Size distributions reveal regime transition of dominant driving force in lake systems

Power law size distribution, associated with important system behaviors including scale-invariance, critical tipping and self-organization, has been observed in many 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 featured by exponential, stretched-exponential and power law distribution. These three distributions are referred to as three phases which represent system (size) states with successively increasing degrees of heterogeneity and orderliness, and more importantly, indicate the dominance of exogenic and endogenic forces in lake systems, 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” with reduced system resilience. Besides, the change may also lead to a rising proportion of small lakes in the whole size distribution, which would increase the overall greenhouse gas emissions from natural lakes.