According to the known statistic characteristics of
input parameters, the computer can generate many realizations of the input
289
subject to constraints:
Z2(q+, q-) ~ li,
o ~ q+ ~ Q+, 0 ~ q- ~ Q-,
(8.3.40)
(8.3.41 )
where li is the limited remediation budget, Q+ and Q- are the upper limits
of q+ and q-, respectively, which are determined by the capabilities of the
equipment and limitations of hydraulic conditions.
The alternative formulation of minimizing the cost subject to residual
contaminant standards may be stated as
subject to constraints:
Zl(q+,q-) ~ C,
o ~ q+ ~ Q+, 0 ~ q- ~ Q-,
(8.3.42)
(8.3.43)
(8.3.44)
where C is the maximum allowable contaminant concentration in the wh oie
aquifer when the remediation is completed. Equation (8.3.43) mayaiso be
transformed into
(8.3.45)
where C k is the concentration of the kth subdomain and C k is the given
standard of water quality in the subdomain.
Both formulations for the optimal remediation of aquifers are classified
as nonlinear programming problems. Zl(q+,q-) and C k in Eq. (8.3.45) can be
computed by an established water quality model. During the process of
.
.
.
OZl
OZl (
oCk OCk )
solvmg the nonlmear programmmg, oq+ and oq- or oq+' oq- also need
to be calculated, wh ich can be obtained with the aid of the water quality
model and using finite difference or variational methods (see Section 7.3.2).
Gorelick et al. (1984) combined a contaminant transport model with a
non-linear programming technique to solve the aquifer reclamation problem.
Ahlfeld et al. (1988a, b) gave a detailed introduction to the numerical solutions for the above two types of problems, as weIl as some examples.
8.3.6 The Reliability of Management Models
The solution of a management model depends on the established water
flow and water quality models. In the simulation models, however, there are
always uncertainties associated with model structure and model parameters.
We should estimate the effects of these uncertainties on the optimal management decision so as to determine the reliability of the management model.
The Monte-Carlo method provides the most general way for solving
this kind of problem. According to the known statistic characteristics of
input parameters, the computer can generate many realizations of the input