A STOCHASTIC MODEL OF VEGETATION-EROSION INTERACTION AND ITS INFLUENCE ON DENUDATION TIME SERIES

Over time scales of years to decades, denudation rates and patterns in semi-arid landscapes are known to be temporally variable and, in many cases, sensitive to external perturbation. Episodic development of gully systems and landslide complexes, for example, can produce large, localized sediment inputs to fluvial systems. These landscape features develop and heal in response to both internal and external controls, often producing a highly episodic denudation pattern at the hillslope scale. Such observed variability raises fundamental questions regarding the timescales of denudation and sediment yield in semi-arid landscapes. To what degree does short-range variability persist on longer time scales and at larger spatial scales? To what extent is variability enhanced by self-enhancing feedbacks between erosion rates and vegetation cover? And, more generally, how “steady” is steady state? Here we examine erosional time series produced by a model of drainage basin evolution. We focus in particular on the role of vegetation as the source of a space-time variable erosion threshold. The time series that emerge reveal some surprising properties. The dynamic erosion-vegetation feedback mechanism can significantly increase short-term temporal variability in denudation rates. Erosion rates can vary in space as well as time, even under uniform, quasi-steady forcing, with spatial variability manifested in episodic erosion and healing of gully complexes. Because of internal system feedbacks, variability in sediment yield may extend over significantly longer timescales than the intrinsic time scale of forcing. Model behavior also suggests a high sensitivity to climatic or tectonic perturbation associated with vegetation-erosion thresholds. These findings are compared with observations of gully morphology and dynamics in the Colorado High Plains. The implied variability in denudation rates suggests that frequency-magnitude distributions of sediment yield are likely to provide a stricter test of geomorphic models than simple comparison of mean rates.