QUANTITATIVE MODELING OF KARST TERRANES: INSIGHTS, PROGRESS AND PROBLEMS

Advances in karst science have been significant in the last decade. Particular progress focuses on the hydrochemistry of carbonate solution kinetics, mega-pore development, and conduit initiation. Some progress has occurred in quantifying relationships between carbonate hydrology and surface karst initiation as well as modeling initiation and evolution of doline populations. Significant work remains to translate this recent progress into robust quantitative relationships capable of computer simulations and “what if” queries in a Geographic Information Systems format. This study reviews recent progress and offers insights into mathematically modeling initiation and evolution of doline populations using contagion theory and logistic growth functions. The spatial dimensions in karst initiation and development can be modeled quantitatively using geospatial methods and geostatistical models based on regionalization theory. Kriging techniques belong to the group of best linear, unbiased estimates for capturing spatial dependency among the environmental factors that control karst initiation and development. In this study, doline long-axis orientation and length/width ratio were selected as principal variables for co-kriging in identifying an important spatial dependency related to collapse hazards.

Accomplishing these tasks will significantly advance karst science in both theoretical and applied problems ranging from computer simulations of karst evolution to probabilistic hazard mapping in areas prone to doline collapse and chronic depression flooding.