Quantitative relationships describing the nature of surface drainage networks have been used to examine flood characteristics, sediment yield, and the evolution of basin morphology. However, these methods have not been widely used to explore the same information for karst flow systems. While karst drainage systems share many characteristics with surface flow networks, the fact that karst streams may flow through the subsurface has meant that sufficiently detailed data have generally been lacking for morphometric analysis. Over the last five decades, cave exploration and survey in the Turnhole Bend Basin of the Mammoth Cave Watershed have yielded 161 km of mapped cave passage, including over 40 km of perennial subsurface streams. Simultaneously, Geographic Information System (GIS) technology has provided tools to 1) manage the karst system's complex spatial data sets, 2) analyze and quantitatively model karst processes, and 3) visualize spatially and temporally complex data. The purpose of this investigation is to explore techniques by which quantitative methods of drainage network analysis can be applied to the organization and flow patterns in the Turnhole Bend Basin.

Four methods were developed to estimate perennial stream lengths within the Turnhole Bend Basin, resulting in values ranging from 0.24 km/km² to 1.13 km/km². A nearby, climatologically similar, nonkarst surface drainage system yielded a drainage density value of 1.36 km/km². Since the mapped cave streams necessarily represent only a fraction of the total of underground streams within the study area, the actual subsurface values are likely to be much higher. A potential upper limit on perennial drainage density for the Turnhole Bend Basin was calculated by making the assumption that each sinkhole drains at least one first-order stream. With an average of 74 sinkholes per km² for the Turnhole Bend Basin, the minimum flow-length draining one km² is 6.25-7.22 km.