Size Distributions Reveal Regime Transition of Lake Systems Under Different Dominant Driving Forces

Power law size distribution is found to associate with fractal, self‐organized behaviors and patterns of complex systems. Such distribution also emerges from natural lakes, with potentially important links to the dynamics of lake systems. But the driving mechanism that generates and shapes this feature in lake systems remains unclear. Moreover, the power law itself was found inadequate for fully describing the size distribution of lakes, due to deviations at the two ends of size range. Based on observed and simulated lakes in China's 11 hydro‐climatic zones, we established a conceptual model for lake systems, which covers the whole size range of lake size distribution and reveals the underlying driving mechanism. The full lake size distribution is composed of three components, with three phases featured by exponential, stretched‐exponential and power law distribution. The three phases represent system states with successively increasing degrees of heterogeneity and orderliness, and more importantly, indicate the dominance of exogenic and endogenic forces, respectively. As the dominant driving force changes from endogenic to exogenic, a phase transition occurs with lake size distribution shifted from power law to stretched‐exponential and further to exponential distribution. Apart from compressing the power law phase, exogenic force also increases its scaling exponent, driving the corresponding lake size power spectrum into the regime of “blue noise.” During this process, the autocorrelation function of the lake system diverges with a possibility of going to infinity, indicating the loss of system resilience. Plain Language Summary We examined the observed and simulated lakes distributed in China's 11 hydro‐climatic zones to fill two knowledge gaps related to lake size distribution: first, the power law distribution cannot describe the whole size range of lakes; second, the driving mechanism underlying this distribution is unclear. We found that the lake size distribution consists of three components featured by exponential, stretched‐exponential and power law distribution over the whole size range. These three distributions represent three phases of the lake system state under different dominant driving forces. Specifically, the power law phase dominated by the Earth's internal force is heterogeneous and ordered; the exponential phase under the control of the Earth's external force is a random state; and the stretched‐exponential phase with properties of h