Universal discontinuous percolation transition in the Earth's terrestrial topography

Abstract

Based on the Topographic Wetness Index (TWI), we studied the percolation process of water on the Earth's land surface and discovered a universal discontinuous phase transition across scales, with a critical TWI threshold of 0.671 (0.054). The discontinuity is attributed to the long-range correlation and directionality of the percolation process. Furthermore, the criticality is shown to extend from the critical point to a region corresponding to the Griffiths phase, where natural lake systems are found to develop, indicating the governess of self-organized criticality within the Earth system.