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

TL;DR

This study analyzes the distribution of sinkholes along the Dead Sea, revealing a scale-free power-law pattern, and introduces a cellular automata model that explains their growth without critical thresholds.

Contribution

It is the first to demonstrate the scale-free distribution of Dead Sea sinkholes and to develop a stochastic model explaining their formation and growth dynamics.

Findings

Sinkhole sizes follow a power-law distribution with an exponent close to 2.

The cellular automata model reproduces the observed distribution.

Sinkhole growth dynamics do not involve critical threshold behavior.

Abstract

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.