Scale-free distribution of Dead Sea sinkholes--observations and modeling

There are currently more than 5500 sinkholes along the Dead Sea in Israel. These were formed due to the dissolution of subsurface salt layers as a result of the replacement of hypersaline groundwater by fresh brackish groundwater. This process has been associated with a sharp decline in the Dead Sea water level, currently more than one meter per year, resulting in a lower water table that has allowed the intrusion of fresher brackish water. We studied the distribution of the sinkhole sizes and found that it is scale-free with a power-law exponent close to 2. We constructed a stochastic cellular automata model to understand the observed scale-free behavior and the growth of the sinkhole area in time. The model consists of a lower salt layer and an upper soil layer in which cavities that develop in the lower layer lead to collapses in the upper layer. The model reproduces the observed power-law distribution without involving the threshold behavior commonly associated with criticality.