Gao Spatial Operation

Environ Geol DOI 10.1007/s00254-007-0896-2

ORIGINAL PAPER

Spatial operations in a GIS-based karst feature database Yongli Gao

Received: 31 December 2005 / Accepted: 2 April 2007
Springer-Verlag 2007

Abstract This paper presents the spatial implementation of the karst feature database (KFD) of Minnesota in a GIS environment. ESRI’s ArcInfo and ArcView GIS packages were used to analyze and manipulate the spatial operations of the KFD of Minnesota. Spatial operations were classified into three data manipulation categories: single layer operation, multiple layer operation, and other spatial transformation in the KFD. Most of the spatial operations discussed in this paper can be conducted using ArcInfo, ArcView, and ArcGIS. A set of strategies and rules were proposed and used to build the spatial operational module in the KFD to make the spatial operations more efficient and topographically correct. Keywords Karst feature database (KFD)
Single layer operation
Multiple layer operation
Map projection
Grid-based transformation

Introduction Manipulation of spatial data is an essential function in both GIS (Demers 1997) and spatial information systems (Laurini and Thompson 1992). Chou (1997) divided spatial operations in GIS into single layer and multiple layer operations. Barnett (1994) constructed a complex 8 · 8 spatial transformation matrix in a conceptual digital cartographic generalization model. The development, management, and data analyses of the Minnesota karst feature

Y. Gao (&) Department of Physics, Astronomy, and Geology, East Tennessee State University, Johnson City, TN 37614, USA e-mail: [email protected]

database are described in a series of papers (Gao et al. 2006; Gao and Alexander 2003; Gao et al. 2005a, b, c). This paper presents the spatial implementation of the karst feature database (KFD) of Minnesota in a GIS environment. Spatial operations were classified into three data manipulation categories: single layer operation, multiple layer operation, and other spatial transformation in the KFD. Single layer operations, also known as horizontal operations, apply to only one data layer and provide the most fundamental tools of data preparation for spatial analysis (Chou 1997). Single layer operations in the spatial operation module are divided into three categories: feature manipulation, feature selection, and feature classification. Feature manipulation changes the spatial features of a data layer. Feature selection identifies features by using spatial manipulation or logical expressions. Feature classification classifies features into groups. Multiple layer operations, also known as vertical operations, concurrently operate on more than one data layer (Chou 1997). Chou (1997) classified multiple layer operations into overlay, proximity, and spatial correlation analyses. In the KFD, proximity and spatial correlation analyses were built into the spatial analysis module. The multiple layer operations in the KFD include overlay, feature selection, and feature classification. Overlay operations manipulate different spatial data layers to generate combined spatial features according to logical connections between data layers (Chou 1997). Feature selection and feature classification operations are similar to those operations described in the single layer operations except that they operate on multiple layers. Other spatial transformations in the spatial operation module include digitization and map generalization, projection, and grid-based transformation. Digitizing and map generalization include operations about how to generate

123

Environ Geol

georeferenced coverages through on-screen and off-screen digitization, tabulated data, and scanned images. Transforming three-dimensional space onto a two-dimensional map is called ‘‘projection’’ (ESRI 1994). Map projection in the spatial operation module involves defining map projections for data layers and conversions between different types of map projections. In GIS and spatial information systems, spatial data are commonly represented by two different data models, vector and raster data models. Vector data model represents the points, lines, and areas of geographical space by exact X and Y coordinates. In the raster data model, space is represented as a continuous surface that is divided into grid cells. Most of the spatial operations discussed above focus on the vector data structure. Grid-based transformation includes operations involving one or more grid data layers. ESRI’s ArcInfo and ArcView GIS packages were used to analyze and manipulate the karst feature database management system (DBMS). Similar operations in other GIS packages may be different. Many other GIS packages have normally identical tools. The same tool in different GIS packages, even in ArcInfo and ArcView can give different results.

Single layer operations Single layer operations apply to only one data layer in GIS. GIS-based spatial operations implemented three kinds of single layer operations on the karst feature DBMS and related geological and geographic data layers. These operations are feature manipulation, feature selection, and feature classification. Feature manipulation Feature manipulation on a single GIS data layer usually changes the spatial objects in the data layer. Operations such as add, delete, move, split, eliminate, dissolve, and buffer were conducted on single data layers in the KFD.

edit mode, any selected objects can be deleted by pressing the delete key of the keyboard. Delete command can be used in Arc/Info to remove certain objects. Adding new spatial features in a data layer is straightforward in both ArcView and ArcInfo. Drawing tools can be used to draw different spatial objects in a georeferenced environment. Clicking the pointer tool once creates a point at the location of the pointer. A line segment, called arc in GIS, is a basic unit for both line and polygon coverage. The arc-node data model is widely used in modern GIS to represent and produce arcs and polygons. In this model, an arc is connected by two nodes, a start node and an end node, and zero or any number of vertices in between. The difference between a node and a vertex is that a node has topological meaning besides geographic coordinates. A polygon is an area connected and closed by individual line segments. In ArcInfo and ArcView, drawing a line segment can be done by double clicking at the starting point (the start node), single clicking a series of points (vertices), and double clicking at the last point (the end node). The vertices define the shape of a line segment. A polygon is added by continuously drawing a series of line segments and ending at the starting point to close the polygon. A node in a polygon is a start node of one line segment and an end node of the other. To be topologically correct, a polygon must be closed. All spatial objects can be moved easily if the data layer is in editing mode. Moving the nodes and vertices of a line segment or polygon can change the shapes and locations of these objects. Split and merge A split operation is conducted by drawing straight lines through existing line segments or polygons to split them. Any polygon or line segments through which the straight line passes would be split into smaller line segments or polygons. The merge operation is the opposite of split. It combines selected adjacent line segments or polygons to form a new longer line segment or larger areas.

Add, delete, and move Eliminate Any individual spatial object can be added, deleted, or moved from the GIS data layer. For instance, users can use the applications of karst feature DBMS built in ArcView GIS to add, delete, or move point features such as sinkholes, springs, and stream sinks in a GIS data layer or a GIS-based database. Any selected points, lines, and polygons can be removed from the data layer in an intuitive way in both ArcView and ArcInfo. For example, in ArcView GIS, if a data layer is in

123

The eliminate operation is commonly used to remove unwanted sliver polygons. Sliver polygons are very small polygons along the boundary of normal polygons. In many cases, they are invisible at normal scales. Sliver polygons may occur as a result of map overlay, mapjoin, or building topography after a map is digitized. In ArcInfo, the command ‘‘Eliminate’’ can be used to merge very small polygons with neighboring polygons that

Environ Geol

Fig. 1 Eliminating sliver polygons along the border between Fillmore and Olmsted Counties after their bedrock geology layers were combined as one single layer. a Before elimination. b The sliver polygons were eliminated

have the largest area. With the LINE option, ELIMINATE merges selected arcs separated by unwanted nodes (called pseudo nodes in GIS) into single arcs. The areas of sliver polygons are usually significantly smaller than normal polygons. They can be selected based on a threshold value of polygon areas. Any polygons with areas smaller than that threshold value can be selected and then removed from the polygon coverage. This procedure can be achieved in both ArcView and ArcInfo and is very effective to remove unwanted small polygons. Figure 1 illustrates the removal of sliver polygons along the bounder between Fillmore and Olmsted Counties after their bedrock geology layers were combined as one single layer. Dissolve The dissolve operation is used to eliminate unwanted boundaries between adjacent polygons, line segments, and regions to merge adjacent objects having the same value for a specified attribute. This operation can be used after multiple GIS coverages are joined or combined to eliminate

the boundaries between adjacent spatial objects having the same value for the identifying attribute. The dissolve operation can also be used to reclassify an existing layer based on a different classification attribute. Figures 2 and 3 illustrate that the original bedrock geology in Fillmore County was reclassified into three different bedrock groups: non-carbonate, Galena-Maquoketa, and Devonian. The boundaries between adjacent polygons belonging to the same group were eliminated using the dissolve operation in ArcView GIS. Buffer The buffer operation creates buffer zones around selected features based on the distances from these features. The input layer could be any feature type, but the results of buffer operations are polygon features. Users can specify the option to keep or to dissolve the boundaries among intersected buffer zones. The distances of buffer zones could be a constant distance or a series of equal distance zones. The equal-distance option can be used to investigate the relationship of a spatial occurrence and the proximity to a set of spatial features (Chou 1997). This operation is used to study sinkhole distribution and to construct sinkhole probability maps. Feature identification and selection Features in a single layer can be identified or selected using the graphical user interface (GUI) or logical expressions. Both ArcInfo and ArcView have GUI tools to identify or to select features in a single data layer. GUI tools can directly select features from the maps by moving the pointer to the features to be selected or to delineate an area to select all features falling in the delineated area. Logical expression such as Structured Query

Fig. 2 Bedrock geology in Fillmore County classified by bedrock formations (data source: Mossler 1995)

123

Environ Geol Fig. 3 Karst areas in Fillmore County generated by feature classification and the dissolving operation. Bedrock geology in Fillmore County was reclassified into three different bedrock groups and adjacent polygons belonging to the same group were combined using the dissolve operation

Language (SQL) is used in ArcView and ArcInfo to select features based on the values of specified attributes. Figure 4 shows a query expression used in ArcView GIS to select all sinkholes from the karst feature index layer. In addition, users can develop specific GUI tools for feature identification and selection. Some GUI tools were developed for the applications built on the karst feature DBMS to identify and select karst features in ArcView GIS. Feature classification Spatial data are usually classified for spatial analysis or modeling. A spatial data set can be classified into any number of classes. The fundamental issue in spatial feature classification is to determine the number of classes specified for a spatial theme. In a single data layer, feature classification can be specified based on field observation and scientific visualization, properties and distributions of the specified identifying attributes, and the purpose of the classification.

Figures 2 and 3 show that bedrock geology in Fillmore County can be classified into individual bedrock formations or into three major groups with each group including several bedrock formations. Note that some frequency distributions have conventional classification formula or methods. For instance, equal interval or equal frequency can be used to classify uniformly distributed features or variables. Mean and standard deviation are used to classify normally distributed attributes. A bimodal distribution can be classified into two groups. If the distribution of a feature shows a very complex pattern, that feature can be classified into several subclasses, and each subclass can be classified further based on its distribution within the subclass. This process can be repeated until the classes and subclasses are clearly defined. Feature classifications based on different attributes can also be superimposed to reach a final decision-making classification. For example, karst feature classification based on county and bedrock geology can be superimposed to generate karst groups for each county.

Multiple layer operations Multiple layer operations manipulate more than one data layer in a GIS. GIS-based spatial operations implemented three kinds of multiple layer operations on the karst feature DBMS and related geological and geographic data layers. These operations are overlay, feature identification and selection, and feature classification. Overlay

Fig. 4 Using a logical expression to identify or select features in ArcView GIS. The example above selects all sinkholes in the karst index layer

123

Overlay operations on multiple GIS data layers create combined or mutual-exclusive features from the input spatial features in different data layers. Operations such as union, identity, intersect, clip, erase, update, mapjoin, append, and edgematch were conducted on multiple data layers in the KFD.

Environ Geol

Union, identity, and intersect Union, identity, and intersect are the most commonly used overlay operations in ArcInfo. All three operations superimpose two GIS layers to compute the geometric intersection of the input and overlay coverages. The basic structure of these three operations can be represented as: Input theme þ overlay theme ¼ output theme The main difference among these three operations is the way in which spatial features from the input coverages are preserved. The output theme should have the same feature type as the input theme. For example, if the input theme is a polygon coverage, the result of the overlay operation will also be a polygon coverage. The output theme should contain attributes from both the input and the overlay themes. The overlay coverage should always be a polygon theme. The union operation generates a new theme containing the features and attributes of two polygon themes. All polygons from both coverages will be split at their intersections and preserved in the output coverage. The input theme for the union operation has to be a polygon coverage, therefore the output theme will be a polygon coverage as well. The intersect operation only preserves the portion of the input that falls inside the overlay theme. The input theme can be a point, line, or polygon coverage. The overlay theme’s features will split the input theme. The identity operation preserves all features of the input theme as well as those features of the overlay theme that overlap the input coverage. The input theme can be a point, line, or polygon coverage. The overlay theme’s features will split the input theme. Users need to select an appropriate operation, based on what they want to preserve in the output layer. Figure 5 illustrates the use of the union operation in combining active karst areas from different counties. Intersecting bedrock geology coverage and areas whose depth to bedrock is less than 50 ft (15 m) produced the active karst areas in each county. Clip, erase, and update These three operations extract, erase, or replace a portion of an input theme using selected or all features from a polygon theme. The input theme of clip and erase operations can be a point, line, or polygon coverage. The input theme of the update operation must be a polygon coverage. The clip operation extracts a portion of the input theme using a polygon theme as a ‘‘cookie cutter’’. For example, the Fillmore County outline can be used to clip the karst

Fig. 5 Generate a combined active karst area using the union and intersect operations. Active karst areas from different counties were combined together using the union operation. Active karst areas in each county were generated by intersecting bedrock geology coverage (Mossler 1995) and depth to bedrock coverage (Mossler and Hobbs 1995)

feature index coverage to generate all karst features in Fillmore County. The erase operation is the opposite of the clip operation. It erases features from the input theme that overlap with the erase polygon theme. For example, the Fillmore county outline can also be used to exclude all karst features from the karst feature index coverage that fall inside Fillmore County. Instead of extracting or erasing a portion of an input theme, the update operation replaces features from the input theme that overlap with the update polygon theme. Figure 6 illustrates the use of a newly developed bedrock geology map in replacing the southwestern corner of the bedrock geology map in the seven-county metropolitan Twin Cities area, Minnesota. Mapjoin, append, and edgematch Mapjoin and append operations combine adjacent coverages into one coverage. The main difference between mapjoin and append is that the mapjoin operation recreates topography but applies only to polygon themes. The append operation applies to point, line or polygon themes, but the topography needs to be rebuilt after the operation. Overlay operations discussed above apply to only two themes, an input theme and an overlay theme. Mapjoin and append operations can combine up to 500 coverages. Mapjoin and append operations can generate many errors and discontinuities and are usually followed by edgematch, dissolve, clean, and build operations to recreate a clean topography. The edgematch operation is used to

123

Environ Geol

Fig. 6 Updating the bedrock geology (Mossler and Tipping 2000) in the seven-county metropolitan Twin Cities area using the update operation. a Old bedrock geology map. b A new bedrock geology

map for the southwestern corner of the metropolitan area. c Updated bedrock geology after the update operation

align features along the edges of adjoining coverages. Figure 7 demonstrates that a gap along the Olmsted County border was aligned and merged using edgematch and dissolve operations. The resulting coverage combines 350 m buffer zones of sinkholes from different counties.

of sinkhole locations and bedrock geology or depth to bedrock boundaries.

Feature identification and selection Features from one GIS theme can be identified or selected based on their locations and relationships with other themes. For example, sinkholes falling outside of active karst areas can be selected to verify their locations and the accuracy of the active karst boundaries. Figure 8 is a portion of such a selection. The input theme is the sinkhole coverage and the identifying theme is the active karst theme in southeastern Minnesota. It first selects sinkholes falling inside the active karst areas and the selection is then switched to select sinkholes falling outside the active karst areas. The selected sinkholes are then converted to a separate coverage for verification

Fig. 7 The cleanup of appended coverages using edgematch and dissolve operations. a A gap along the Olmsted County boundary after combining the 350 m buffer zones of sinkholes from counties. b Filling the gap after edgematching. c Dissolving the boundary to merge the two polygons

123

Feature classification Features of one GIS theme can be classified based on its spatial relationships with other themes. For example, sinkholes can be classified based on the underlying bedrock geology. This can be done by spatially linking the sinkhole and the bedrock geology coverages and then classifying the sinkholes based on their bedrock formations.

Other spatial transformations Some spatial transformations need special procedures or data models different from those discussed in the single and multiple layer operations. These operations are digitizing and map generalization, projection, and grid-based transformation.

Environ Geol

can be registered and rectified in ArcInfo and then traced to generate a georeferenced coverage. Digitization and image tracing are techniques to convert cartographic maps into GIS coverages. Tabulated data can also be loaded into ArcInfo or ArcView and then converted into GIS coverages based on their geographic coordinates. Data stored in the KFD can be linked and converted into GIS coverages based on the karst feature’s Universal Transverse Mercator (UTM) coordinates. Map projection Fig. 8 Select sinkholes based on their spatial relationship to active karst areas. a Sinkholes on top of active karst. b Sinkholes falling outside of active karst areas were selected and then converted into a separate coverage

Digitizing and map generalization Digitizing and map generalization include operations on how to generate georeferenced coverages through onscreen and off-screen digitization, scanned images, and tabulated data. On-screen digitization can be done based on a feature’s relative location on a background map. Figure 9 shows that karst outcrops were digitized based on their locations on a registered topographic map in the Lewiston Quadrangle, Minnesota in ArcView GIS. The outcrops were originally mapped and drawn on U.S. Geological Survey (USGS) 1:24,000 topographic maps. Off-screen digitization can be done by connecting a computer to a digitizer. The map to be digitized is taped on the digitizer tablet and then registered and digitized from the digitizer. Scanned images

Transforming three-dimensional space onto a two-dimensional map is called ‘‘projection’’ (ESRI 1994). Many types of projections exist and different projections preserve different spatial characteristics such as area, azimuth, and distance. The different ways of projecting the spherical earth onto two-dimensional maps result in different distortions. The UTM and geographic projections are the two commonly used projections for the karst feature DBMS. During map projection, a spheroid that approximates the actual earth must be defined. Since North America has been surveyed many times in the past, many spheroids for the earth have been defined (ESRI 1994). Spheroids defined by North American Datum 1927 and 1983 (NAD27 and NAD83), and World Geodetic System 1984 (WGS84) are used on the karst feature DBMS. Map projection in the karst feature DBMS involves defining map projections for data layers and conversions between different types of map projections. The ArcView GIS does not have the capability to define or convert map projections. The command Projectdefine and Project in ArcInfo can be used to accomplish these operations. The following is a projection file associated with the Project command to convert a coverage from UTM NAD27 to UTM NAD83: input projection utm zone 15 datum nad27 parameters output projection utm zone 15 datum nad83 parameters end.

Fig. 9 Digitize karst outcrops on USGS 1:24,000 topographic maps in ArcView GIS. The outcrops were originally mapped and drawn on topographic maps. This example is from the Lewiston Quadrangle, Minnesota–Winona Co., 7.5 min series topographic map, 1974

Geographic Calculator, developed by Blue Marble Geographics (Bell 2000) was used as a coordinate conversion tool for the KFD. The Arctoolbox in ArcGIS (A new GIS package from ESRI that combines ArcInfo, ArcView, and many other tools and extensions) has the capabilities to define and to convert map projections for a

123

Environ Geol

GIS coverage through a graphic user interface (Tucker 2000). Projecting geographic data from one projection system to another system usually results in some errors. Projection errors in the karst feature DBMS generally can be omitted since the error of the location itself is much larger than the projection error. In order to maintain a spatially compatible database, the projections of all the karst feature data are defined as UTM NAD83. If a set of GIS data is systematically shifted to different locations, this may indicate that the projection definition for this set of data is wrong. This happened to the Winona data set in the karst feature DBMS. The data set was projected multiple times and the final projection was defined as UTM NAD83 instead of NAD27. The actual projection was UTM NAD27. The systematic error was corrected to project the data set from NAD27 to NAD83. Fig. 10 Generating a sinkhole density grid from the sinkhole coverage in southeastern Minnesota

A polygon coverage of shallow bedrock covert to shape file Smoothed shallow bedrock grid Boundary clean

Grid-based transformation Grid-based transformations include operations involving one or more grid data layers. Grid data can be converted into vector data and vice versa. Spatial relation types of vector data such as neighborhood statistics, distance to spatial feature, spatial density, and proximity analysis can be used to generate spatial analysis and convert the results of the analysis into a grid. The spatial analyst provides many GUI tools in ArcView GIS to manipulate and analyze grid-based data (Ormsby and Alvi 1999). Figure 10 is

Nibbled shallow bedrock

nibble small regions

Mask layer

Regions of shallow bedrock

set small regions to null Regions of shallow bedrock region group Shallow bedrock reselect (< 50 ft.) Depth to bedrock grid subtract

Surface DEM

Grid of Bedrock Topography topogrid Bedrock Topography

Fig. 11 Cartographic model flow chart to generate shallow bedrock coverage from bedrock topography

123

Fig. 12 Bedrock topography for the seven-county metropolitan Twin Cities area (data source: Mossler and Tipping 2000)

Environ Geol

area. The input layer is a line coverage of bedrock topography. Figure 12 is the original bedrock topography map and Fig. 13 is the depth to the bedrock grid. Figure 14 demonstrates the map query and map calculator tools used to execute processes from reselect to boundary clean as shown in the cartographic model (Fig. 11) to clean up the topography of the depth to bedrock grid. Figure 15 is the final polygon coverage of shallow bedrock.

Discussion

Fig. 13 Grid of depth to bedrock coverage for the seven-county metropolitan Twin Cities area

a sinkhole density grid generated from the sinkhole coverage in southeastern Minnesota in ArcView GIS. Grid-based transformations and analyses are usually combined with vector-based operations and analyses to extract useful information and generate desired coverages. Figure 11 shows a cartographic model flowchart that generates a shallow (less than 50 ft or 15 m) depth to bedrock coverage for the seven-county metropolitan Twin Cities

Most of the spatial operations discussed in this paper can be conducted using both ArcInfo and ArcView. ArcView is more user-friendly with many GUI tools and extensions. However, many spatial operations in ArcView GIS result in some node and intersection errors, many unnecessary nodes, and incorrect topography. These problems become more evident if complex data sets are involved in these operations. Compared with ArcView, ArcInfo is not as user friendly as ArcView, but usually generates cleaner topography and fewer errors. One approach using ArcView and ArcInfo is to use ArcView to preprocess the data and then use ArcInfo to correct errors and build topography. Users can use ArcInfo commands such as nodeerrors, labelerrors, intersecterr, generalize, clean, and build to correct ArcView processed coverages. Users can also use ArcInfo Macro Language (AML), ArcView Avenue scripts, and ArcView ModelBuilder to

Fig. 14 Map query and map calculator tools used to clean up the topography of the depth to bedrock grid

123

Environ Geol

Fig. 16 A working model built in ArcView GIS using ModelBuilder. This model builds several depths to bedrock grids from 95% randomly selected water wells in Olmsted County using different interpolation methods

3.

Fig. 15 Shallow bedrock coverage for the seven-county metropolitan Twin Cities area

automate a series of spatial operations. ArcView applications written in ArcView Avenue scripts for the karst feature DBMS automatically conduct many spatial and analytic procedures. Figure 16 is a working model built in ArcView using ModelBuilder tools. This model builds several depths to bedrock grids from 95% randomly selected water wells in Olmsted County using different interpolation methods. The model can be saved and modified for future work. For example, the remaining 5% of the water wells can be added to the model to evaluate the accuracy of the different interpolation methods. Any spatial model used in a GIS should be optimized to make the spatial operations more efficient and topographically correct. The following strategies are used to build spatial operational models in the karst feature DBMS: 1.

2.

If a model involves both single layer and multiple layer operations, single layer operations should be conducted as early as possible. This can reduce many errors and improve the performance of multiple layer operations. The topography of the result of any spatial operation should be cleaned and rebuilt. Many spatial operations result in many errors for the intermediate coverages and these errors can propagate into future operations. Some propagation errors are very hard to detect and may corrupt the GIS data and system if not detected and fixed earlier.

123

4.

The number of spatial features involved in any spatial operation should be minimized to exclude unnecessary features. Feature selection and classification are very useful approaches to limit the number of spatial features for a spatial operation. If attribute tables are also involved in a spatial operation, DBMS optimization techniques can be implemented to maintain data consistency. Combining DBMS’s query optimization and concurrency control techniques and GIS’s spatial operational optimization techniques can result in more efficient and robust spatial data models.

These strategies and techniques were used to build the DBMS and GIS applications for the karst feature DBMS. These rules and strategies were also enforced in the spatial operations for the spatial analyses and probability models of sinkhole distribution in Minnesota.

References Barnett ML (1994) Extending database management systems to support semantic information in geographic information systems. Ph.D. thesis, University of Minnesota Bell J (2000) Hands on: blue marble’s geographic calculator. Professional Surveyor 20 (11): http://www.profsurv.com/ archive.php?issue = 48&article = 674 (accessed 14 December 2006) Chou Y (1997) Exploring spatial analysis in geographic information systems. OnWorld Press, Albany, p 474 Demers MN (1997) Fundamentals of geographic information systems. Wiley, New York, p 486 ESRI (1994) Map projections: georeferencing spatial data. Environmental Systems Research Institute, Redlands Gao Y, Tipping RG, Alexander EC Jr (2006) Applications of GIS and database technologies to manage a karst feature database. J Cave Karst Stud 68(3):144–152

Environ Geol Gao Y, Alexander EC Jr (2003) A mathematical model for a sinkhole probability map in Fillmore County, Minnesota. In: Beck BF (ed) Sinkholes and the engineering and environmental impacts of karsts. Proceedings of the 9th multidisciplinary conference, Huntsville, Alabama, September 6–10, ASCE Geotechnical special publication, no. 122, pp 439–449 Gao Y, Alexander EC Jr, Barnes RJ (2005a) Karst database implementation in Minnesota: analysis of sinkhole distribution. Environ Geol 47(8):1083–1098 Gao Y, Alexander EC Jr, Bounk M, Tipping RG (2005b) Metadata development for a multi-state karst feature database. In: Beck BF (ed) Sinkholes and the engineering and environmental impacts of karst. Proceedings of the 10th multidisciplinary conference, San Antonio, Texas, September 24–28, ASCE Geotechnical special publication, no. 144, pp 629–638 Gao Y, Alexander EC Jr, Tipping RG (2005c) Karst database development in Minnesota: design and data assembly. Environ Geol 47(8):1072–1082

Laurini R, Thompson D (1992) Fundamentals of spatial information systems. Academic, San Diego, p 680 Mossler JH (1995) Bedrock geology. Geologic Atlas Fillmore County, Minnesota, County Atlas Series C-8, Part A, Plate 2 (1:100,000). Minnesota Geological Survey, University of Minnesota Mossler JH, Hobbs HC (1995) Depth to bedrock and bedrock topography. Geologic Atlas Fillmore County, Minnesota, County Atlas Series C-8, Part A, Plate 4 (1:100,000). Minnesota Geological Survey, University of Minnesota Mossler JH, Tipping RG (2000) Bedrock geology and structure of the seven-county metropolitan Twin Cities area, Minnesota. Miscellaneous map series, m-104 (1:100,000). Minnesota Geological Survey, University of Minnesota Ormsby T, Alvi J (1999) Extending ArcView GIS. Environmental Systems Research Institute, Redlands, p 527 Tucker C (2000) Using ArcToolbox: GIS by ESRI. Environmental Systems Research Institute, Redlands, p 105

123