Table 1 Experimental rill-bed profiles and signal processing with singular spectrum analysis.

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

Rill profile

Length (m)

Detrended signal strengtha

Oscillatory components

In-situ rill profiles

5 sl–2500 Lh−1

11.23

28%

2.03 m (21%), 1.30 m (7%)

5 sl–5000 Lh−1

15.08

52%

4.26 m (24%), 5.66 m (28%)

15 sl–160 Lh−1

4.220

35%

0.68 m (18%), 0.65 m (10%), 0.61 m (7%)

15 sl–780 Lh−1

13.23

38%

0.80 m (15%), 0.50 m (23%)

15 sl–900 Lh−1

11.90

39%

0.80 m (25%), 0.20 m (13%)

Flume (loamy sand) profiles

8 sl–1000 Lh−1

1.78

77%

0.25 m (68%), 0.28 m (5%), 0.30 m (4%)

8 sl–2200 Lh−1

1.79

88%

0.24 m (73%), 0.18 m (11%), 0.30 m (3%)

8 sl–3600 Lh−1

1.80

73%

0.16 m (41%), 0.14 m (16%), 0.17 m (16%)

12 sl–1000 Lh−1

1.80

77%

0.18 m (37%), 0.13 m (40%)

12sl–2200Lh−1

1.80

80%

0.39 m (30%), 0.34 m (30%), 0.25 m (20%)

Flume (silt loam) profiles

8 sl–1000 Lh−1

1.18

85%

0.21 m (65%), 0.11 m (20%)

8 sl–3600 Lh−1

1.80

76%

0.40 m (64%), 0.66 m (12%)

12 sl–1000 Lh−1

1.20

73%

0.28 m (42%), 0.16 m (15%), 0.08 m (15%)

12 sl–2200 Lh−1

1.79

86%

0.70 m (43%), 0.25 m (29%), 0.19 m (15%)

12 sl–3600 Lh−1

1.79

92%

0.41 m (60%), 0.18 m (21%), 0.39 m (11%)

  1. aThe percent of total variation in the detrended rill-bed elevation profile accounted for by the detrended signal.