On the size-distribution of solution dolines in carbonate karst: Lognormal or power model?

Abstract

Dolines, or closed karst depressions, are the most characteristic feature of karst landscapes. The two main types of doline are those formed by the removal of material by solution and those formed by the geological processes of collapse or suffosion. Solution dolines are most frequently found in carbonate karst in high relief karst massifs. Various algorithms can be used to identify and delineate dolines in high-resolution digital elevation models (DEM) where the lower size limit is determined by the resolution of the DEM, i.e., the size of the cell or the DEM pixel in terrain units. The work presented here addresses the size distribution of dolines, which is a significant component of the geomorphometric analysis of dolines. On the basis of experimental results, various authors have advocated the lognormal or the power distribution as the best fit to experimental data. A power distribution is consistent with a fractal structure implying the fractal nature of the sizes of dolines which, in turn, may reflect a relationship between size and the structural controls of fracture networks and the fractal fragmentation of the terrain. This paper presents case studies of four karst landscapes that are representative of karst massifs in Spain. Two of these are located in the Pyrenees in the north of Spain and two are located in the Betic mountains in the south of Spain. In all four cases, a lognormal distribution provides a bad fit while a power law distribution provides a good fit in three cases and in the fourth case provides a good fit for dolines that have a diameter greater than 50 m.