Fig. 2.

Early warning signals of transformation recorded in tephra depth across the edge of a deflation patch (Fig. 1D). (A) Thickness measurements of tephra (gray) with a Gaussian filter (black). Autocorrelation at-lag-1 (B), SD (C), and skewness (D) are calculated with a rolling window half the length of the dataset for both the original dataset (black) and residuals of the detrended dataset (gray). The strengths of trends estimated by the Kendall τ correlation coefficient are indicated on the graphs. Dashed vertical lines indicate transitions to tephra absence. (E) Probability density functions for three sections of the transect indicate that a changing distribution of measurement in the middle of the transect is not a simple transition from one state (0–354 cm) to the other (707–1,060 cm). (F) Moving average skewness calculated for the previous 30 points.