Self-organized criticality of natural lakes revealed by the percolation model based on topographic wetness index

Despite the growing interest in studying lakes as complex systems, the principle underlying lake formation and the observed power law size distributions remains unclear, limiting our ability to better understand the complexity of this hydrological system and to address the related challenges of water security and climate change. By introducing the topographic wetness index (TWI) into the percolation theory, we simulated the connectivity of water on the land surface in 14 regions of varying sizes, scales and topographic features. We uncovered that discontinuous percolation transitions are prevalent in the Earth’s topography, with critical TWI thresholds between 0.617 and 0.724, and this criticality extends beyond the critical point with the presence of a Griffiths phase. Natural lake systems were found to develop within the criticality regime, as evidenced by the emergence of the largest lake and the power law distribution of lake sizes. We therefore conjectured that self-organized criticality plays a governing role in the development of lake systems, which is likely driven by the quest for system stability. These results can also contribute to better understanding of the evolutionary mechanisms of other natural complex systems that develop on the Earth’s land surface. Lake formation and their power law size distribution remain poorly understood. By introducing the topographic wetness index into percolation theory, the authors find that lake systems develop in the critical region of discontinuous percolation transitions of topography, implying the key role of self-organized criticality in this complex system.