Calculated !"# is summarized in Table 3.1. Each basin contains a slope break knickpoint and can be divided into two segments: a downstream segment with larger !"# and an upstream segment with smaller !"# (Fig. 3.7–3.9). Downstream segments of basin 2–6 are much steeper than that of basin 1, which probably indicates an uplift rate in basin1 is much smaller than other basins. The lowermost part of basin 3 intersects with the fault. The downstream reach of that intersection is composed of sedimentary rocks, and its !"# is around 60–70, which is much smaller than reaches upstream from the intersection. A knickpoint in basin 3 is at around a lithologic boundary between granitic rocks and schist (Fig. 3.8), suggesting the increase in !"# in basin 3 might be attributed to differential rock erodibility (Eq. 3.3). However, !"# does not change significantly at other lithologic boundaries within basin 3.
Therefore, an increase in !"# at a slope-break knickpoint in basin 3 should be attributed to other factors other than substrate erodibility such as an increase in local erosion rates.
Channel width
Channel width in basin 1, 2, and 4 monotonically increases with drainage area (Fig. 3.10; Table 3.2) and follow a general scaling relationship between channel width and upstream drainage area (Eq.
3.6). Normalized channel wideness (!%#) in basin 1, 2, and 4 are almost uniform over the entire reaches (Fig. 3.10). In basin 3, 5, and 6, trunks streams consist of two parts: upstream segments where channel width increases with drainage area and downstream segments where channel width does not change or decreases with drainage area (Fig. 3.10). The upstream segment of basin 3 and the downstream segment of basin 1 lie on different substrates (granitoid and schist). Although their normalized channel steepness are similar, normalized wideness is larger in the upstream segment of the basin 3 underlain by granitoid, suggesting substrate rock type partly controls channel width. Also, while !"# for the downstream segment of basin 1 is half of that of basin 2, their !%# are almost identical (Table 3.2).
Table 3.1. Basin characteristics along the Yunodake Fault Basin/
Segment ID Min area (km2) Max area
(km2) θ* Ave ksn
(m0.9)
1 0.025 24.1 0.19 28 ± 17
1-1 2.5 24.1 0.53 33 ± 16
1-2 0.025 2.5 0.34 11 ± 6
2 0.2 4.6 0.24 57 ± 19
2-1 0.2 4.6 0.46 62 ± 14
2-2 0.021 0.2 0.10 15 ± 5
3 1.0 6.9 0.11 69 ± 54
3-1 4.9 6.9 1.66 120 ± 46
3-2 0.021 4.7 0.48 31 ± 15
4 0.2 1.6 -1.05 61 ± 53
4-1 0.9 1.6 0.40 122 ± 21
4-2 0.1 0.9 -0.52 21 ± 11
5 0.3 3.4 0.26 83 ± 15
5-1 1.0 3.4 0.38 88 ± 11
5-2 0.4 1.0 0.88 57 ± 9
6 0.3 3.8 -0.69 64 ± 53
6-1 1.5 3.8 0.31 94 ± 44
6-2 0.3 1.4 0.68 12 ± 8
* Calculated by fitting data to Eq. (3.1)
53
Fig. 3.7. Slope-Area plot for trunk streams. (i=j is a critical drainage area above which !"# is calculated.
104 105 106 107
0.001 0.01 0.1
Slope
104 105 106 107
0.1 0.2
Slope
104 105 106 107
0.01
Slope 0.1
104 105 106
0.1 1
Slope
104 105 106 107
0.1 0.2
Slope
104 105 106 107
Drainage area (m2) 0.01
0.1
Slope
Acrt Acrt
Acrt Acrt
Acrt Acrt
Acrt Acrt
Acrt Acrt
Acrt Acrt Basin1
Basin1
Basin2 Basin2
Basin3 Basin3
Basin4 Basin4
Basin5 Basin5
Basin6 Basin6
Fig. 3.8. Distribution of !"# for trunks and tributaries. Trunk streams are highlighted with thick white lines. Red lines represent the surface rupture traces of the 2011 earthquake (Toda and Tsutsumi, 2013).
The background is a geologic map simplified from Geological Survey of Japan (2020).
37.15°
37.15° 37.1°37.1°
37.05°
37.05°
140.8°
140.8°
140.7°
140.7°
1 1
Trunk Trunk
2 2 33
4 4
5
5 66
Cretaceous granitic rock Cretaceous schist
Cretaceous gabbro Oligocene–
Miocene sedimentary rock
0–20
ksn (m0.9) 20–40 40–60
60–80 80–100 100–235 Slope-break
knickpoint
55
Fig. 3.9. $-plots for basin 1–6. Relative elevation is a height from each outlet. White circles represent approximate positions of slope-break knickpoints separating downstream steeper segments and upstream gentler segments. The slope of each segment represents average !"# of the segments.
0 100 200 300 400 500
Relative elevation (m)
1-1, 33
1-2, 11 1-2,11
(Slope-break knickpoint) (Segment ID, ave. ksn)
χ=5 2-1, 62
2-2, 15
3-1, 120
3-2, 31
4-1, 122
4-2, 21
5-1, 88
5-2, 57
6-1, 94
6-2, 12
Fig. 3.10. Width-Area plots (left) and !%#-Area plots (right) for basin 1–6. In log-log space, channel width at steady state increases linearly with drainage area. !%# at steady state is uniform over a segment.
107 5
10 20
Width (m)
107 10
20 kwn (10-3 )
106 5 10 15
Width (m)
106 10 20 kwn (10-3 )
106 107
5 10 15
Width (m)
106 107
10 20 kwn (10-3 )
1 1.5 2 2.5 3
106 2
4 6
Width (m)
1 1.5 2 2.5 3
106 10
20 kwn (10-3 )
106 5
10
Width (m)
106 10
20 kwn (10-3 )
106
Drainage area (m2) 5
10
Width (m)
106
Drainage area (m2) 10
20 kwn (10-3 )
Basin1 Basin1
Basin2 Basin2
Basin3 Basin3
Basin4 Basin4
Basin5 Basin5
Basin6 Basin6 Basin1
Basin1
Basin2 Basin2
Basin3 Basin3
Basin4 Basin4
Basin5 Basin5
Basin6 Basin6
2×107 2×107
2×106
2×106 2×106
2×106 2×106
2×106
Table 3.2. Results of field measurement and regression of channel width.
Basin/
Segment ID
Max area (km2)
Min area (km2)
The number of
measurements kw b* R2 Ave kwn
(10-3 m0.16)
1 24.1 0.025 61 3.45 0.43 0.73 10.6 ± 1.7
2 4.6 0.021 48 3.43 0.40 0.41 10.2 ± 2.3
3 6.9 0.021 78 5.37 0.20 0.20 12.0 ± 2.7
3-downstrem 6.9 6.2 14 2.52 0.52 0.03 9.2 ± 2.4
3-upstream 5.4 0.021 46 4.70 0.35 0.51 13.2 ± 2.2
4 1.6 0.1 16 2.69 0.52 0.73 8.1 ± 0.9
5 3.4 0.4 32 4.75 0.30 0.64 13.4 ± 2.3
5-downstream 3.4 2.8 12 5.28 0.18 0.00 12.1 ± 1.7
5-upstream 2.4 0.4 16 4.79 0.39 0.65 14.3 ± 2.5
6 3.8 0.3 69 4.73 0.26 0.13 12.8 ± 3.7
6-downstream 3.8 1.7 42 7.19 -0.17 0.03 12.6 ± 3.5
6-upstream 1.6 0.3 25 2.96 1.77 0.53 12.7 ± 3.9
* Bold and underlined numbers were used to calculate bref.
57
While !"# for upstream segments of basin 3 and 5 are uniform, that for the upstream segment of basin 6 increases at a drainage area of 1.5 km2. A coefficient $ in Eq. (3.6) for the upstream segment of basin 6 is much larger than a steady-state value ($~0.3– 0.5, Table 3.2). Reaches of drainage areas smaller than 1.5 km2 are covered by thick alluvium, which is probably related to logging activity in basin 6 (Fig.
3.11). Based on aerial photographs taken in 1976 and 1986, many trees upstream of basin 6 were cut during 1976–1986, and the surrounding areas were widely excavated (Fig. 3.11). These artificial modifications caused an excess amount of soil transported into the channels, which currently occupies and narrow the channel. Therefore, the channel width upstream of basin 6 (Area < 1.5 km2) has not achieved a steady-state form.
Hillslope angle
Hillslope angles along trunk streams are much steeper than those over the whole basins (Fig. 3.12).
This discrepancy suggests hillslope forms in each basin are gradually adjusted to increased erosion rates of adjacent streams. Distributions of hillslope angle along trunk streams are skewed to the right, indicating the hillslope angles are close to the angle of repose (e.g., DiBiase et al., 2012). Hillslopes are steeper in the downstream and gentler in the upstream (Fig. 3.13, Table 3.3). Hillslope angles along downstream segments are ~35° and almost uniform among the basins despite large differences in !+# (Fig. 3.9, 3.13). Hillslope angles along upstream segments are 17°–30° and tend to increase with !+# (Fig. 3.9, 3.13).
Basin-averaged erosion rate
Results of 10Be analysis in fluvial sediments and the resulting basin-averaged erosion rates are summarized in Table 3.4. I took two samples from basin 4 (Fig. 3.14) and calculated average erosion rates for downstream halves of the basin 4 (IWK-4d; Fig. 3.14b) based on Eq. (3.10). The erosion rates mostly ranged between 200 and 450 g/m2yr, which are equivalent to 0.1–0.23 mm/yr assuming the bulk density of hillslope sediments is 2.0 g/cm3. The 10Be concentration of basin 2 was much lower than those of other basins, and its erosion rate was 0.61 mm/yr. There is a tunnel and are many retaining walls in basin 2.
During their constructions, rocks at deeper parts at which 10Be production rates were rather slow were excavated and transported to the channel, which probably explains the low 10Be concentration of basin 2 (IWK-2, Table 3.4).
59
Fig. 3.11. Topography around the channel head in basin 6. (a) Current topography based on 5-meter DEM constructed in 2011. (b)(c) Aerial photography taken in (b) 1986 and (c) 1976. Intense deforestation occurred during 1976-1986. The photographs were obtained from Geospatial Information Authority of Japan.
(b) (b)
(c) (c)
1976 1976 1986 1986 2011(DEM) 2011(DEM) Divide
Divide
Trunk Trunk
Basin 6 Basin 6
140.78 140.78
37.05 37.05 (a) (a)
Intense logging
Intense logging
Fig. 3.12. Probability distribution of (a) hillslope angle along trunk streams and (b) slope over the whole basins. Probabilities for basin1–3 are elevated by 0.02 for better visibility.
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05
Probability
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05 0.06
Probability
Basin1 Basin2 Basin3 Basin4 Basin5 Basin6
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05
Probability
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05 0.06
Probability
Basin1 Basin2 Basin3 Basin4 Basin5 Basin6
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05
Probability
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05 0.06
Probability
Basin1 Basin2 Basin3 Basin4 Basin5 Basin6
0.01 0.02 0.03 0.04 0.05
Probability
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05 0.06
Probability
Basin1 Basin2 Basin3 Basin4 Basin5 Basin6
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05
Probability
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05 0.06
Probability
Basin1 Basin2 Basin3 Basin4 Basin5 Basin6
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05
Probability
0 10 20 30 40 50 60
Slope (deg) 0
0.01 0.02 0.03 0.04 0.05 0.06
Probability
Basin1 Basin2 Basin3 Basin4 Basin5 Basin6
Whole basin
Hillslope along trunk
(b) (a)
61
Fig. 3.13. Average hillslope angles along trunk streams. Red dots represent those presumably adjusted to accelerated erosion rates, and blue dots are those not adjusted yet.
1 2 3 4 5 6
Basin 10
20 30 40
Hillslope angle (deg)
Upstream gentler segment Downstream steeper segment
Table 3.3. Average hillslope angles along trunk streams.
Basin/
Segment ID Min distance (m) Max distance (m) Ave angle (deg)
1-downstream 0 6925 33.5
1-upstream 7875 10225 18.4
2-downstream 0 2812 37.6
2-upstream 3908 4425 17.1
3-downstream 325 2712 38.0
3-upstream 2975 6375 25.5
4-downstream 0 950 37.8
4-upstream 1110 3190 26.6
5-downstream 150 1650 34.7
5-upstream 1770 2770 30.9
6-downstream 0 1830 38.2
6-upstream 1930 3850 23.3
63
Fig. 3.14. 10Be sampling sites and erosion rates. (a) Sampling sites of fluvial sediments. (b) Erosion rates of subcatchments in basin 3 and 4. Subscripts u and d mean upstream (shown in blue) and downstream (shown in red) subcatchments.
37.15°
37.15° 37.1°37.1° 37.1°37.1°
140.7°
140.7°
140.7°
140.7°
140.6°
140.6°
IWK-1 IWK-1
0.20 mm/yr 0.20 mm/yr
0.16 mm/yr 0.16 mm/yr
0.23 mm/yr 0.23 mm/yr IWK-2
IWK-2
IWK-3 IWK-3
IWK-3u IWK-3u (b)
(b)
(b) (b) (a)
(a)
IWK-4 IWK-4 IWK-4u IWK-4u
IWK-4d IWK-4d IWK-3u
IWK-3u
IWK-4u IWK-4u
IWK-5 IWK-5
Cretaceous granitic rock Cretaceous schist
Cretaceous gabbro Oligocene–
Miocene sedimentary rock
0–20
ksn (m0.9) 20–40 40–60
60–80 80–100 100–235
10Be sample
(a)Sample name (b)Erosion rate
IWK-1 0.10mm/yr
(a) (a,b)
Table 3.4. Results of 10Be analysis.
Sample name
Mass sample (g)
Mass 9Be carrier (g)
10Be/9Be (×10-14)
10Be concentration
(atoms/g)a
10Be production rate (atoms/g
yr)b
Erosion rate (g/m2yr)
Erosion rate (mm/yr)
Basin ave. slope
(deg)
Upstream ave. ksn
(m0.9) IWK-1 26.4364 3.4882 7.5 ± 0.51 55627 ± 4929 7.0 ± 0.4 264 ± 38 0.13 ± 0.02 22.5 28.0 ± 18.9 IWK-2 26.8246 2.5084 3.5 ± 0.77 11013 ± 5239 6.4 ± 0.4 1217 ± 595 0.61 ± 0.30 28 47.6 ± 24.6 IWK-3 40.172 2.5067 10.9 ± 0.63 38484 ± 2952 6.9 ± 0.4 376 ± 51 0.19 ± 0.03 22.4 33.8 ± 28.6 IWK-4 39.3525 2.4981 17.5 ± 2.2 67402 ± 9578 6.7 ± 0.4 396 ± 64 0.20 ± 0.03 24.2 58.9 ± 51.1 IWK-5 40.2372 2.4985 12.3 ± 0.82 43856 ± 3683 6.9 ± 0.4 208 ± 38 0.10 ± 0.02 25.4 79.5 ± 16.0 IWK-3u 39.4954 2.4994 10 ± 0.90 34884 ± 4041 6.6 ± 0.4 409 ± 63 0.21 ± 0.03 19.7 25.0 ± 10.2 IWK-4u 40.0002 2.4809 10.6 ± 0.88 36878 ± 3920 7.2 ± 0.4 330 ± 46 0.17 ± 0.02 21.1 17.1 ± 8.9
IWK-4d* 454 ± 80 0.23 ± 0.04 26.9 89.9 ± 47.1
* Calculated from Eq. (3.10).
a KNB5-1 10Be standard (Nishiizumi et al., 2007). The 10Be/9Be ratio for the chemical blank was 1.8×10-14 ± 0.30×10-14.
b Atmospheric scaling factors are after Stone (2000). Attenuation lengths and relative contributions of nucleon spallation, negative muon capture, and fast muon reaction are after Gosse and Phillips (2001), Heisinger et al. (2002), and Braucher et al. (2003).
64
65
Basin-averaged erosion rates often increase with average !"# or basin-averaged slope upstream from the sampling points (e.g., DiBiase et al., 2010). While the results along the Yunodake fault generally follow such a relationship explicitly (Fig. 3.15), the erosion rate of basin 5 (IWK-5) is anomalously slow.
Basin 1 (IWK-1) and 5 (IWK-5) have similar erosion rates; however, average !"# of basin 1 was less than half of basin 5 (Fig. 3.9 and 3.15).
Knickpoint travel time
To calculate knickpoint travel time based on Eq. (3.14), I first estimated erodibility and uplift rates at an initial and final steady state using Eq. (3.3b). The erodibility coefficient ($) of granitoid was calculated using basin-averaged erosion rates and !"# presented in Regalla et al. (2013), who studied rivers flowing over the similar granitic rocks to that along the Yunodake fault. The erodibility coefficient ($) of schist was determined from the basin-averaged erosion rate (IWK-1, Table 3.4) and average !"# of basin 1. Uplift rates at an initial and final steady state (%&#& and %'&# in Eq. 3.14) were calculated using average !"# of upstream gentler segments and of downstream steeper segments (Fig. 3.9, Table 3.5).
Resulting knickpoint travel times are summarized in Table 3.6. Knickpoints in basin 1 and 2 requires a much longer time to travel from the outlets compared to other basins.
Response time
To estimate the response and delay times of channel width and hillslope angles (Fig. 3.6), I determined points where changes in width or hillslope angle started and ended (Fig. 3.16–3.21, Table 3.7).
When determining those points for channel width, I used width (!(#) -area plots (Fig. 3.10) and !(# -distance plots (Fig. 3.16c-3.21c). When there were some candidates for starting and ending points, I determined the points to estimate the maximum and minimum response and delay times. Because this study aims to reveal the timescales of channel and hillslope adjustment to an increase in erosion rates, I excluded basin 1. Although basin 1 contains a slope break knickpoint (Fig. 3.9), basin 1 is far from active fault traces, and there is no lineament crossing the basin 1 (Fig. 3.1 and 3.2), which makes it difficult to ascertain changes in river morphology in basin 1 were triggered by tectonic activity.
Fig. 3.15. 10Be-derived erosion rates and (a) average !"# upstream from the sampling sites, (b) average slope upstream from the sampling sites. Numbers correspond with basin or segment ID.
0 50 100 150
Average ksn 100
200 300 400 500 600
Erosion rate (g/m2 yr)
20 25 30
Average slope (deg) 100
200 300 400 500 600
Erosion rate (g/m2 yr)
1
4d
4u 3
4 3u
5
1
4d
4u
4 3u 3
5
(a) (b)
Table 3.5. Initial and Final uplift rates calculated from normalized channel steepness.
n=2/3 n=1 n=5/3
Basin ksn ini ksn fin Uini (mm/yr) Ufin (mm/yr) Uini (mm/yr) Ufin (mm/yr) Uini (mm/yr) Ufin (mm/yr)
1 11.2 32.6 0.07 0.14 0.05 0.14 0.02 0.14
2 15.1 61.7 0.08 0.21 0.06 0.26 0.04 0.41
3 31 120 0.13 0.32 0.12 0.51 0.09 1.30
4 20.5 122.4 0.10 0.33 0.08 0.46 0.05 0.94
5 57.2 87.9 0.20 0.27 0.22 0.33 0.26 0.54
6 12 94 0.07 0.28 0.05 0.35 0.02 0.60
67
Table 3.6. Knickpoint travel time.
Basin ID Knickpoint position (m)
Travel time (My), n=2/3
Travel time (My), n=1
Travel time (My), n=5/3
1 9230 0.97 2.04 2.67
2 3908 0.89 1.70 2.65
3 2896 0.40 0.62 1.21
4 1154 0.28 0.54 0.91
5 1933 0.54 0.67 1.31
6 2550 0.38 0.80 1.33
69
Fig. 3.16. Channel and hillslope morphologies and knickpoint travel time in basin 1. (a) Hillslope angles along trunk. Colored square dots represent hillslope angles averaged every 20 meters horizontally and 5 meters vertically (left y-axis). White circles represent hillslope angles averaged every 20 meters along trunk. See Fig. 3.5. for details. (b) Time since the passage of a slope-break knickpoint. Knickpoint travel time was calculated from Eq. (3.14).
(c) Along-trunk variation of !"# (m0.9). (d) Along-trunk variation of !$# (m0.16).
Basin1
0 2000 4000 6000 8000 10000 12000
0 50 100
Height from the bed (m)
0 10 20 30 40 50
Ave. Hillslope angle (deg)
10 15 20 25 30 35 40 45 50
0 2000 4000 6000 8000 10000 12000
0 1 2 3
Time since the passage of knickpoint (My)
n=2/3 n=1n=5/3
0 2000 4000 6000 8000 10000 12000
0 20 40 60
ksn
0 2000 4000 6000 8000 10000 12000
Distance from outlet (m) 5
10 15
kwn (*10-3 )
Hillslope angle (deg) (a)
(b)
(c)
(d)
Fig. 3.17. Channel and hillslope morphologies and knickpoint travel time in basin 2. (a) Hillslope angles along trunk. Colored square dots represent hillslope angles averaged every 20 meters horizontally and 5 meters vertically (left y-axis). White circles represent hillslope angles averaged every 20 meters along trunk. See Fig. 3.5 for details. (b) Time since the passage of a slope-break knickpoint. Knickpoint travel time was calculated from Eq. (3.14).
(c) Along-trunk variation of !"# (m0.9). (d) Along-trunk variation of !$# (m0.16).
Basin2
0 500 1000 1500 2000 2500 3000 3500 4000 4500
0 50 100 150 200
Height from the bed (m)
0 10 20 30 40 50
Ave. Hillslope angle (deg)
5 10 15 20 25 30 35 40 45 50
0 500 1000 1500 2000 2500 3000 3500 4000 4500
0 1 2 3
Time since the passage of knickpoint (My)
n=2/3 n=1n=5/3
0 500 1000 1500 2000 2500 3000 3500 4000 4500
0 50 100
ksn
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Distance from outlet (m) 10
15 20 25
kwn (*10-3 ) (a)
(b)
(c)
(d)
Hillslope angle (deg)
71
Fig. 3.18. Channel and hillslope morphologies and knickpoint travel time in basin 3. (a) Hillslope angles along trunk. Colored square dots represent hillslope angles averaged every 20 meters horizontally and 5 meters vertically (left y-axis). White circles represent hillslope angles averaged every 20 meters along trunk. See Fig. 3.5 for details. (b) Time since the passage of a slope-break knickpoint. Knickpoint travel time was calculated from Eq. (3.14).
(c) Along-trunk variation of !"# (m0.9). (d) Along-trunk variation of !$# (m0.16).
Basin3
0 1000 2000 3000 4000 5000 6000 7000
0 50 100 150 200 250
Height from the bed (m)
0 10 20 30 40 50
Ave. Hillslope angle (deg)
10 20 30 40 50 60
0 1000 2000 3000 4000 5000 6000 7000
0 0.5 1 1.5
Time since the passage of knickpoint (My)
n=2/3 n=1n=5/3
0 1000 2000 3000 4000 5000 6000 7000
0 100 200
ksn
0 1000 2000 3000 4000 5000 6000 7000
Distance from outlet (m) 10
15 20
kwn (*10-3 ) (a)
(b)
(c)
(d)
Hillslope angle (deg)
Fig. 3.19. Channel and hillslope morphologies and knickpoint travel time in basin 4. (a) Hillslope angles along trunk. Colored square dots represent hillslope angles averaged every 20 meters horizontally and 5 meters vertically (left y-axis). White circles represent hillslope angles averaged every 20 meters along trunk. See Fig. 3.5 for details. (b) Time since the passage of a slope-break knickpoint. Knickpoint travel time was calculated from Eq. (3.14).
(c) Along-trunk variation of !"# (m0.9). (d) Along-trunk variation of !$# (m0.16).
Basin4
0 500 1000 1500 2000 2500 3000 3500
0 20 40 60 80
Height from the bed (m)
0 10 20 30 40 50
Ave. Hillslope angle (deg)
15 20 25 30 35 40 45 50
0 500 1000 1500 2000 2500 3000 3500
0 0.5 1
Time since the passage of knickpoint (My)
n=2/3 n=1n=5/3
0 500 1000 1500 2000 2500 3000 3500
0 100 200
ksn
0 500 1000 1500 2000 2500 3000 3500
Distance from outlet (m) 6
8 10
kwn (*10-3 ) (a)
(b)
(c)
(d)
Hillslope angle (deg)
73
Fig. 3.20. Channel and hillslope morphologies and knickpoint travel time in basin 5. (a) Hillslope angles along trunk. Colored square dots represent hillslope angles averaged every 20 meters horizontally and 5 meters vertically (left y-axis). White circles represent hillslope angles averaged every 20 meters along trunk. See Fig. 3.5 for details. (b) Time since the passage of a slope-break knickpoint. Knickpoint travel time was calculated from Eq. (3.14).
(c) Along-trunk variation of !"# (m0.9). (d) Along-trunk variation of !$# (m0.16).
Basin5
0 500 1000 1500 2000 2500 3000 3500
0 50 100
Height from the bed (m)
0 10 20 30 40 50
Ave. Hillslope angle (deg)
10 15 20 25 30 35 40 45 50
0 500 1000 1500 2000 2500 3000 3500
0 0.5 1 1.5
Time since the passage of knickpoint (My)
n=2/3 n=1n=5/3
0 500 1000 1500 2000 2500 3000 3500
60 80 100
ksn
0 500 1000 1500 2000 2500 3000 3500
Distance from outlet (m) 10
15 20 kwn (*10-3 ) (a)
(b)
(c)
(d)
Hillslope angle (deg)
Fig. 3.21. Channel and hillslope morphologies and knickpoint travel time in basin 6. (a) Hillslope angles along trunk. Colored square dots represent hillslope angles averaged every 20 meters horizontally and 5 meters vertically (left y-axis). White circles represent hillslope angles averaged every 20 meters along trunk. See Fig. 3.5 for details. (b) Time since the passage of a slope-break knickpoint. Knickpoint travel time was calculated from Eq. (3.14).
(c) Along-trunk variation of !"# (m0.9). (d) Along-trunk variation of !$# (m0.16).
Basin6
0 500 1000 1500 2000 2500 3000 3500 4000
0 50 100 150
Height from the bed (m)
0 10 20 30 40 50
Ave. Hillslope angle (deg)
5 10 15 20 25 30 35 40 45 50
0 500 1000 1500 2000 2500 3000 3500 4000
0 0.5 1 1.5
Time since the passage of knickpoint (My)
n=2/3 n=1n=5/3
0 500 1000 1500 2000 2500 3000 3500 4000
0 100 200
ksn
0 500 1000 1500 2000 2500 3000 3500 4000
Distance from outlet (m) 10
15 20 kwn (*10-3 ) (a)
(b)
(c)
(d)
Hillslope angle (deg)
75
Table 3.7. Starting and ending point of morphological adjustment.
Width adjustment Hillslope adjustment Basin
ID
Knickpoint position (m)
Starting point (m)
Ending point (m)
Starting point (m)
Ending point (m)
1 9230 - -
7650-8050 7050
2 3908 - - 3908
2812-3250
3 2896 2100 680-1495
2770-2896
2470-2650
4 1154 - - 1097 950-1070
5 1933 870-1310 590-750 1762
1588-1662
6 2550
1355-2330 970
1930-2130
1750-1850
While starting and ending points for changes in hillslope angles could be readily identified (Fig. 3.16a–3.21a), those for width changes were not obvious due to natural variability in channel width (Fig. 3.10, 3.16c–3.21c). Also, the extent of channel segments whose channel width seems to be adjusted were rather limited, and the results of regression analysis (exponent % in Eq. 3.6, Table 3.2) for those segments (downstream segments of basin 3, 5, and 6) were distinct from those for channel segments at a steady state (%~0.3– 0.5).
Therefore, channel width in basin 3, 5, and 6 might not have achieved a new steady-state form, and the resulting response times of channel width are minimum values.
The response and delay times were at least several tens of thousands of years and up to ~1 My (Fig. 3.22). The hillslope-response time in basin 2 was as large as ~1.3 My and much longer than other basins. The response and delay times of channel width were longer than those of hillslope angle, and total response times (sum of a response and a delay time) of channel width were more than double those of hillslope angle.