Scale‐free distribution of Dead Sea sinkholes: Observations and modeling

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 1 m/yr, 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.

Scale‐Dependent Patterning of Wetland Depressions in a Low‐Relief Karst Landscape

“…Size limitation has been previously demonstrated for other South Florida carbonate landscapes (Harris et al, ) although the mechanisms for this patterning are not yet clear. Moreover, both patterns are notable departures from the size distributions evident for karst features in other carbonate settings, which follow clear power law scaling (Yizhaq et al, ) and, more generally, for surface depressions that support shallow lakes and wetlands in other landscapes (Le & Kumar, ; van Meter & Basu, ). Evidence for power law scaling of depression features is interpreted as the outcome of scale‐free constraints on local positive feedbacks that allow large features to continue to expand (Scanlon et al, ).…”

“…In landscapes where spatial self-organization occurs without scale-dependent constraints on patch expansion (i.e., global negative feedbacks; Scanlon et al, 2007), patch areas follow power law scaling. This has been observed in the prairie potholes of North Dakota (van Meter & Basu, 2015), woody patches on some arid landscapes (Scanlon et al, 2007), in the surface areas of karst sinkholes (Yizhaq et al, 2017), and in lake depressions (Le & Kumar, 2014) where power law scaling is used to describe lake size-abundance relationships (McDonald et al, 2012) and extrapolate to global distributions. While power law scaling is diagnostic of scale-free processes, scale-dependent constraints on patch expansion associated with regular landscape patterning yield patch area distributions that depart markedly from power law scaling.…”

“…Second, regular patterning should yield landscapes with a characteristic wavelength representing the spatial frequency of wetland basins; fractal or random patterning yields contrary evidence. Third, regular patterning, wherein wetland basin expansion is constrained by competition between adjacent basins, should result in marked departure from power law distributions observed for depressions and karst feature elsewhere (Yizhaq et al, ). Fourth, local reinforcing feedbacks that induce vertical divergence between wetlands and uplands should result in bimodal distributions of elevation.…”

Geomechanical modelling of sinkhole development using distinct elements: model verification for a single void space and application to the Dead Sea area

“…This approach is possibly suitable for assessing the factor of safety of an individual, fully developed cave and for deriving a relation between measured surface subsidence and cavern configuration. However, the geometries of voids involved in sinkhole development are often non-singular, irregular and distributed on lots of scales (Abelson et al, 2017;Al-Halbouni et al, 2017;Ezersky et al, 2017;Gutiérrez et al, 2016;Parise et al, 2018;Yizhaq et al, 2017). Alternatively, continuum-based corrosion models have addressed the rock dissolution and void growth in a hydrogeological framework (Kaufmann and Romanov, 2016;Shalev and Lyakhovsky, 2012).…”

“…Tharp, 1999;Zeev et al, 2017;Clément et al, 2018) and has been ignored in these simulations for simplicity. A possible DEM approach is to apply forces to the boundary particles of the void space to simulate the pressure inside a water-filled cavity or to apply forces related to the pore spaces between particles to simulate hydrofractures (Yoon et al, 2015). An alternative is the combination of FEM and DEM with accounting for drag forces due to fluid flow or other combined particle-lattice model schemes (Ghani et al, 2013).…”