A Mathematical Model for a Map of Relative Sinkhole Risk in Fillmore County, Minnesota

Abstract

Sinkhole probability maps have been constructed for southeastern Minnesota in Winona, Olmsted, Fillmore Counties and Leroy Township in Mower County. A new sinkhole probability map for Goodhue County is in production. The existing maps were constructed as paper maps with boundaries drawn by the maps' authors using subjective criteria. As part of the transition of this mapping effort into a digital GIS environment, we have attempted to quantify the map-making process to reduce the potential for subjective biases for developing sinkhole probability maps. Based on the distribution of distances to the nearest sinkhole and the sinkhole density in Fillmore County, a mathematical decision tree model has been developed to construct maps of relative sinkhole risk. The decision tree model was implemented to construct a revised map of relative sinkhole risk in Fillmore County using ArcView and ArcInfo GIS. To facilitate the comparison with the original maps the six probability zones were revised as six relative risk zones. 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. The model is less successful in capturing the details of the lower density areas where the subjective criteria are more significant and has no simple way of extrapolating across areas in which the sinkholes have not been mapped.