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O R I G I N A L P A P E R

Sinkhole hazard assessment in Minnesota using a decisiontree model

Yongli Gao E. Calvin Alexander Jr

Received: 31 December 2005 / Accepted: 23 March 2007/ Published online: 18 July 2007

Springer-Verlag 2007

Abstract An understanding of what influences sinkhole

formation and the ability to accurately predict sinkholehazards 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 south-

eastern 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

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 anal-

yses 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 Wil-

liams (1972) criticized some of his geomorphic assump-

tions. 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.

Y. Gao (&)

Department of Physics, Astronomy and Geology,

East Tennessee State University,

Johnson City, TN 37614, USA

e-mail: gaoy@etsu.edu

E. C. Alexander Jr

Department of Geology and Geophysics,

University of Minnesota, 310 Pillsbury Dr.,

SE, Minneapolis, MN 55455, USA

e-mail: alexa001@umn.edu

123

Environ Geol (2008) 54:945956

DOI 10.1007/s00254-007-0897-1

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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 anal-

yses. 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 Littlefields (1987) moving-average analyses and chi-

square tests showed that ancient sinkholes in bare karstareas of twelve 7.5 quadrangles in Hillsborough County,

Florida, could significantly predict the locations of modern

sinkholes. Venis (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 decision-

making on sinkhole hazard analysis in the last decade (Gao

and Alexander 2003). Whitman and Gubbels (1999) dem-

onstrated the importance of hydrostatic loads in sinkhole

hazard, and this information can then be used to constructpredictive models of sinkhole hazard. Lei et al. (2001)

investigated sinkhole distributions based on factors such as

types of carbonate rock, the geomorphologic settings, hy-

drogeologic 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 de-

velop 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

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 includesnorthwestern Illinois, southwestern Wisconsin, and north-

eastern 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 partsof 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 Ordo-

vician/Middle Devonian), and Prairie du Chien Karst

(Lower Ordovician). Gao et al. (2005) revised the classi-

fication to Prairie du Chien Karst (Lower Ordovician,

closest to Mississippi river valley), Galena-Maquoketa

Fig. 1 Minnesota Karst lands.

This map overlays the areas

with 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 ofsite-specific information for

land-use decisions

946 Environ Geol (2008) 54:945956

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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 ofnodes: (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 prob-

ability 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 karstdataset 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.

Model implementation

Based on the available karst feature data stored in the Karst

Feature Database (KFD) of Minnesota, the primary con-trols 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 land-

scape. However, the majority of the sinkhole population

tends to form in highly concentrated zones. Neighborhood

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

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