Gao Calvin

Environ Geol (2008) 54:945–956 DOI 10.1007/s00254-007-0897-1

ORIGINAL PAPER

Sinkhole hazard assessment in Minnesota using a decision tree model Yongli Gao Æ E. Calvin Alexander Jr

Received: 31 December 2005 / Accepted: 23 March 2007 / Published online: 18 July 2007 Ó Springer-Verlag 2007

Abstract An understanding of what influences sinkhole formation and the ability to accurately predict sinkhole hazards is critical to environmental management efforts in the karst lands of southeastern Minnesota. Based on the distribution of distances to the nearest sinkhole, sinkhole density, bedrock geology and depth to bedrock in southeastern Minnesota and northwestern Iowa, a decision tree model has been developed to construct maps of sinkhole probability in Minnesota. The decision tree model was converted as cartographic models and implemented in ArcGIS to create a preliminary sinkhole probability map in Goodhue, Wabasha, Olmsted, Fillmore, and Mower Counties. This model quantifies bedrock geology, depth to bedrock, sinkhole density, and neighborhood effects in southeastern Minnesota but excludes potential controlling factors such as structural control, topographic settings, human activities and land-use. The sinkhole probability map needs to be verified and updated as more sinkholes are mapped and more information about sinkhole formation is obtained. Keywords Decision tree model
Sinkhole probability
Karst feature database (KFD)
Knowledge discovery in

Y. Gao (&) Department of Physics, Astronomy and Geology, East Tennessee State University, Johnson City, TN 37614, USA e-mail: [email protected] E. C. Alexander Jr Department of Geology and Geophysics, University of Minnesota, 310 Pillsbury Dr., SE, Minneapolis, MN 55455, USA e-mail: [email protected]

database (KDD)
Nearest neighbor analysis (NNA)
Minnesota

Introduction An understanding of what influences sinkhole formation and the ability to accurately predict sinkhole hazards is critical to environmental management efforts in the karst lands of southeastern Minnesota. Several regression analyses and mathematical models have been conducted to assess sinkhole hazards and develop sinkhole probability maps. Matschinski (1968) treated sinkholes as points and did not consider their dimensions and orientations. LaValle (1967, 1968) investigated the sinkhole morphology in south central Kentucky. Multiple regression analyses were used to study the relationships among drainage systems, karst relief, structurally aligned depressions, limestone density index, insoluble residue content, flank slope, and bedding thickness. However, despite his elegant statistical arguments, his conclusions are not convincing and Williams (1972) criticized some of his geomorphic assumptions. For instance, the karst relief ratio seems insufficient as a measure of hydraulic gradient. Williams (1972) emphasized that a firm geomorphic foundation is necessary prior to morphometric studies. McConnell and Horn (1972) tested several hypotheses about sinkhole development. These hypotheses included Poisson models (single random process), Negative Binomial models (contagious process), and Mixed Poisson models (two mutually independent random processes). The Mixed Poisson models fitted the sinkhole data in Mitchell Plain of southern Indiana. McConnell and Horn (1972) interpreted this fit in terms of two mutually independent random processes of ‘‘cavern roof collapse’’ and ‘‘corrosion’’ for sinkhole development.

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Palmquist (1977) demonstrated that the major control on doline density is the amount of groundwater recharge in three counties of northern Iowa by using regression analyses. According to Kuhns et al. (1987), a loose zone of mixtures of sand, silt and clay was a possible indicator of ongoing sinkhole activity in Maitland, Florida. Upchurch and Littlefield’s (1987) moving-average analyses and chisquare tests showed that ancient sinkholes in bare karst areas of twelve 7.5’ quadrangles in Hillsborough County, Florida, could significantly predict the locations of modern sinkholes. Veni’s (1987) research showed that fracture permeability should be considered when assessing the sensitivity of a karst area to human development based on a survey of over 300 caves and sinkholes in the southeastern corner of Edwards Plateau, Texas. GIS based models have been widely used for decisionmaking on sinkhole hazard analysis in the last decade (Gao and Alexander 2003). Whitman and Gubbels (1999) demonstrated the importance of hydrostatic loads in sinkhole hazard, and this information can then be used to construct predictive models of sinkhole hazard. Lei et al. (2001) investigated sinkhole distributions based on factors such as types of carbonate rock, the geomorphologic settings, hydrogeologic conditions, human activities, and land use. All factors were digitized as corresponding GIS coverages and processed in a grid-based IDRISI GIS system. A series of grid-based relative risk maps of sinkhole hazard were developed for four cities, Tangshan, Xiangtan, Yulin, and Liupanshui in China (Lei et al. 2001). Jiang et al. (2005) expanded the sinkhole hazard assessment to a national scale and applied analytic hierarchy process (AHP) to develop a relative sinkhole risk map in China. Zhou et al. (2003) conducted orientation analysis of sinkholes along I-70 highway near Fredrick, Maryland and demonstrated

Fig. 1 Minnesota Karst lands. This map overlays the areas with <50 ft (15 m), 50–100 ft (15–30 m), and >100 ft (30 m) of surficial cover over the areas underlain by carbonate bedrock. This map emphasizes the patchy nature of the thick sediment cover and the importance of site-specific information for land-use decisions

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that orientations of sinkhole pairs correspond to regional and local structures.

Minnesota karst and sinkhole distribution Southeastern Minnesota is part of the Upper Mississippi Valley Karst (Hedges and Alexander 1985) that includes northwestern Illinois, southwestern Wisconsin, and northeastern Iowa. Karst lands in Minnesota are developed on Paleozoic carbonate and sandstone bedrock. Most surficial karst features such as sinkholes, stream sinks, springs, and caves are found only in those areas with less than 50 ft (15 m) of sedimentary cover over bedrock surface (Fig. 1). Data sources for bedrock geology and depth to bedrock geology in southeastern Minnesota are listed in Table 2. Figure 2 shows significant sandstone karst developed in Pine County (Shade 2002). Much of the scientific karst literature (Davies and Legrand 1972; Dougherty et al. 1998; Troester and Moore 1989) has focused on other parts of the country and world and few scientific descriptions of the Upper Mississippi Valley Karst exist. Nevertheless, the karst lands of southeastern Minnesota present an ongoing challenge to environmental planners and researchers and have been the focus of a series of research projects and studies by researchers for more than 30 years (Giammona 1973; Wopat 1974). Gao et al. (2001) divided the sinkholes in southeastern Minnesota into three karst groups: Cedar Valley Karst (Middle Devonian), Galena/Spillville Karst (Upper Ordovician/Middle Devonian), and Prairie du Chien Karst (Lower Ordovician). Gao et al. (2005) revised the classification to Prairie du Chien Karst (Lower Ordovician, closest to Mississippi river valley), Galena-Maquoketa

Environ Geol (2008) 54:945–956

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Fig. 2 Sandstone Karst in Pine County. The red triangles are mapped sinkholes that indicate a sandstone karst area developed in the Mesoproterozoic Hinckley Sandstone. Pine County is in east central Minnesota, about 100 miles north of Twin Cities (data sources: Boerboom 2001; Shade et al. 2001)

Karst (Upper Ordovician) and Devonian Karst (the most distant from Mississippi river valley) based on more recent sinkhole and bedrock distribution in southeastern Minnesota and northwestern Iowa. Figure 3 shows the three bands of sinkholes distributed in these three karst groups. All analyses of sinkhole distribution in southeastern Minnesota reveal that sinkholes in Minnesota tend to be clustered at a regional scale (Gao et al. 2002; Magdalene and Alexander 1995). Gao et al. (2005) studied sinkhole distribution in Minnesota at different scales using nearest neighbor analysis (NNA). The sinkhole distribution pattern changes from clustered to random to regular as the scale of the analysis decreases from 10–100 km2 to 5–30 km2 to 2– 10 km2. The distribution of distance to the nearest neighbor (DNN) within the sinkhole plains of Fillmore County fits a lognormal distribution (Gao et al. 2005). Isolated sinkholes occur more often in Prairie du Chien Karst (Gao et al. 2002) compared to sinkholes in Devonian Karst and Galena-Maquoketa Karst. Sinkhole probability maps have been developed for southeastern Minnesota in Winona County (Dalgleish and Alexander 1984), Olmsted County (Alexander and Maki 1988), Fillmore County (Witthuhn and Alexander 1995), and Goodhue County (Alexander et al. 2003). A Karst Hydrogeomorphic Unit map, which includes known karst features has been developed for Mower County (Green et al. 2002a, b). These mapping efforts occurred during the time period that digital GIS technology was introduced and became an integral part of geologic mapping in Minnesota. As part of the transition of this mapping effort into a digital GIS environment, a decision tree model is created to

quantify the map-making process to reduce the potential for subjective biases for developing sinkhole probability maps. A revised map of relative sinkhole risk in Fillmore County (Gao and Alexander 2003) was constructed by implementing a decision tree model in a GIS system. This paper describes the expansion of the Fillmore County sinkhole hazard assessment to southeastern Minnesota using the decision tree model. The resulting regional sinkhole probability map includes Fillmore, Goodhue, Mower, Olmsted, and Wabasha Counties where relatively complete sinkhole datasets exist.

Knowledge discovery and decision tree model Spatial data mining aims at discovering spatial patterns embedded in large spatial databases (Shekhar and Chawla 2002). The goal of Knowledge Discovery in Database (KDD) is to extract knowledge from data in the context of large databases (Fayyad et al. 1996). Machine learning is one of the most popular methods for both KDD and spatial data mining. Machine learning was originally developed in the field of artificial intelligence and became an important approach in data mining in the 1990s. The process of machine learning allows systems to learn and improve with experience (Mitchell 1997). Most machine learning models use inductive inference to predict the overall system from a set of training examples. Decision tree learning is one of the most widely used methods for inductive inference (Mitchell 1997; Winston 1992). Decision trees are constructed from top-down, divide-and-conquer strategies that

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Fig. 3 Sinkhole distribution and bedrock geology in southeastern Minnesota. Notice the three bands of karst development that are arranged parallel to the Mississippi River: Prairie du Chien Karst (Lower Ordovician), Galena-Maquoketa Karst (Upper Ordovician) and Devonian Karst

partition sets of objects into smaller subsets along with the growth of the tree (Quinlan 1990). The structures of decision trees include series of tree nodes and branches. Decision trees have three types of nodes: (1) root nodes that have no incoming braches; (2) internal nodes that connect with one incoming branch and two or more outgoing branches; and (3) leaf nodes that have one incoming branch and no outgoing branches. Each non-leaf node is associated with attribute values of the database. A test condition will be made for each non-leaf node to partition the data set (Tan et al. 2005). The leaf node represents the classification of the decision tree model. Figure 4 illustrates how to classify sinkhole probability using a decision tree model. For example, the root node at the top is associated with the test condition of bedrock formation in southeastern Minnesota. The karst dataset is then partitioned into two sets of data. Areas on top of bedrocks that are older than Ordovician or younger than Devonian can be classified as no probability area since no sinkholes have been found in those areas. This classification is represented as the first leaf node of the decision tree, ‘‘no sinkhole probability’’. Areas underlain by bedrocks in Ordovician or Devonian will be further tested down the decision tree to define other sinkhole probability areas.

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Model implementation Based on the available karst feature data stored in the Karst Feature Database (KFD) of Minnesota, the primary controls on sinkhole development are stratigraphic position or bedrock geology and the thickness of surficial cover over bedrock surface. Major secondary controls appear to be structural geology such as joints and position in the landscape. However, the majority of the sinkhole population tends to form in highly concentrated zones. Neighborhood

Root Node

B e d r o ck U n it s

Below CJDN or Above DCUU N o S i n kho l e probabilit y

Between CJDN and KRET

Depth to Bedrock

≥ 50 ft. (15m)

< 5 0 ft . ( 1 5 m )

Int ernal Nodes

Le af N o d e s Low probability

B e d r o c k U ni t s

Fig. 4 The structure of a decision tree to classify sinkhole probability in southeastern Minnesota (See Table 1 for the sequence of bedrock units)

Environ Geol (2008) 54:945–956 Fig. 5 Decision Tree model for sinkhole probability map in southeastern Minnesota (See Table 1 for the sequence of bedrock units)

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Bedrock Units Between CJDN and KRET

Below CJDN or Above DCUU No sinkhole probability

D e p t h t o B e d r oc k

≥ 50 ft.(15 m)

< 50 ft. (15 m) Bedrock Units

L o w p r o b ab i li ty

Karst Bedrock DCLC, ODPG, or OGCM Sinkhole Density L o w p r o b a b i l i ty

≥ 1/km2

< 1/km2

Bedrock Units

Low to moderate probability OPDC o r OSTP

OGPR – OMAQ, DSPL, DCLP, DCUM, or DCUU

Dist. to Nearest S i n kh o le

Dist. to Nearest S in k h o le

≥ 700 m M ode rate t o hig h prob ab ili ty

effect plays a very important role in sinkhole distribution and formation (Gao and Alexander 2003). Based on the sinkhole distribution of distances to the nearest sinkhole, sinkhole density, bedrock geology and depth to bedrock in southeastern Minnesota and northwestern Iowa, a decision tree model has been developed to construct sinkhole probability maps. This model quantifies bedrock geology, depth to bedrock, sinkhole density, and neighborhood effects in southeastern Minnesota but does not include potential controlling factors such as structural control, topographic settings, human activities and land-use. The mean and standard deviation of DNN were used to define boundaries for extended NNA and sinkhole probability modeling (Gao and Alexander 2003). According to Gao (2002), 95% of Devonian sinkholes and 99% of the Galena-Maquoketa sinkholes are less than 400 m away to their nearest neighbor; 70% of Prairie du Chien sinkholes are less than 700 m away to their nearest neighbor. Therefore, 400 and 700 m were used to define concentrated sinkhole zones for the two highest sinkhole probability areas. The non-leaf nodes of the decision tree are associated with attributes such as bedrock geology, depth to bedrock, sinkhole density, and distances to the nearest sinkhole stored in the KFD of Minnesota. A test condition was conducted on each non-leaf node to partition the decision tree. By sorting down the decision tree from the top to the bottom recursively, the karst land of southeastern Minnesota can be classified into six probability areas which are represented by the leaf nodes of the decision tree (Fig. 5). Figure 6 is the cartographic model used to create reclassified karst areas in Goodhue, Wabasha, Olmsted, Fillmore, and Mower Counties. Bedrock geology and depth

< 700 m

Hig h p rob ab il it y

≥ 700 m

.

Mo de ra te to h igh pr o b ab il i t y

400 – 700 m

H i gh pr ob a bi lit y

< 400 m

Sinkhole plain

to bedrock coverages from each county were reclassified and merged to generate reclassified bedrock geology and depth to bedrock coverages in the five county areas. An intersection of reclassified bedrock geology and depth to bedrock coverages generates reclassified karst coverage in the five-county area. The karst areas were reclassified as non-carbonate, active karst, transition karst, and covered karst. Figure 7 represents the cartographic model to create a sinkhole probability map in Goodhue, Wabasha, Olmsted, Fillmore, and Mower Counties. This model first creates sinkhole buffer zones and densities. The sinkhole density and buffer zones were then intersected to generate a coverage including attributes of both buffer distances and sinkhole density. The final intersection of buffer zone, density, and reclassified karst areas is reclassified according to the decision tree model to construct the final sinkhole probability in the five-county area. The cartographic models illustrated by Figs. 6, 7 were implemented using ArcView GIS. The intermediate coverages were cleaned or built prior to proceeding to the next step to ensure correct topography and to reduce propagation errors (Gao and Alexander 2003).

Results Figure 8 is a draft of sinkhole probability map in Goodhue, Wabasha, Olmsted, Fillmore, and Mower Counties by implementing the decision tree model in ArcView GIS. Relative ‘‘Sinkhole risk’’ was used in the early attempt of sinkhole hazard assessment using decision tree model (Gao and Alexander 2003). However, the model did not capture

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Environ Geol (2008) 54:945–956 Bedrock Geology Goodhue Co.

Reclass

Grouped Bedrock Units Goodhue Co.

Bedrock Geology Wabasha Co.

Reclass

Grouped Bedrock Units Wabasha Co.

Bedrock Geology Olmsted Co.

Reclass

Grouped Bedrock Units Olmsted Co.

Bedrock Geology Fillmore Co.

Reclass

Grouped Bedrock Units Fillmore Co.

Bedrock Geology Mower Co.

Reclass

Grouped Bedrock Units Mower Co.

Intersect

Depth to Bedrock Goodhue Co.

Reclass

Grouped Depth to Bedrock Goodhue Co.

Build or Clean

Depth to Bedrock Wabasha Co.

Reclass

Grouped Depth to Bedrock Wabasha Co.

Depth to Bedrock Olmsted Co.

Reclass

Grouped Depth to Bedrock Olmsted Co.

Depth to Bedrock Fillmore Co.

Reclass

Grouped Depth to Bedrock Fillmore Co.

Depth to Bedrock Mower Co.

Reclass

Grouped Depth to Bedrock Mower Co.

Union

Build or Clean

Reclassified Bedrock Units Five Counties

Reclass

Union

Build or Clean

Reclassified Karst areas Five Counties

Reclassified Depth to Bedrock Five Counties

Fig. 6 Cartographic modeling flowchart to create reclassified karst areas in Goodhue, Wabasha, Olmsted, Fillmore, and Mower Counties. The reclassified karst areas are used to construct a sinkhole probability map for the five-county area

Reclassified Karst Areas Five Counties

Intersect

Buffer Sinkholes Five Counties Build or Clean

Build or Clean

Sinkhole Zones Five Counties Intersect

C on v e r t t o Calculate

Density Sinkholes Five Counties

Polygon Sinkhole Density Grid F i v e C o u n ti e s

Densities Five Counties

Build or Clean

Reclass

Sinkhole Probability Five Counties

Density and Buffer Zones Five Counties

Fig. 7 Cartographic modeling flowchart to create a sinkhole probability map in Goodhue, Wabasha, Olmsted, Fillmore, and Mower Counties

the detailed ‘‘risk’’ level in moderate to low ‘‘risk’’ areas. The term sinkhole probability is resumed for sinkhole hazard assessment in southeastern Minnesota. To be consistent with the published sinkhole probability maps in Winona, Fillmore, Olmsted, and Goodhue Counties, the sinkhole probability map includes six probability zones, NO SINKHOLE PROBABILITY, LOW PROBABILITY, LOW TO MODERATE PROBABILITY, MODERATE TO HIGH PROBABILITY, HIGH PROBABILITY, and

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SINKHOLE PLAINS. The descriptions of these probability areas are as follows: No sinkhole probability The only places where sinkholes cannot form are those areas where non-carbonate formations are the uppermost bedrock. Many of these areas are in deep river valleys in which erosion has removed all of the carbonate bedrock.

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Fig. 8 A partial sinkhole probability map in Goodhue, Wabasha, Olmsted, Fillmore, and Mower Counties

Low probability

Moderate to high probability

Areas underlain by carbonate bedrock or mixtures of carbonate and non-carbonate bedrocks where the boundaries are not clearly defined, but in which essentially no sinkholes were observed, are shown on the map as having low probability for sinkhole development. Some of these areas are slopes containing abundant evidence of past karst solution, such as caves and enlarged joints. If new sinkholes do form, they may not be noticed because of the rapid erosion of the down slope rim of the sinkhole and filling of the sinkhole with sediments.

Areas in which sinkholes are a routine part of the landscape. Sinkholes occur as diffuse clusters of three or more sinkholes. The minimum sinkhole density is 1 per square kilometer.

Low to moderate probability Areas underlain by carbonate rock covered with only a thin layer of surficial material, but containing only widely scattered individual sinkholes or isolated clusters of two or three sinkholes. The sinkhole density is less than one sinkhole per square kilometer. The expected future sinkhole development is generally low in these areas, but is moderate where small sinkhole clusters have developed. These areas of low to moderate probability are underlain by any of the carbonate bedrock units, but coverage by unconsolidated materials and soils is usually less than 50 ft (15 m). The near-surface carbonate aquifers in these areas are clearly karst aquifers, although the distribution of sinkholes within these units varies considerably. The presence or absence of sinkholes alone is not a sufficient predictor of susceptibility of the groundwater to contamination.

High probability Areas in which sinkholes are a common part of the landscape. The minimum distance to the nearest sinkhole is 700 m, and the minimum sinkhole density is 1 per square kilometer. New sinkholes periodically appear and many more are expected to form. These areas are usually near areas where sinkhole density exceeds 10 per square kilometer, but exhibit a noticeably lower density within the area or areas where sinkholes describe obvious visible trends, such as along fractures in the bedrock. Clusters of sinkholes may develop in response to local changes, such as fluctuation of the water table, construction of a building or water-retention facility, or hydraulic changes due to the formation or reactivation of isolated sinkholes. Sinkhole plains Areas in which sinkholes are the dominant landscape features. The minimum distance to the nearest sinkhole is 400 m, and the minimum sinkhole density is 1 per square kilometer. Essentially all of the precipitation that is not lost to evapotranspiration either infiltrates or runs into a

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Table 1 Lithostratigraphic codes and karst groups in southeastern Minnesota as used in spatial analysis and probability modeling (modified from Gao et al. 2005) Series

Group, formation, member

Unit symbol

Karst group

Middle Devonian

Lithograph city formation–Hinkle & Eagle Center Mbrs

DCUU

Devonian Karst

Chickasaw member–Spillville formation

DCUM DCLC

a

DCLP

Devonian Karst

DSPL Upper Ordovician

Maquoketa & Dubuque formations; Galena Group (Stewartville, Prosser and Cummingsville formations)

OMAQ

Galena-Maquoketa Karst

ODUB OGAL

OGSV OGPR OGCM

Lower Ordovician

Decorah Shale–Glenwood formations St Peter Sandstone

ODPG OSTP

Prairie du Chien Group (Shakopee and Oneota formations)

OPDC

b Prairie du Chien Karst OPSH OPOD

a The Devonian karst as defined above may need to be subdivided in future work b For map compatibility reasons, the map bottom of the Galena-Maquoketa karst in this paper is taken to be the Cummingsville/Prosser (OGCM/ OGPR) contact. The top two thirds of the Cummingsville formation is an active part of this karst, but does not contain many sinkholes

sinkhole. New sinkholes often appear. Sinkholes are a major problem for agriculture and prevent the cultivation of a significant fraction of many fields. Sinkhole collapse is a major, ongoing concern for roads and any structures or facilities.

Discussion This sinkhole probability map is mainly based on sinkhole distribution in Devonian and Galena-Maquoketa karst areas. The sinkhole distribution in the Prairie du Chien Karst is significantly different and may not be adequately described by this algorithm. A second problem in Prairie du Chien Karst is that these areas are not fully mapped. Sinkholes in Winona County were more intensively investigated and present more small clusters of sinkholes than the rest of Prairie du Chien Karst. As shown in Table 1, boundaries for karst areas, especially in Devonian Karst, are not well defined. Approximately 75% sinkholes concentrate in 3% of active karst areas in the Devonian Karst. Even for carbonate bedrock units, different counties may have different standards. For example, in Goodhue County, few sinkholes were observed in the Oneota Dolomite, the lower formation in the Prairie du Chien Group. However, in Olmsted County, Oneota Dolomite is not separated from the Prairie du Chien Group. Another problem associated with this sinkhole probability map is that the boundaries for bedrock geology and depth to bedrock are not accurately known. While some

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sinkholes exist outside of the active karst areas, they are near the boundary between active and non-active karst areas and this probably indicates that some errors exist in the bedrock geology and depth to bedrock maps. There are also major scale problems. The bedrock geology and depth to bedrock information was mapped at 1:100,000 scale and becomes increasingly inaccurate as the scale is increased (Table 2). Other analyses that were conducted to look for controlling factors of sinkhole distributions include searches for correlations with land surface slope, depth to bedrock, and bedrock dips. Slope values were derived from USGS 30 m DEMs for the locations of the sinkholes. Figure 9 shows the histogram of the slopes of the land at sinkhole locations in Olmsted County. The slopes on which 64 and 83% sinkholes are located in this county are less than 5° and 10°, respectively. The majority of the sinkholes are on relatively flat surface. No detailed correlation has been detected between sinkhole distribution and surface slope. The slope values derived from the 30 m DEM are not accurate enough in many areas in southeastern Minnesota due to the widely distributed river and stream valleys. This correlation need to be further tested when more accurate DEM data is developed. Correlation between sinkhole distribution and depth to bedrock is limited by the 50 ft (15 m) resolution of available depth to bedrock information and the absence of structural contour maps. Refined depth to bedrock and structural contour maps were attempted. Figure 10 shows the distribution of sinkholes and water wells used to obtain

Environ Geol (2008) 54:945–956 Table 2 Data sources for bedrock geology and depth to bedrock in southeastern Minnesota

953

County or multi-county area

Bedrock geology

Fillmore County

(Mossler 1995a)

(Mossler and Hobbs 1995)

Goodhue County

(Runkel 1998)

(Setterholm and Bloomgren 1998)

Houston County Mower County

(Runkel 1996) (Mossler 1998a)

(Runkel 1996) (Mossler 1998b)

Olmsted County

(Olsen 1988a)

(Olsen 1988b)

Rice County

(Mossler 1995b)

(Mossler 1995c)

Wabasha County

(Mossler 2001a)

(Mossler 2001b)

Steele, Dodge, Olmsted and Winona Counties

(Mossler 2004a)

(Mossler 2004b)

Seven-county metropolitan Twin Cities area

(Mossler and Tipping 2000)

(Mossler and Tipping 2000)

13 counties of south central Minnesota

(Water Resources Center 1999a)

(Water Resources Center 1999b)

original depth to bedrock information. A model was built in ArcView GIS to derive several depth to bedrock grids from 95% randomly selected water wells in Olmsted County using different interpolation methods (Gao 2007). The remaining 5% of the water wells were used to evaluate the accuracy of the different interpolation methods. A similar model was also constructed to calculate the bedrock dips in this county. These models were implemented in ArcView GIS and the results show that the depth to bedrock and bedrock dip are statistically acceptable in areas where water wells are highly concentrated. Unfortunately, the water wells are usually not drilled in areas where many sinkholes exist. Therefore, more accurate depth to bedrock and bedrock dips do not exist in areas of highly concentrated sinkholes due to the lack of water well data. Geophysical explorations such as seismic exploration, microgravity surveys, electrical resistivity, and ground penetrating radar (GPR) could be used to detect more accurate information about depth to bedrock and bedrock dips in selected areas with highly concentrated sinkholes.

Frequency

500 400

cumulative fraction

300 200 100 0 0

5

10 15 Slope

20

Depth to bedrock

Conclusions This decision tree model quantifies bedrock geology, depth to bedrock, sinkhole density, and distances to the nearest sinkhole in southeastern Minnesota but potential controlling factors such as structural control, topographic settings, human activities, and land-use are not yet built into the model due to the lack of data coverage. Compared with earlier, conventional versions of county scale sinkhole probability map, the decision tree model reproduces most of the important features seen on the original maps in the high density areas and has led to new insights about the internal structure of high density areas. However, the decision tree model is less successful in capturing the details of the lower density areas especially in Prairie du

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

More

Fig. 9 Histogram of the slopes of the land surfaces at sinkhole locations in Olmsted County

Fig. 10 Distributions of water wells and sinkholes in Olmsted County

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Chien Karst, where the subjective criteria are more significant and has no simple way of extrapolating across areas in which the sinkholes have not been mapped. This result confirms and expands Gao and Alexander’s (2003) conclusions with regard to the entire Minnesota data set. Even though the decision tree model defines some mathematical boundaries such as the minimum distance to the nearest sinkhole and minimum sinkhole density for relatively higher sinkhole risk areas, the sinkhole probability map developed using this model does not replace original county scale probability maps. Boundaries of the probability map developed for the five-county area need to be adjusted based on local karst feature distribution, detailed depth to bedrock, topographical setting, structural controls, human activities, and land-use. The sinkhole probability map needs to be verified and updated as more sinkholes are mapped and more information about sinkhole formation is obtained. Acknowledgements The decision tree model is built upon a database including karst feature data collected by a series of research and mapping projects by researchers for three decades. The karst feature locating and verification efforts of Scott Alexander, David Berner, Janet Dalgleish, Jeff Green, Sue Magdalene, Geri Maki, Ron Spong, Robert Tipping, Bev Shade, Betty Wheeler, Kathleen Witthuhn, and many karst workers and researchers are greatly appreciated. These research projects were supported by a series of grants and contracts from the Legislative Commission on Minnesota Resources via the Minnesota Geological Survey (MGS), Minnesota Department of Natural Resources (MnDNR) and the University of Minnesota Department of Geology and Geophysics and support from the Minnesota Department of Health (MnDH) and the Counties involved. We thank Professor Shashi Shekhar and research fellow Ranga Raju Vatsavai of the Department of Computer Science at the University of Minnesota, for sharing their ideas and experience of using decision tree model in spatial data mining.

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