Environ Geol
DOI 10.1007/s00254-007-1125-8
ORIGINAL ARTICLE
Numerical simulation of groundwater flow for a coastal plain
in Japan: data collection and model calibration
Bin He Æ Keiji Takase Æ Yi Wang
Received: 16 April 2007 / Accepted: 2 November 2007
Ó Springer-Verlag 2007
Abstract Using a three-dimensional finite element
model, this study characterizes groundwater flow in a
costal plain of the Seto Inland Sea, Japan. The model
characterization involved taking field data describing the
aquifer system and translating this information into input
variables that the model code uses to solve governing
equations of flow. Geological geometry and the number of
aquifers have been analyzed based on a large amount of
geological, hydrogeological and topographical data.
Results of study demonstrate a high correlation between
the ground surface elevation and the groundwater level in
the shallow coastal aquifer. For calibrating the numerical
groundwater model, the groundwater flow was simulated in
steady state. In addition, the groundwater level and trend in
the transient state has also been elucidated. The numerical
result provides excellent visual representations of groundwater flow, presenting resource managers and decision
makers with a clear understanding of the nature of the types
of groundwater flow pathways. Results build a base for
further analysis under different future scenarios.
Keywords Coastal aquifers Groundwater flow Numerical modeling Japan
B. He (&)
Institute of Industrial Science, The University of Tokyo,
Be505, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
e-mail: [email protected]
K. Takase
Faculty of Agriculture, Ehime University,
3-5-7 Tarumi, Matsuyama 790-8566, Japan
Y. Wang
United Graduate School of Agricultural Sciences,
Ehime University, 3-5-7 Tarumi, Matsuyama 790-8566, Japan
Introduction
In the coastal Dogo Plain of the Seto Inland Sea, owing to
the absence of reliable water resources, groundwater is the
primary source of water supply for domestic, municipal,
industrial and agricultural uses. In recent decades,
increasing concerns over agricultural water use, surface
water reliability and groundwater storage changes have
increased demand for sustainable groundwater management. Previous studies in the coastal plain have shown that
the groundwater level fluctuation and long term trends
depend on the groundwater recharge, which is a function
of precipitation, evapotranspiration, and pumped water
(Takase 2000; He et al. 2005). As a part of regional
development planning, research has begun to estimate the
impact of future urbanization on the hydrologic cycle and
to propose effective alternatives in the laboratory of
hydrology for environmental engineering (LHEE), Ehime
University, Japan. The research includes both long-term
monitoring and assessment of changes in hydrologic cycle
due to this planned development. For this reason, the seasonal changes of hydrologic cycle and water balance in the
Dogo Plain have been studied in the preliminary studies
(He et al. 2005, 2006, 2007; Yamane et al. 2003).
In the present study, the three-dimensional finite element groundwater model (FEM) is used to simulate
groundwater flow. Finite element groundwater model is the
most efficient and powerful current method to analyze
groundwater flow (Kinzelbach et al. 1986; Anderson et al.
1992; Elkadi et al. 1994). In addition, groundwater model
defines vertical dimensions, geological geometry and the
number of aquifers to be modeled (Bear et al. 1987; Winter
et al. 1998). This most difficult part of the groundwater
modeling process requires large amount of geological,
hydrogeological and topographical data, which are usually
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Environ Geol
expensive and hard to get (Gumbricht et al. 1996). Construction of the groundwater model’s layers is based on
geological maps, boreholes and deep wells’ drilling diaries
(Gogu et al. 2001). In this study, the hydrogeological
database was built and a three-dimensional finite element
model was constructed to simulate the groundwater flow in
both steady and transient state.
Materials and methods
Study site description
The site chosen for this study is located on the northeastern
part of the Dogo Plain in Ehime Prefecture of Japan, which
is included in the Shigoku Island (Fig. 1). The study site is
situated at a longitude of 132.46° east and 33.50° north, 7°
further south than Tokyo. The Dogo Plain has a mild climate, characteristic of the Seto Inland Sea, with an average
temperature of 15.8°. The average annual precipitation is
1,286 mm, with a lot of rain in June and only a little in
January. The coastal plain covers an area of 83 km2, with
elevations ranging from 13 to 150 m above sea level. The
Dogo Plain is one of the major plains in the Shigoku Island
of Japan. For ecological considerations, the Dogo Plain has
been continuously monitored for rainfall, stream flow,
groundwater level, groundwater temperature and electrical
conductivity, etc., for about 30 years. Such continuously
monitored datasets can be helpful in the detailed conceptualization of the hydrogeological environment in the Dogo
Plain.
Fig. 1 Map of study site
showing the location of the
basin and the experimental
Gauges in it
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Finite element method
Finite element method is a general algorithm for
groundwater flow analysis (Kazda 1990; Konikow 1998).
In this study, FEMWATER (Yeh et al. 1992) has been
applied to simulate the groundwater in the Dogo Plain.
FEMWATER is a public domain code of 3D finite element program and is currently maintained by the US
Army Corps of Engineers, waterways experiment station
(WES). It is a high-quality computer code as developed
and maintained through research programs funded by the
US government and has been extensively validated and
verified by a wide range of government agencies, consultants and universities.
FEMWATER simulates the flow of water and transport
of contaminants in the unsaturated media. The modified
Richards equation, subject to initial and boundary condition equations, is the governing flow equation describing
flow through the saturated-unsaturated porous media in
FEMWATER. The modified Richards equation is thus used
for computations required in a flow-only simulation in
FEMWATER. The set of matrix equations generated in
FEMWATER are solved using the Galerkin finite element
method. The modified Richards equation for three-dimensional water movement in saturated-unsaturated media
used in FEMWATER is as shown:
q oh
q
q
F ¼ r K rh þ rz þ q
ð1Þ
q0 ot
q0
q0
h
dS
F ¼ a 0 þ b0 h þ n
n
dh
ð2Þ
Environ Geol
where F = storage coefficient [L-1], h = pressure head [L],
t = time, K = hydraulic conductivity tensor [LT-1], z =
potential head [L], q = source and/or sink [L2T-1], q =
water density at chemical concentration C [ML-3],
q0 = referenced water density at zero chemical concentration [ML-3], q* = density of either the injection fluid or
the withdrawn water [ML-3], h = moisture content,
a’ = modified compressibility of the medium [LT2M-1],
b’ = modified compressibility of the water [LT2M-1],
n = porosity of the medium, and S = saturation.
The flow Eq (1) is subject to the following initial
conditions:
h ¼ hi ðx; y; zÞ in R;
ð3Þ
where R is the region of interest and hi is the prescribed
initial condition. The flow equation is also subject to
boundary conditions such as Dirichlet, gradient flux,
specified flux, and variable conditions during precipitation
and no precipitation conditions. The Dirichlet boundary
condition is a specified head boundary condition where the
pressure head over a boundary can be assigned and maintained constant throughout the length of simulation. The
gradient boundary condition allows the user to assign a flux
rate variable with time. The variable boundary condition is
applied to the top face of the model and is used to simulate
evaporation and seepage. Variable boundary conditions
change between Dirichlet and flux boundary conditions
depending on the potential evaporation, the conductivity of
the media, and the availability of water such as rainfall and
the level of the groundwater in the model. Further information about the boundary condition equations can be
found in Lin et al. (1997).
Topographic points, DEM, and boundary conditions
In this study, as much dataset as possible on the climate,
geology, and hydrology of the Dogo Plain were collected. Based on those datasets, hydrogeological
conditions were described and groundwater flow characteristics were also elucidated in He (He et al. 2007).
Meteorological conditions including daily precipitation,
daily average temperature, and daily potential evapotranspiration in the whole Dogo Plain has also been
collected by the LHEE.
A general view of the overall dataset structure needed
in the numerical simulation is shown in Fig. 2. Topography is an essential component. Correct analysis result
requires an accurate description of terrain. For the construction of the groundwater model, the topological
discretization (river cross-sections, floodplain basins and
hydraulic links) was available from GIS digital element
model (DEM) analysis. In this study, the 50mesh DEM
was used as the initial topographic information layer
(Fig. 3.) In this DEM, 293, 460 points with different x, y, z
(elevation data) information was shown in different color.
The data layer with x, y, z information can also be created
from the 50mesh DEM information file, which is shown at
different angles (Fig. 3). Triangular mesh from DEM can
be zoomed to view the element and node (Fig. 4). The
Dogo Plain system was characterized by (1) no-flow
(Neumann) boundary conditions along the sides and base
of the hill slopes, (2) a variable infiltration-seepage
boundary along the ground surface, and (3) a single constant head (Dirichlet) node at the foot of the slope
representing a first-order stream.
3D Point: X Axis: Position In X Axis
Y Axis: Position In Y Axis
Z Axis: √Topographic Elevation
√Geological Elevation(1.Surface, Bottom, Height of 1'st Geological Layer
2.Surface, Bottom, Height of 2'nd Geological Layer
......
n.Surface, Bottom, Height of n'th Geological Layer)
√Hydrologic Information: Groundwater Elevation
Rainfall
Irrigaiton
Well Pumping
River, Lake, Ponds, Estuaries,Ocean shorelines
Human-made Reservoirs
Impermeable Barries( Due to changes in geologic material
Due to human-made barriers such as walls)
Human-made sink terms such as drains
Human-made source terms such as infiltration galleries
√Land Use Data
√Population data
Fig. 2 Available dataset for the numerical simulation
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Environ Geol
Fig. 3 Ground surface elevation map (ELEV Unit: m surrounding colored boundary is mountain)
Results and discussion
Relation between groundwater level and ground surface
elevation
All FEMWATER simulations require a set of initial conditions from which the numerical simulation will progress.
To determine the initial groundwater head, the relation
between groundwater level and ground surface elevation
has been analyzed (Fig. 7) because the sufficient data were
not available within the study area for the water table
within the shallow unconfined aquifer. High correlation
between them can be found for this coastal plain (Fig. 7).
The groundwater level in the shallow aquifer depends
greatly on the ground surface elevation. By using the
relation equations (Fig. 7), the initial condition of
groundwater level distribution may be obtained.
Fig. 4 Triangular mesh from DEM data
Aquifer and hydraulic geology
FEM mesh
The Dogo Plain consists of four layers. The deeper layer is
old terrace sediment layer, with a maximum thickness of
120 m. New terrace sediment layer overlies the old terrace
sediment layer. The surface in the lower part of the Dogo
Plain consists of sediment layer with an upper zone of fan
sedimentary deposits. Judging from the results of field
measurements conducted by Matusyama city, confined
aquifer formation does not seem to have been developed in
this area (Figs. 5, 6, cited from Fujihara et al. 2000).
Based on the results of field survey, coefficient of hydraulic
conductivity and effective porosity in each layer were estimated (Table 1). Since these values change according to the
location in the plain, they have ranges (Fujihara et al. 2000).
The required numerical run time varies with many factors.
One of the most important factors is the finite element
mesh. From a computational point of view, time interval
and mesh resolution are closely related. Usually a finer
mesh will require smaller time intervals to obtain accurate
solutions, which is especially true for a nonlinear system.
Thus, placing enough resolution on the computational
mesh for the study region is important. Triangular meshes
are created using automatic mesh generation tools. With
interactive editing tools meshes can be easily edited by
point, click and drag techniques. In addition, the point and
element information of each cell can be output as excel or
text file, which can be accessed by GIS and groundwater
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Environ Geol
Fig. 5 Geological survey cross sections and observed groundwater levels in the Dogo Plain
C
Shigenoburiver m
B
Table 1 Estimated coefficients of hydraulic conductivity and effective porosity
150
A
Hydraulic
conductivity
(m/d)
Shigenoburiver
100
m
Shigenoburiver
50
50
0
0
-50
-100
Effective
porosity
River sedimentary layer
200.0*100.0
0.11*0.14
Alluvium
80.0*40.0
0.16*0.20
Fan sedimentary layer
40.0*0.8
0.18*0.215
New terrace sediment layer
20.0*4.0
0.215*0.23
Old terrace sediment layer
10.0*1.0
0.21*0.235
-150
fansedimentarylayer
Shigenoburiver
m
Shigenoburiver
alluvium
D
flow model. Finite element groundwater model has been
constructed in this study (Fig. 8).
newterracesedimentlayer
50
0
-50
riversedimentarylayer
Steady state analysis
oldterracesedimentlayer
-100
-150
5
10
15
20km
Fig. 6 Geologic cross-sections along four lines
Calibration of a groundwater model generally involves
adjusting parameters (such as hydraulic conductivity and
recharge) so that the modeled values resemble as closely
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Environ Geol
140
100
80
60
40
20
0
100
80
60
40
20
0
1998/7/14
0
60
40
0
20 40 60 80 100 120 140
Ground Surface Elevation (m)
120
60
40
1998/9/28
0
80
60
40
1998/5/9
0
20 40 60 80 100 120 140
Ground Surface Elevation (m)
140
y = -1.5412 + 0.9842x
R= 0.9996
80
0
y = -1.6594 + 0.9799x
R= 0.9995
100
0
20 40 60 80 100 120 140
Ground Surface Elevation (m)
100
20
120
20
1998/3/18
140
y = -1.9792 + 0.9834x
R= 0.9995
Groundwater Level (m)
Groundwater Level (m)
140
120
80
0
20 40 60 80 100 120 140
Ground Surface Elevation (m)
140
y = -2.1813 + 0.9794x
R= 0.9992
100
20
1998/1/28
0
120
Groundwater Level (m)
140
y = -1.9077 + 0.9808x
R= 0.9993
20 40 60 80 100 120 140
Ground Surface Elevation (m)
Groundwater Level (m)
120
Groundwater Level (m)
Groundwater Level (m)
Fig. 7 Relation between
groundwater level and ground
surface elevation
120
y = -1.9346 + 0.9778x
R= 0.9994
100
80
60
40
20
0
1998/11/25
0
20 40 60 80 100 120 140
Ground Surface Elevation (m)
Fig. 8 FEM mesh and
isometric view of the Dogo
Plain
Fig. 9 Simulated groundwater
level contour (color contour)
and measured groundwater level
contour as an example (unit: m)
as possible the field monitoring data. Initial steady state
runs appeared to support the basic principles of the
hydrogeological model used to define the model. The
main controls on the simulated heads were the vertical
hydraulic conductivities in the aquitard units with heads
remaining relatively consistent in the confined areas of the
model regardless of changes in hydraulic conductivity
or changes in recharge.
123
Thus, the process of steady-state calibration primarily
focused on achieving results in line with those measured
groundwater level to provide a useful benchmark for further simulations. For each model run, an analysis of the
observed versus computed water levels was conducted to
determine the accuracy of the numerical simulations. The
values of hydraulic head collected from the field to be used
as targets in the model consist of monitoring data collected
Environ Geol
Fig. 10 Simulated groundwater level contour (transient simulation)
by LHEE. The groundwater distribution in steady state has
been analyzed for January 2003 (Fig. 9). The comparison
between the measured and simulated groundwater demonstrated a good correlation.
sample of the locations where the transient simulations
were evaluated.
Conclusion
Transient state analysis
As with the steady-state calibration, transient runs were
expected to be very similar to previous model results
because the same data was used to construct the transient
model. This proved to be the case. The groundwater simulation in transient state was analyzed from 1 January 2003
to 31 December 2003 (Fig. 10). The transient state calibration concluded when a reasonable match was observed
between the computed and measured values based on
previous results. Figure 11 is the time series graphs for a
This paper outlines the development of the numerical
groundwater model and presents some of the outcomes by
using the three-dimensional numerical finite element
model for groundwater flow assessment in the coastal
Dogo Plain. Results of study demonstrate a high correlation between the ground surface elevation and the
groundwater level in the shallow coastal aquifer. For
calibrating the numerical groundwater model, the
groundwater flow was simulated in steady state. In addition, the groundwater level and trend in the transient state
has also been elucidated. These results built a base for
123
Environ Geol
54.00
Gr oun d wa te r E le va t io n ( m )
Fig. 11 Transient calibration
comparisons at example wells
Measured GW Elevation
53.00
Simulated GW Elevation
52.00
51.00
50.00
49.00
48.00
2002/12/31
2003/03/11
2003/05/20
2003/07/29
2003/10/07
2003/12/16
Date (Year/Month/Day)
Groundwater Elevation (m)
19.00
18.50
Measured GW Elevation
18.00
17.50
Simulated GW Elevation
17.00
16.50
16.00
15.50
15.00
14.50
14.00
2002/12/31
2003/03/11
2003/05/20
2003/07/29
2003/10/07
2003/12/16
Date (Year/Month/Day)
further analyzing the groundwater flow under different
simulation scenarios.
Acknowledgments The research was financially supported by the
Sasakawa Scientific Research Grant from The Japan Science Society.
The authors are grateful for their supports. Dr. J. Takahashi and Dr. H.
Cheng in Ehime University are also thanked for their help with the
GIS software and digital data. The authors wish to extend the
acknowledgement to the support and technical guidance given by the
laboratory of hydrology for environmental engineering in Ehime
University for undertaking this research. We would also like to thank
anonymous reviewers for the valuable and helpful comments to the
early drafts of this paper.
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