4
1. Introduction
The distributions of water head, concentration, temperature, and land
subsidence are variables representing the states of a groundwater system,
which are called state variables. To find the distributions of state variables in
accordance with given decision variables is called the prediction problem.
The management problem involves the prediction problem. To anSwer
whether or not adecision is feasible, we should first predict the response of
the system to the decision. For example, let the number, locations and rates
of pumping wells be decision variables of a management problem. For each
decision, the distribution of water level, especially in the weIls, can be obtained by solving the prediction problem. The prediction results can tell us
whether the lowering of water table exceeds the given value, and allow us to
calculate the power consumption for drawing water. Another example occurs
when the locations of the recharge wells and the quality of the recharged
water are considered as decision variables. We can solve the prediction problem first in order to compute the concentration of the contaminants in the
supply wells. Then, we can judge whether the quality of the water supply
meets the given standard, and calculate the treatment cost of the recharged
water.
How is the prediction problem solved? The most reliable way, of course, is
to conduct a field test and directly observe the state of the aquifer. Unfortunately, this is unrealistic because the field test cannot tell us what will
happen in the future. It is impossible to conduct field tests for all feasible decisions and then compare them. Although theoretical analysis is important for
solving practical problems, it cannot give prediction results for an individual
problem. The modeling method, therefore, becomes the only way for solving
the prediction problem. A physical or mathematical model is built based on
the internal structures and external conditions of a real system. It combines
common physical rules (mass balance, Darcy's law, for example) with particular conditions (values of parameters, initial and boundary conditions, for
example) of the system. The excitation-response relation of the real system
can be described by the input-output relation of the model. Thus, the model
is helpful for better understanding the system and may provides invaluable
tools for prediction purposes. All feasible decisions can be inputted to the
model, and the resulting states can be observed after the model is run. With
a model, we can search for the optimal decisions based On the given objective
functions.
1.3 Groundwater Modeling
Many types of models have been used for simulating groundwater flow, such
as sand trough, vertical or horizontal Hele-Shaw, membrane, R-R and R-C
electric analogue, as weIl as various mathematical models.
1. Introduction
The distributions of water head, concentration, temperature, and land
subsidence are variables representing the states of a groundwater system,
which are called state variables. To find the distributions of state variables in
accordance with given decision variables is called the prediction problem.
The management problem involves the prediction problem. To anSwer
whether or not adecision is feasible, we should first predict the response of
the system to the decision. For example, let the number, locations and rates
of pumping wells be decision variables of a management problem. For each
decision, the distribution of water level, especially in the weIls, can be obtained by solving the prediction problem. The prediction results can tell us
whether the lowering of water table exceeds the given value, and allow us to
calculate the power consumption for drawing water. Another example occurs
when the locations of the recharge wells and the quality of the recharged
water are considered as decision variables. We can solve the prediction problem first in order to compute the concentration of the contaminants in the
supply wells. Then, we can judge whether the quality of the water supply
meets the given standard, and calculate the treatment cost of the recharged
water.
How is the prediction problem solved? The most reliable way, of course, is
to conduct a field test and directly observe the state of the aquifer. Unfortunately, this is unrealistic because the field test cannot tell us what will
happen in the future. It is impossible to conduct field tests for all feasible decisions and then compare them. Although theoretical analysis is important for
solving practical problems, it cannot give prediction results for an individual
problem. The modeling method, therefore, becomes the only way for solving
the prediction problem. A physical or mathematical model is built based on
the internal structures and external conditions of a real system. It combines
common physical rules (mass balance, Darcy's law, for example) with particular conditions (values of parameters, initial and boundary conditions, for
example) of the system. The excitation-response relation of the real system
can be described by the input-output relation of the model. Thus, the model
is helpful for better understanding the system and may provides invaluable
tools for prediction purposes. All feasible decisions can be inputted to the
model, and the resulting states can be observed after the model is run. With
a model, we can search for the optimal decisions based On the given objective
functions.
1.3 Groundwater Modeling
Many types of models have been used for simulating groundwater flow, such
as sand trough, vertical or horizontal Hele-Shaw, membrane, R-R and R-C
electric analogue, as weIl as various mathematical models.