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).

ArcInfo Data Model

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.

Conceptual Model

Figure 2a. GIS Objects Used for the Adaptive Tessellation Algorithm.

Mesh Created from Conceptual Model

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.

Surface Water Modeling System (SMS)

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.

TIFF Image

Figure 3a. TIFF Image Used in Defining Arcs and Polygons.

SMS Conceptual Model

Figure 3b. Completed Conceptual Model.

SMS Finite Element Mesh

Figure 3c. Finite Element Mesh Generated from Conceptual Model.

Groundwater Modeling System (GMS)

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.

GMS Conceptual Model

Figure 4a. Conceptual Model for a Groundwater Model.

GMS Numerical Model

Figure 4b. Numerical Model.

GMS Groundwater Solution

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.

Watershed Modeling System (WMS)

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.

WMS Conceptual Model

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.

WMS Delineated Subbasins

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.

WMS Computed Hydrographs

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.

References

Holland, J.P., (1992), "Development of a comprehensive system for remediation of contaminated groundwater," ASCE Water Forum 1992, Aug 3-5, Baltimore, Maryland, pp. 1178-1183.

Jones, Norman L. and Stephen G. Wright, (1993), "Subsurface characterization with solid models," ASCE Geotechnical Engineering Journal., Vol. 119, No. 11, November, pp. 1823-1839.

Jones, Norman L., D. R. Richards, and J. P. Holland, (1994), "The Department of Defense groundwater modeling system," Geotechnical Engineering News, Vol. 12, No. 2, June, pp. 41-44.

Jones, N.L., A.K. Zundel, & R.M. Wallace, (1995), "A comprehensive graphical environment for surface water flow modeling," Water Resources Engineering, Proceedings of the First International Conference, San Antonio, Texas, Aug. 14-18, Vol 1., pp. 405-409.

Nelson, E.J., N.L. Jones, and A.W. Miller (1994), "Algorithm for precise drainage-basin delineation," ASCE Journal of Hydraulic Engineering, Vol. 120, No. 3, pp. 298-312.

Nelson, E.J., N.L. Jones, and J.D. Jorgenson, (1995), "A comprehensive environment for watershed modeling and hydrologic analysis," Water Resources Engineering, Proceedings of the First International Conference, San Antonio, Texas, Aug. 14-18, Vol 1., pp. 829-833.


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