Experimental evidence that rill-bed morphology is governed by emergent nonlinear spatial dynamics.

Past experimental work found that rill erosion occurs mainly during rill formation in response to feedback between rill-flow hydraulics and rill-bed roughness, and that this feedback mechanism shapes rill beds into a succession of step-pool units that self-regulates sediment transport capacity of established rills. The search for clear regularities in the spatial distribution of step-pool units has been stymied by experimental rill-bed profiles exhibiting irregular fluctuating patterns of qualitative behavior. We hypothesized that the succession of step-pool units is governed by nonlinear-deterministic dynamics, which would explain observed irregular fluctuations. We tested this hypothesis with nonlinear time series analysis to reverse-engineer (reconstruct) state-space dynamics from fifteen experimental rill-bed profiles analyzed in previous work. Our results support this hypothesis for rill-bed profiles generated both in a controlled lab (flume) setting and in an in-situ hillside setting. The results provide experimental evidence that rill morphology is shaped endogenously by internal nonlinear hydrologic and soil processes rather than stochastically forced; and set a benchmark guiding specification and testing of new theoretical framings of rill-bed roughness in soil-erosion modeling. Finally, we applied echo state neural network machine learning to simulate reconstructed rill-bed dynamics so that morphological development could be forecasted out-of-sample.