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.

This paper presents the overall sinkhole distributions and conducts hypothesis tests of sinkhole distributions and sinkhole formation using data stored in the Karst Feature Database (KFD) of Minnesota. Nearest neighbor analysis (NNA) was extended to include different orders of NNA, different scales of concentrated zones of sinkholes, and directions to the nearest sinkholes. The statistical results, along with the sinkhole density distribution, indicate that sinkholes tend to form in highly concentrated zones instead of scattered individuals. The pattern changes from clustered to random to regular as the scale of the analysis decreases from 10-100 km2 to 5-30 km 2 to 2-10 km2. Hypotheses that may explain this phenomenon are: (1) areas in the highly concentrated zones of sinkholes have similar geologic and topographical settings that favor sinkhole formation; (2) existing sinkholes change the hydraulic gradient in the surrounding area and increase the solution and erosional processes that eventually form more new sinkholes.