Improving sinkhole hazard models incorporating magnitude-frequency relationships and nearest neighbor analysis

This work presents a methodology for elaborating sinkhole hazard models that incorporate the magnitude and frequency relationships of the subsidence process. The proposed approach has been tested in a sector of the Ebro valley mantled evaporite karst, where sinkholes, largely induced by irrigation practices, have a very high occurrence rate (>50 sinkholes/km2/yr). In this area, covering 10 km2, a total of 943 new cover collapse sinkholes were inventoried in 2005 and 2006. Multiple susceptibility models have been generated analyzing the statistical relationships between the 2005 sinkholes and different sets of variables, including the nearest sinkhole distance. The quantitative evaluation of the prediction capability of these models using the 2006 sinkhole population has allowed the identification of the method and variables that produce the most reliable predictions. The incorporation of the indirect variable nearest sinkhole distance has contributed significantly to increase the quality of the models, despite simplifying the modeling process by using categorical rather than continuous variables. The best susceptibility model, generated with the total sinkhole population and the selected method and variables, has been transformed into a hazard model that provides minimum estimates of the spatial-temporal probability of each pixel to be affected by sinkholes of different diameter ranges. This transformation has been carried out combining two equations derived from the more complete 2006 sinkhole population; one of them expressing the expected spatial-temporal probability of sinkhole occurrence and the other the empirical magnitude and frequency relationships generated for two different types of land surfaces, which control the strength of the surface layer and the size of the sinkholes. The presented method could be applied to predict the spatial-temporal probability of events with different magnitudes related to other geomorphic processes (e.g. landslides).