Figure 2
From: Experimental evidence that rill-bed morphology is governed by emergent nonlinear spatial dynamics
Workflow for reconstructing spatial dynamics from experimental rill-bed profiles. (a) We applied singular spectrum analysis to separate signal from noise in rill profiles and remove low-frequency trend components from the signal to isolate higher-frequency cyclical components expected to contain step-pool units and to promote nonlinear stationarity. (b) We screened for emergent nonlinear-deterministic dynamics in detrended rill signals with nonlinear time series methods. We reverse-engineered (reconstructed) rill-bed morphology dynamics from each detrended rill signal with time-delay embedding, and statistically tested whether apparent nonlinear structure in reconstructed dynamics was likely mimicked by a linear-stochastic process with surrogate data testing. (c) We used space–time separation plots to screen for nonlinear stationarity in reconstructed rill-bed dynamics to ensure that rill signals were long enough to adequately sample dominant low-frequency cycles isolated by singular spectrum analysis. (d) We applied echo state neural network16 machine learning to simulate and forecast reconstructed nonlinear-deterministic dynamics. We used out-of-sample forecasts to increase profile length of rill signals screened to be non-stationarity and re-tested for stationarity.
