E. James Nelson, Norman L. Jones
Utilizing the ArcInfo Data Model to Build Conceptual Models for Environmental/Hydraulic/Hydrologic Simulations
Abstract
Pre-processors for surface and groundwater models have traditionally
been designed so that the majority of the model definition and editing is performed directly on the grid or mesh used in the simulation. A more effective approach is to define the model at the conceptual level. This high-level definition
is constructed using a data model patterned after Geographic Information Systems
(GIS) such as ArcInfo. The boundary conditions and model parameters can then be assigned
directly to the objects in the conceptual model. Once the conceptual model is
defined, a numerical model in the form of a finite element mesh or finite
difference grid is automatically generated and the boundary conditions and
model parameters are assigned to the appropriate cells, nodes , or elements.
The advantages of a conceptual model approach to environmental/hydrologic/hydraulic modeling
includes increased modeling efficiency since time-consuming cell by cell
editing is eliminated and increased accuracy since a large number of candidate
conceptual models can be evaluated in the time traditionally required to
develop one model. Further, existing ArcInfo databases which include coverages
of model supporting parameters such as hydraulic conductivity, land use, soil
type, etc. can be used to develop the conceptual model and provide the
parameter values necessary to drive the analytical model.
Introduction
The Engineering Computer Graphics Laboratory (ECGL) of Brigham Young
University in cooperation with the U.S. Army Engineer Waterways Experiment
Station (WES) in Vicksburg, Mississippi has developed a suite of
applications for environmental, hydraulic, and hydrologic simulation. These
applications include the Dept. of Defense Groundwater Modeling System (GMS),
the Surface water Modeling System (SMS), and the Watershed Modeling System
(WMS). All three systems include a set of modeling codes along with
extensive grid and mesh generation utilities and sophisticated
post-processing and visualization tools in both two and three dimensions.
The vast majority of modeling codes are based on either the finite
difference or finite element approach. Traditionally, most programs
designed for pre-processing of these types of models require the user to
construct a computational grid that encompasses the problem domain. The
user then selects nodes or cells in the grid to assign model parameters such
as boundary conditions and material properties. The problem with this
approach is that is often requires extensive effort to enter the data and if
significant modification is required, the data entry process must be repeated.
In light of the limitations inherent in traditional pre-processing
applications, the ECGL and WES have developed a new approach within GMS,
SMS, and WMS for model development and pre-processing. With the new
approach, a high-level representation of the model is constructed using an
ArcInfo data model consisting of points, nodes, arcs, and polygons. Model
parameters are assigned directly to the GIS entities as attributes. For
example, lakes are represented as polygons, rivers are represented as arcs,
wells are represented as points, etc. This model is constructed
independently of the numerical grid and is referred to as a "conceptual
model". Once the conceptual model is developed, a mesh or grid is
automatically constructed to fit the conceptual model and all of the model
parameters are "transferred" to the proper cells or elements. The
advantage of the conceptual model approach is that it greatly simplifies
model creation and if the user modifies the conceptual model, a new
computational model can be constructed in seconds. Since the data model
utilized in GMS, WMS, and SMS is patterned after the ArcInfo data model,
conceptual models and attributes can be shared freely between the three
applications and ArcInfo or ARCVIEW.
Model Definition
The data model chosen for development of a conceptual model, model building
approach was patterned after the ArcInfo data model. This data model uses
points, arcs, nodes, and polygons to represent spatial information (Figure 1).
Figure 1. Illustration of the ArcInfo Data Model
Points are used in the conceptual modelling approach to represent objects
such as wells, drop inlets, watershed confluences or locations where
bathymetry has been sampled. Points can be created inside of GMS, SMS, or
WMS, or imported from GIS file.
Arcs are used to represent linear objects such as rivers, canals, streets,
or polygon boundaries. Arcs may also be used to define ridges and other
important linear features which need to be preserved in the final model
topology.
Polygons represent areal data such as model boundaries, lakes, or zones
defining different soil types. Besides being used as a conceptual model
for creating the mesh or grid, separate coverages of soil type, or other
paramaters can be created and used for definition of model input parameters.
Sets of points, arcs, and polygons can be grouped into layers or "coverages".
Each coverage represents a particular set of data. A set of coverages provides
a complete description of the conceptual model.
Since the ArcInfo data model has been adopted for the creation of conceptual
models, data can easily be exchanged with ArcInfo. Existing GIS databases
can be used to set up and define analytic models, and once a final solution
has been obtained result can be exported back to the GIS database.
Digital Images
Although GIS objects can be created by digitizing a map with a traditional
digitizing tablet, a more convenient approach is to create them directly within
the modeling software using on-screen digitizing. This is accomplished by
importing a digital image to the modeling software in the form of a TIFF image.
The image could represent a scanned map or an aerial photograph of the site to
be modeled. The user identifies three points on the map where the world
coordinates are known. These three points are then used to stretch or map the
image from image coordinate space to world coordinate space when the image is
drawn on the screen. Using the map as a background, the user can then quickly
and accurately construct the objects defining the conceptual model.
Model Conversion
Once a conceptual model is defined, it must be converted to a numerical model.
This process varies based on the type of numerical model to be generated.
Finite Element Meshes
For finite element models, a meshing algorithm called adaptive tessellation is
used to generate a mesh which honors the conceptual model (Figure 2). The
model domain which will be meshed is defined by a set of polygons and arcs, each
polygon representing a different zone of the modelling domain. Additional
arcs and points in the interior of the model may be defined that represent
important features which must be preserved in the mesh. Mesh density
parameters are assigned to the arcs and points.
The adaptive tessellation algorithm generates a mesh of triangular elements.
The mesh lies within the model domain and interior edges of the conceptual
model are honored by the finite element edges. The mesh can automatically be
refined around features where high gradients are expected.
Figure 2a. GIS Objects Used for the Adaptive Tessellation Algorithm.
Figure 2b. Resulting Mesh.
Once the mesh is generated, boundary conditions associated with the feature obje
cts are automatically assigned to the appropriate nodes and elements and paramet
ers such as bathymetry are automatically interpolated.
Finite Difference Grids
Finite difference grids are constructed from feature objects by creating points
at key locations in the model and assigning grid refinement data to the points.
Refinement data guide the positioning of the cell rows and columns and include
whether the point should coincide with a cell center or cell boundary, the row
and column width at the point, and a bias term defining how the row and columns
vary from one row or column to the next moving away from the point. Once the
refine points are defined, a grid is constructed which just surrounds the
model. The cells which are outside the model domain are made inactive and the
cells which are inside the model domain are made active.
Once the grid is constructed, the attributes defined by the points, arcs, and
polygons are overlaid with the grid cells and cell-by-cell parameters needed
by the numerical model are automatically assigned to the appropriate cells.
Applications
The conceptual model approach to environmental/hydraulic/hydrologic modeling
has been successfully implemented in three modeling applications: the Department of
Defense Groundwater Modeling System (GMS), the Surface water Modeling System
(SMS), and the Watershed Modeling System (WMS). Each of these systems was
developed through a partnership between the U.S. Army Engineer Waterways
Experiment Station (WES) and the Brigham Young University Engineering Computer
Graphics Laboratory. The systems have been designed with a consistent
interface. Thus, users can transfer data between the systems and learn to use
all three systems with ease.
Map Module
The interfaces of the GMS, SMS, and WMS are designed in a modular fashion. The
user can switch from one module to the next by clicking on the module's icon.
The menu commands and tools presented to the user switch as the module is
switched. The conceptual modeling tools described in this paper were
implemented by adding a new module to each of the three systems called the
"Map Module." The Map Module contains tools for creating GIS objects and
assigning attributes to the objects. The module also contains tools for
importing digital images for on-screen digitizing and importing CAD drawings
from DXF files for background display. A simple set of drawing tools is also
provided for adding annotation to a model.
The Surface water Modeling System (SMS) is a graphical pre- and post-processor
for a variety of 1D, 2D, and 3D surface water models (Jones et al., 1995). The
system currently supports only finite element models, but boundary fitted finite
difference models will be supported in the coming year.
An example application of the conceptual model approach in SMS is shown in
Figure 3. A TIFF image of a potential modeling site is shown in Figure 3a. The
TIFF image allows the conceptual model to be built using on-screen digitization.
The completed conceptual model, shown in Figure 3b, includes a set of
arcs/polygons defining different regions of the model.
The model domain, which is to be simulated with a finite element mesh, is
covered with a set of polygons. Each polygon represents a region of the model
which has a unique value of Manning's n or eddy viscosity. Boundary conditions
are defined on the perimeter of the model using arcs. The bathymetry of the
model is defined by interpolating from a set of points which were digitized
from a bathymetric map. The smaller channel will be modelled with one-
dimensional elements whereas the polygonal regions will be filled with a set
of two-dimensional triangular elements.
The numerical model generated from the conceptual model is shown in Figure 3c.
The arcs defining the smaller channel feeding into the primary domain are
converted to one-dimensional elements. Each of the polygons in the primary
model domain have been meshed and the boundaries between the zones have been
preserved. After the meshing is complete, the boundary conditions and
material properties are automatically assigned and the bathymetry is
interpolated from the scatter points.
Figure 3a. TIFF Image Used in Defining Arcs and Polygons.
Figure 3b. Completed Conceptual Model.
Figure 3c. Finite Element Mesh Generated from Conceptual Model.
The Department of Defense Groundwater Modeling System (GMS) is a comprehensive
multi-dimensional groundwater modeling environment (Holland, 1992; Jones, et
al., 1994). The system consists of a suite of groundwater models and a
graphical user interface for pre- and post-processing. GMS supports surface
modeling with triangulated irregular networks (TINs), borehole data, solid
modeling, 2D and 3D finite element models, 2D and 3D finite difference models,
and 2D and 3D geostatistics. The groundwater models supported include MODFLOW,
MT3D, MODPATH, and FEMWATER.
An application of the conceptual model approach within GMS is shown in Figure 4.
Figure 4a. Conceptual Model for a Groundwater Model.
Figure 4b. Numerical Model.
Figure 4c. Computed Heads from Groundwater Model.
The GIS objects defining the conceptual model are shown in Figure 4a. These
objects were created by on screen digitizing with a digital map of the site
displayed in the background. The map is a portion of a U.S. Geological Survey
Quadrangle Map which was scanned with a standard desktop scanner. The
conceptual model consists of three coverages: a coverage defining the locations
of the sources/sinks and the boundary of the model (the coverage shown in
Figure 4a), a coverage defining the recharge zones, and a coverage defining the
zones of hydraulic conductivity. The bottom elevations of the aquifer were
interpolated from a set of scattered observation points.
The MODFLOW numerical model produced by the conceptual model is shown in
Figure 4b. The model consists of a single unconfined layer. The grid is
automatically refined in the vicinity of the wells and the cells outside the
domain of the model have been inactivated. The wells, drains, and specified
head boundaries have been superimposed on the grid and assigned to the
appropriate cells. In the case of the drains, the length of the drain segment
overlying each cell is computed and used to calculate an appropriate
conductance term. The entire model conversion process is fully automated and
takes only seconds.
Finally, the computed solution for the model in Figure 4a&b is shown in Figure
4c. Once a solution is computed, the values of the boundary conditions and
model parameters can be adjusted in the conceptual model, and the values can
be converted to the numerical model in seconds and a new solution can be
computed. Thus, the conceptual model approach can simplify the calibration
phase as well as the initial model creation phase.
The Watershed Modeling System (WMS) is a comprehensive environment for
hydrologic modeling (Nelson, et al., 1995). WMS can be used to automatically
delineate watersheds and subbasin boundaries from digital elevation models
(DEMs). U.S. Geological Survey DEM data can be downloaded from the Internet
for any location in the U.S. In some cases, a digital image of the map in
TIFF format is also available and can be used to aid in the creation of a
conceptual model.
An example application of the conceptual model approach within WMS is shown in
Figures 5a-c below.
Figure 5a. Conceptual Model Defined in WMS.
Using a TIFF image of the site in the background, the stream network a
nd the approximate boundary for a watershed are digitized (Figure 5a). The
streams are represented with arcs and the model boundary is represented with a
polygon. In some cases, lakes are represented in the interior of the model
using polygons. Arcs may also be used to define canals, railroads, streets, or
other urban features which tend to act like streams during a rainfall/runoff
event.
Using the rough boundary and stream network defined in the conceptual model,
WMS creates a Triangulated Irregular Network using the adaptive tessellation
algorithm described above. The boundary defines the TIN extents, and stream
and ridge arcs are enforce in the TIN as breaklines. This ensures that triangle
edges will be enforced along all streams and ridges. A stream is creating
from the triangle edges underlying stream arcs and elevations of the TIN
vertices are generated by interpolating from a background elevation map such
as a DEM or TIN. Once the TIN has been constructed, precise basin boundaries
are computed for the watershed (Nelson, et al., 1994). In Figure 5b the red
area on the exterior of the model represents portions of the TIN outside the
actual watershed boundary. Subbasins are created by placing additional
outlets at selected locations along the stream network. Figure 5b also shows
the individual triangl facets of the TIN that are created during the adaptive
tessellation process.
Figure 5b. Delineated Subbasins in WMS.
In addition to the stream and watershed boundary, other watershed data are
represented using GIS coverages. A coverage defining land use polygons and a
coverage defining soil type polygons can also be generated in WMS or imported
from a GIS such as ArcInfo. These two coverages are combined to compute a
composite SCS curve runoff number for each basin.
Once the basins have been defined, geometric attributes including stream
lengths, stream slopes, basin areas, basin slopes, maximum draining distance
within a basin, etc. are automatically computed from the TIN model. These
attributes are combined with the runoff numbers and set of user-defined data
including rainfall intensity to generate a complete set of input for a runoff
model. Several runoff models are supported in WMS included the lumped
parameter models HEC-1, TR-20, the Rational Method, and NFF, and both finite
element and finite difference distributed models. A sample solution for the
watershed model shown in Figures 5a&b is shown in Figure 5c. In this figure
the triangles exterior to the watershed boundary have been removed and areas
are shown in acres.
Figure 5c.Computed Hydrograph for Watershed in WMS.
As with the other models, if any changes that need to be made to the input
data during the iterative calibration stage can be made to either the
conceptual model or the numerical model, whichever is most convenient.
Using the Conceptual Model Approach with Three-Dimenstional Models
To this point, the conceptual models have been primarily two-dimensional.
However, a fully three-dimensional conceptual model based system is also being
developed for groundwater applications. In this case, the stratigraphy is
represented using boundary representation solid models constructed from
borehole data (Jones & Wright, 1993). The boundary conditions and material
properties are assigned directly to the solids. Once the conceptual model is
defined, three-dimensional grid or mesh-based models are generated directly
from the solids. In the case of finite element meshes, a three-dimensional
version of the adaptive tessellation algorithm is used to automatically
generate a tetrahedral finite element mesh.
Conclusions
There are three principal advantages of the conceptual model approach. First
of all, generation of the numerical model is much more efficient. The modeler
can focus on high level representations of the site rather than on a
discretized representation of the site. Thus, data entry is greatly
simplified. The second advantage of the conceptual model approach is that the
overall modeling process is enhanced. If a calibration attempt fails and a
modification of the conceptual model is needed, the modification can be made
and a new numerical model can be immediately generated. This makes it
possible to evaluate numerous candidate conceptual models quickly and cheaply.
As a result, the final model is much more accurate. Finally by patterning
the data structure of the conceptual model after the ArcInfo data model, input
data can be shared more easily between a GIS and the pre/post-processing
system.
Acknowledgements
Much of the work described herein results from research sponsored by the
Waterways Experiment Statition, and the Federal Highways Administration.
Their involvement is acknowledged and greatly appreciated.
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E. James Nelson Ph.D.
Engineering Computer Graphics Laboratory
Brigham Young University
Department of Civil and Environmental Engineering
300 CB
Provo, Utah 84602
jimn@byu.edu