7.2. Model Calibration and Parameter Estimation
201
choose advection-dispersion models to simulate the groundwater quality.
Another reason for using advection-dispersion models is that we have already had various effective numerical techniques for solving the advectiondispersion equation.
7.2 Model Calibration and Parameter Estimation
7.2.1 Parameter Identification of Advection-Dispersion
Equations
Constructing a distributed parameter model for a specified system ineludes
finding a set of governing equations and determining the subsidiary conditions. A correct, reliable mathematical model must be a reproduction of the
real system. That is to say, the input-output relation of the mathematical
model must be fully coincident with or very elose to the excitation-response
relation of the real system. Unfortunately, it is very difficult to achieve this
requirement in groundwater modeling. First, the governing equations selected may not be suitable; secondly, we do not know the correct value
of each parameter ente ring the equations; and thirdly, the information on
boundary conditions andjor sourcejsink terms is usually not enough. For
these reasons, after constructing a model based on a preliminary und erstanding of the real system, we have to calibrate the model with observation data
obtained from pumping and tracer tests or from the historical records. The
factors relevant to the model, which inelude the coefficients of the equations,
the subsidiary conditions and the sourcejsink terms, can all be the objects of
calibration. The water flow subproblem and the water quality subproblem
can be calibrated separately, but sometimes joint calibration is necessary.
In the case of a homogeneous fluid, the flow part and the dispersion part
may be calibrated separately. First, identify the values of hydraulic conductivity, storativity, effective porosity, and other parameters related to flow
based on the head observations, and thereby figure out the me an velocity
field. Then, depending on the concentration observations, identify the values
of dispersivity, retardation factor, and other parameters relevant to dispersion. Parameter identification of groundwater flow equations has been
widely studied in the past twenty years (Nelson, 1968; Emsellem and de
Marsily, 1971; Neuman, 1973; Chavent et al., 1975; Neuman and Yokowitz,
1979; Sun, 1981; Yeh and Yoon, 1981; Cooley, 1982; Kitamidis and Vomvoris,
1983; Dagan, 1985; Carrera and Neuman, 1986a, b; Yeh, 1986; Sun, 1994).
Although the basic concepts and methods used for studying the parameter
identification of groundwater flow problems can be borrowed to study the
parameter identification of advection-dispersion equations, there are so me
special difficulties associated with the latter. Uncertainties in the flow param-
201
choose advection-dispersion models to simulate the groundwater quality.
Another reason for using advection-dispersion models is that we have already had various effective numerical techniques for solving the advectiondispersion equation.
7.2 Model Calibration and Parameter Estimation
7.2.1 Parameter Identification of Advection-Dispersion
Equations
Constructing a distributed parameter model for a specified system ineludes
finding a set of governing equations and determining the subsidiary conditions. A correct, reliable mathematical model must be a reproduction of the
real system. That is to say, the input-output relation of the mathematical
model must be fully coincident with or very elose to the excitation-response
relation of the real system. Unfortunately, it is very difficult to achieve this
requirement in groundwater modeling. First, the governing equations selected may not be suitable; secondly, we do not know the correct value
of each parameter ente ring the equations; and thirdly, the information on
boundary conditions andjor sourcejsink terms is usually not enough. For
these reasons, after constructing a model based on a preliminary und erstanding of the real system, we have to calibrate the model with observation data
obtained from pumping and tracer tests or from the historical records. The
factors relevant to the model, which inelude the coefficients of the equations,
the subsidiary conditions and the sourcejsink terms, can all be the objects of
calibration. The water flow subproblem and the water quality subproblem
can be calibrated separately, but sometimes joint calibration is necessary.
In the case of a homogeneous fluid, the flow part and the dispersion part
may be calibrated separately. First, identify the values of hydraulic conductivity, storativity, effective porosity, and other parameters related to flow
based on the head observations, and thereby figure out the me an velocity
field. Then, depending on the concentration observations, identify the values
of dispersivity, retardation factor, and other parameters relevant to dispersion. Parameter identification of groundwater flow equations has been
widely studied in the past twenty years (Nelson, 1968; Emsellem and de
Marsily, 1971; Neuman, 1973; Chavent et al., 1975; Neuman and Yokowitz,
1979; Sun, 1981; Yeh and Yoon, 1981; Cooley, 1982; Kitamidis and Vomvoris,
1983; Dagan, 1985; Carrera and Neuman, 1986a, b; Yeh, 1986; Sun, 1994).
Although the basic concepts and methods used for studying the parameter
identification of groundwater flow problems can be borrowed to study the
parameter identification of advection-dispersion equations, there are so me
special difficulties associated with the latter. Uncertainties in the flow param-