7.2. Model Calibration and Parameter Estimation
213
may be taken in different subareas, so there may be a great number of
unknown parameters to be determined.
There are a number of real world examples of building water quality
models based on existing contamination data and environment al tracers.
For instance, the study of the pollution of a munitions factory in Rocky
Mount, Arsenal, Denver, Colorado, USA, by Konikow (1977). Another exam pIe is the research on the groundwater contamination of Xi'an City, China
by the Hydrogeological Team of Shaanxi Province and Shangdong Uni versity (1985). Herweijer et al. (1985) reported a case of calibrating a water
quality model from historical observations of the environmental isotope
tritium since 1951. They used the Random-Walk model introduced in Section 4.2.6 to simulate the transport of tritium. The paper gives a detailed
introduction of the hydrogeological conditions, observations and the results
of model calibration.
In order to deeply examine the dispersion process and provide validation
data for the stochastic theories, severallarge-scale field dispersion experiments
have been conducted in recent years, ofwhich five comprehensive tracer tests
should be mentioned: Borden Air Force Base (Sudicky, 1986), Cape Cod
(Garabedian et al., 1991), Twin Lake (Killey and Moltyaner, 1988; Moltyaner,
1993), Columbus Air Force Base (Boggs et al., 1992), and Jutland Peninsula,
Denmark (Jensen et al. 1993). The characteristics of these tests include:
• The experimental sc ales were as large as several hundreds of meters, and
the test periods as long as one or more years.
• The observation systems were three-dimensional distributed.
• The tracers used were nonreactive.
• The variabilities in hydraulic conductivities andjor velocities were accurately measured.
• The concentration observations were interpreted by three-dimensional
stochastic and deterministic numerical models.
These experiments have provided important insight into the dispersion
process in natural heterogeneous formations, and have also provided useful
data bases for validation ofboth deterministic and stochastic theories, as weIl
as various numerical models. Readers can find the details of these tests from
references mentioned above. Some results of these tests will be reviewed in
the following sections.
7.2.3 The Relationship Between Values of Dispersivity and
Scales of Experiment
Many field tracer tests have been done which covered various scales as
mentioned previously. Some values of dispersivity obtained on different experiment scales, as quoted from the literat ure, are listed in Tables 7.1 to 7.4.
It has been found that the dispersivity values obtained by using mathematical
models to interpret tracer injection tests are not constant, but depend on the
213
may be taken in different subareas, so there may be a great number of
unknown parameters to be determined.
There are a number of real world examples of building water quality
models based on existing contamination data and environment al tracers.
For instance, the study of the pollution of a munitions factory in Rocky
Mount, Arsenal, Denver, Colorado, USA, by Konikow (1977). Another exam pIe is the research on the groundwater contamination of Xi'an City, China
by the Hydrogeological Team of Shaanxi Province and Shangdong Uni versity (1985). Herweijer et al. (1985) reported a case of calibrating a water
quality model from historical observations of the environmental isotope
tritium since 1951. They used the Random-Walk model introduced in Section 4.2.6 to simulate the transport of tritium. The paper gives a detailed
introduction of the hydrogeological conditions, observations and the results
of model calibration.
In order to deeply examine the dispersion process and provide validation
data for the stochastic theories, severallarge-scale field dispersion experiments
have been conducted in recent years, ofwhich five comprehensive tracer tests
should be mentioned: Borden Air Force Base (Sudicky, 1986), Cape Cod
(Garabedian et al., 1991), Twin Lake (Killey and Moltyaner, 1988; Moltyaner,
1993), Columbus Air Force Base (Boggs et al., 1992), and Jutland Peninsula,
Denmark (Jensen et al. 1993). The characteristics of these tests include:
• The experimental sc ales were as large as several hundreds of meters, and
the test periods as long as one or more years.
• The observation systems were three-dimensional distributed.
• The tracers used were nonreactive.
• The variabilities in hydraulic conductivities andjor velocities were accurately measured.
• The concentration observations were interpreted by three-dimensional
stochastic and deterministic numerical models.
These experiments have provided important insight into the dispersion
process in natural heterogeneous formations, and have also provided useful
data bases for validation ofboth deterministic and stochastic theories, as weIl
as various numerical models. Readers can find the details of these tests from
references mentioned above. Some results of these tests will be reviewed in
the following sections.
7.2.3 The Relationship Between Values of Dispersivity and
Scales of Experiment
Many field tracer tests have been done which covered various scales as
mentioned previously. Some values of dispersivity obtained on different experiment scales, as quoted from the literat ure, are listed in Tables 7.1 to 7.4.
It has been found that the dispersivity values obtained by using mathematical
models to interpret tracer injection tests are not constant, but depend on the