  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 11 hydro-climatic zones of China, 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.
