Stages in gully evolution and self-organized criticality

The process of gully erosion at the active stage is far from equilibrium; rather, the gully shows the characteristics of a self-organizing system that is close to crisis. This qualitative description is similar to the understanding of open dynamic systems at a state of self-organized criticality (SOC). We tried to find the quantitative attributes of SOC in numerical simulations of gully evolution with a dynamic gully erosion model. Three scenarios were used: (1) gully evolution is controlled by initial topography and texture, when the discharge and base level are constant; (2) discharge is constant and the base level lowers over time; (3) the base level is constant and the discharge changes naturally. The results of numerical simulations of gully evolution are consistent with the expectations of the SOC theory. Under the first scenario, when the gully was at the initial active stage of evolution, the system showed all the SOC attributes: a fractal long profile; a 'red-noise' spectrum; and the powerlaw frequency-magnitude relationship (FMR). With gully stabilization, the system had lost SOC behaviour and became non-fractal, with a 'blue-noise' spectrum and exponential FMR. For this scenario SOC criteria can be used to find the boundary between active and stable states of gully evolution. Simulations under the second scenario showed that the riverbed incision made the active stage of the gully evolution with all SOC attributes much longer than with a stable base level. Simulation under the third scenario, with variable discharge (with the elements of SOC), showed that the SOC attributes of the hydrological system could be induced on the landform system. While the gully had evidently reached the stable stage, the process of gully volume change still indicated active-stage SOC attributes. Therefore some landform systems can really be in the SOC stage, which can diagnose their activity; others only show SOC attributes induced by climatic or hydrologic systems. Copyright (c) 2006 John Wiley & Sons, Ltd.