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Sinkhole Hazard Assessment in Minnesota Using a Decision Tree Model

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Sinkhole Hazard Assessment in Minnesota Using a Decision Tree Model 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 database (KDD) Á Nearest neighbor analysis (NNA) Á formation and the ability to accurately predict sinkhole Minnesota 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 Introduction density, bedrock geology and depth to bedrock in south- eastern Minnesota and northwestern Iowa, a decision tree An understanding of what influences sinkhole formation model has been developed to construct maps of sinkhole and the ability to accurately predict sinkhole hazards is probability in Minnesota. The decision tree model was critical to environmental management efforts in the karst converted as cartographic models and implemented in lands of southeastern Minnesota. Several regression anal- ArcGIS to create a preliminary sinkhole probability map yses and mathematical models have been conducted to in Goodhue, Wabasha, Olmsted, Fillmore, and Mower assess sinkhole hazards and develop sinkhole probability Counties. This model quantifies bedrock geology, depth to maps. Matschinski (1968) treated sinkholes as points and bedrock, sinkhole density, and neighborhood effects in did not consider their dimensions and orientations. LaValle southeastern Minnesota but excludes potential controlling (1967, 1968) investigated the sinkhole morphology in factors such as structural control, topographic settings, south central Kentucky. Multiple regression analyses were human activities and land-use. The sinkhole probability used to study the relationships among drainage systems, map needs to be verified and updated as more sinkholes are karst relief, structurally aligned depressions, limestone mapped and more information about sinkhole formation is density index, insoluble residue content, flank slope, and obtained. bedding thickness. However, despite his elegant statistical arguments, his conclusions are not convincing and Wil- Keywords Decision tree model Á Sinkhole probability Á liams (1972) criticized some of his geomorphic assump- Karst feature database (KFD) Á Knowledge discovery in 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) Y. Gao (&) tested several hypotheses about sinkhole development. Department of Physics, Astronomy and Geology, These hypotheses included Poisson models (single random East Tennessee State University, process), Negative Binomial models (contagious process), Johnson City, TN 37614, USA e-mail: [email protected] and Mixed Poisson models (two mutually independent random processes). The Mixed Poisson models fitted the E. C. Alexander Jr sinkhole data in Mitchell Plain of southern Indiana. Department of Geology and Geophysics, McConnell and Horn (1972) interpreted this fit in terms of University of Minnesota, 310 Pillsbury Dr., SE, Minneapolis, MN 55455, USA two mutually independent random processes of ‘‘cavern e-mail: [email protected] roof collapse’’ and ‘‘corrosion’’ for sinkhole development. 123 946 Environ Geol (2008) 54:945–956 Palmquist (1977) demonstrated that the major control on that orientations of sinkhole pairs correspond to regional doline density is the amount of groundwater recharge in and local structures. 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 Minnesota karst and sinkhole distribution ongoing sinkhole activity in Maitland, Florida. Upchurch and Littlefield’s (1987) moving-average analyses and chi- Southeastern Minnesota is part of the Upper Mississippi square tests showed that ancient sinkholes in bare karst Valley Karst (Hedges and Alexander 1985) that includes areas of twelve 7.5’ quadrangles in Hillsborough County, northwestern Illinois, southwestern Wisconsin, and north- Florida, could significantly predict the locations of modern eastern Iowa. Karst lands in Minnesota are developed on sinkholes. Veni’s (1987) research showed that fracture Paleozoic carbonate and sandstone bedrock. Most surficial permeability should be considered when assessing the karst features such as sinkholes, stream sinks, springs, and sensitivity of a karst area to human development based on a caves are found only in those areas with less than 50 ft survey of over 300 caves and sinkholes in the southeastern (15 m) of sedimentary cover over bedrock surface (Fig. 1). corner of Edwards Plateau, Texas. Data sources for bedrock geology and depth to bedrock GIS based models have been widely used for decision- geology in southeastern Minnesota are listed in Table 2. making on sinkhole hazard analysis in the last decade (Gao Figure 2 shows significant sandstone karst developed in and Alexander 2003). Whitman and Gubbels (1999) dem- Pine County (Shade 2002). Much of the scientific karst onstrated the importance of hydrostatic loads in sinkhole literature (Davies and Legrand 1972; Dougherty et al. hazard, and this information can then be used to construct 1998; Troester and Moore 1989) has focused on other parts predictive models of sinkhole hazard. Lei et al. (2001) of the country and world and few scientific descriptions of investigated sinkhole distributions based on factors such as the Upper Mississippi Valley Karst exist. Nevertheless, the types of carbonate rock, the geomorphologic settings, hy- karst lands of southeastern Minnesota present an ongoing drogeologic conditions, human activities, and land use. All challenge to environmental planners and researchers and factors were digitized as corresponding GIS coverages and have been the focus of a series of research projects and processed in a grid-based IDRISI GIS system. A series of studies by researchers for more than 30 years (Giammona grid-based relative risk maps of sinkhole hazard were 1973; Wopat 1974). developed for four cities, Tangshan, Xiangtan, Yulin, and Gao et al. (2001) divided the sinkholes in southeastern Liupanshui in China (Lei et al. 2001). Jiang et al. (2005) Minnesota into three karst groups: Cedar Valley Karst expanded the sinkhole hazard assessment to a national (Middle Devonian), Galena/Spillville Karst (Upper Ordo- scale and applied analytic hierarchy process (AHP) to de- vician/Middle Devonian), and Prairie du Chien Karst velop a relative sinkhole risk map in China. Zhou et al. (Lower Ordovician). Gao et al. (2005) revised the classi- (2003) conducted orientation analysis of sinkholes along fication to Prairie du Chien Karst (Lower Ordovician, I-70 highway near Fredrick, Maryland and demonstrated closest to Mississippi river valley), Galena-Maquoketa 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 123 Environ Geol (2008) 54:945–956 947 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 quantify the map-making process to reduce the potential distant from Mississippi river valley) based on more recent for subjective biases for developing sinkhole probability sinkhole and bedrock distribution in southeastern Minne- maps. A revised map of relative sinkhole risk in Fillmore sota and northwestern Iowa. Figure 3 shows the three County (Gao and Alexander 2003) was constructed by bands of sinkholes distributed in these three karst groups. implementing a decision tree model in a GIS system. This All analyses of sinkhole distribution in southeastern paper describes the expansion of the Fillmore County Minnesota reveal that sinkholes in Minnesota tend to be sinkhole hazard assessment to southeastern Minnesota clustered at a regional scale (Gao et al. 2002; Magdalene using the decision tree model. The resulting regional and Alexander 1995). Gao et al. (2005) studied sinkhole sinkhole probability map includes Fillmore, Goodhue, distribution in Minnesota at different scales using nearest Mower, Olmsted, and Wabasha Counties where relatively neighbor analysis (NNA). The sinkhole distribution pattern complete sinkhole datasets exist. 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 Knowledge discovery and decision tree model (DNN) within the sinkhole plains of Fillmore County fits a lognormal distribution (Gao et al. 2005). Isolated sinkholes Spatial data mining aims at discovering spatial patterns occur more often in Prairie du Chien Karst (Gao et al. embedded in large spatial databases (Shekhar and Chawla 2002) compared to sinkholes in Devonian Karst and 2002). The goal of Knowledge Discovery in Database Galena-Maquoketa Karst. (KDD) is to extract
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