Thresholds for bed load transport and channel initiation in a chert area in Ashio Mountains, Japan: An empirical approach from hydrogeomorphic observations
Abstract
[1] We examined the effect of bed load transport on channel‐head locations where shallow landsliding is infrequent. Area‐slope thresholds for bed load transport estimated from hydrogeomorphic observations were compared with certain area‐slope relations at 24 channel heads in a chert area, the Ashio Mountains, Japan. The hydrogeomorphic observations include (1) spring discharge at 12 sites, (2) rainfall intensity, and (3) peak discharge and bed load transport immediately below two channel heads of differing gradient. We confirmed an increase of spring discharge in proportion to drainage area during a stormflow. We performed regression analyses involving the peak 4‐hour rainfall and the peak discharge per unit area to give the optimal rainfall‐runoff equation. The bed load yield increases abruptly when the peak discharge exceeds a critical discharge. We calculated area‐slope thresholds for bed load transport for 1‐year and 100‐year rainfalls, combining the rainfall‐runoff equation with the critical discharge. More than half of all channel heads are located where peak discharge produced by frequent rainstorms (return intervals of less than 100 years) is sufficient to transport bed load. In mountains where shallow landsliding is infrequent, bed load transport has a strong influence on channel‐head location.
1. Introduction
[2] Channel initiation is a key factor in the evolution of mountain landforms. Previous studies modeled channel initiation by means of mass balance equations [Smith and Bretherton, 1972; Kirkby, 1980, 1986, 1987], thresholds of physical processes [Horton, 1945; Montgomery and Dietrich, 1988, 1989, 1994; Willgoose et al., 1991; Dietrich et al., 1992, 1993], and a probabilistic approach [Istanbulluoglu et al., 2002]. Montgomery and Dietrich [1988, 1989] proposed a physically based area‐slope threshold of shallow landsliding, which successfully explains an inverse area‐slope relation observed at channel heads. Although these studies improved our understanding of channel initiation processes, not all mountain environments experience frequent shallow landsliding. Channel initiation in environments not impacted by shallow landsliding must be included to better understand the development of mountainous topography.
[3] Several studies have attempted to assess slope‐area relationships in a variety of environmental conditions. For example, Montgomery and Dietrich [1994] reported the area‐slope relationships at channel heads under different lithologic and climatic conditions. In semiarid or Mediterranean environments, many researchers compared thresholds predicted by theoretical models with observed area‐slope relations at gully heads [Prosser and Abernethy, 1996; Vandaele et al., 1996; Vandekerckhove et al., 2000; Nachtergaele et al., 2001; Istanbulluoglu et al., 2002; Kirkby et al., 2003]. However, there have been few observations of area‐slope relation at channel heads after Montgomery and Dietrich's work in humid forested mountains.
[4] Shallow landsliding is an often‐recorded geomorphic process in humid forested mountains [Tsukamoto et al., 1973, 1982; Dietrich and Dunne, 1978; Iida and Okunishi, 1983; Dietrich et al., 1986], but chronological studies have found the recurrence intervals of shallow landslides exceed at least 100 years. Therefore the timing of shallow landsliding is considered an “episodic” geomorphic process [Reneau et al., 1986; Shimokawa et al., 1989; Yoshinaga and Saijo, 1989]. The spatial and temporal frequency of shallow landsliding also depends on bedrock lithologies. Almost all zero‐order basins have shallow‐landslide scars in some granitic hillslopes in Japan [Tsukamoto et al., 1973, 1982; Iida and Okunishi, 1983; Onda, 1992], whereas spatial density of shallow landslides is relatively low in two mountainous areas underlain by Mesozoic sedimentary rocks [Onda, 1994; Onda et al., 2004].
[5] Dietrich et al. [1987] suggested that a channel head advances upstream by shallow landsliding and migrates downstream by sediment supply from side slopes during the recurrence interval of landsliding. If the frequency of shallow landsliding is low, sediment supply must facilitate downstream migration of channel heads. Peak discharge in relative frequent rainstorms also affects substantial bed load transport in headwater streams [Gomi and Sidle, 2003]. Thus a frequent rainstorm with return periods shorter than shallow landsliding may trigger bed load transporting events at channel heads. Channel‐head location must be determined by a tradeoff between the frequency of shallow landsliding and the magnitude and frequency of bed load transport. In an extreme case with no landslides, channel‐head locations would be controlled by area‐slope threshold for bed load transport [Dietrich et al., 1992, 1993; Montgomery and Dietrich, 1994]. Therefore we propose a hypothesis that in mountains with infrequent landslides, many channel heads locate where peak discharge produced by frequent rainfall is just sufficient to transport bed sediment.
[6] We examine how frequent storm events cause bed load transport and affect channel‐head locations to test the hypothesis. Hydrogeomorphic observations are presented for headwater streams in a mountainous area where shallow landslides are infrequent, and the effect of bed load transport on channel‐head locations is discussed by using an empirical model of the threshold for bed load transport.
2. Empirical Model
[7] We propose an empirical model for bed load transport in channel heads, based on analyses of hydrogeomorphic observations (Figure 1). Three kinds of hydrogeomorphic data are necessary for the subsequent analyses: (1) discharge in various source areas during storm runoff, (2) rainfall intensity and peak discharge at several channel heads, and (3) bed load transport at several channel heads. Previous hydrogeomorphic studies provide various methodologies to collect these data. Many hydrological studies reported rainfall‐runoff relationship in channel heads [e.g., Montgomery et al., 1997; Uchida et al., 1999]. Onda [1994] and Komatsu and Onda [1996] obtained a relationship between runoff and drainage area by manual measurement at various springs. Bed load transport at channel heads is usually observed with traps [Terajima et al., 2001; Hattanji and Onda, 2004].
[9] Least squares linear regression analyses between observed peak specific discharge, Qp/A, and T‐hour rainfall, RT, with varying time interval T yields many equations with the form of equation (3). A time interval T that minimizes scatter in the relation will be used to estimate peak specific discharge.
[12] This equation indicates area‐slope thresholds for bed load transport under a given rainfall condition, RT. The constants kp, RTcr, and γ can be estimated from the statistical analyses described previously in this section. Analytical methodology in this empirical model requires following two assumptions: (1) peak discharge of a storm event is linearly proportional to drainage areas and maximum T‐hour rainfall of the storm and (2) critical discharge for bed load transport is measurable. Assumption 1 may not be satisfied in mountains where permeable bedrock facilitates groundwater flow, because of the scattered area‐discharge relationship [Onda, 1994; Komatsu and Onda, 1996]. Since measurement of bed load with the smaller mean grain size is more difficult, assumption 2 may require relatively larger mean grain sizes of bed sediment such as sand or gravels. Although these restrictions constrain the application of the presented empirical model to broader areas, methodology of the present study must be applicable to mountains where these assumptions are satisfied.
3. Study Area
3.1. Geology and Climate
[13] We applied the empirical model based on hydrogeomorphic observation to a chert area in the eastern Ashio Mountains, located 100 km north of Tokyo, Japan (Figure 2). The underlying bedrock is Triassic bedded chert with a strike in the N–S direction and an almost vertical dip; it is finely layered with a thickness of 30–50 mm [Aono, 1985; Kamata, 1997]. This area exhibits dissected topography, with steep hillslopes of 30–50° (Figure 3a). The hillslope generally consists of exposed bedrock outcrops and slopes covered with 0‐ to 2‐m of regolith, which is composed of 50–80% gravels by weight [Hattanji and Onda, 2004]. Kanuma Pumice, deposited 29–45 ka [Machida and Arai, 2003], are partly intercalated within sediments on flat valley floors.
[14] The climate around the Ashio Mountains is humid temperate, with humid summers and dry winters. The annual rainfall averaged over 22 years at the nearest meteorological station “Kanuma” (Figure 2) is 1476 mm, of which 76% falls from May to October as a result of monsoon fronts, thunderstorms, and typhoons. Vegetation in the chert area consists mainly of Japanese cedar forest (Sugi: Cryptomeria japonica) including Japanese cypresses (Hinoki: Chamaecyparis obtusa). The forest was planted in the 1960s. Deciduous broad‐leaved forest, including oak trees, remains locally in steep areas. Understory vegetation grows in both the planted and natural forests from spring to fall. The consistent vegetation cover provides some controls on the effect of vegetation on channel‐head location.
3.2. Channel Heads
[15] The general definition of a channel head is “the upstream boundary of concentrated water flow and sediment transport between definable banks” [Dietrich and Dunne, 1993]. In this chert area, channels are distinguished morphologically as having small banks, a stepped structure, and clear traces of debris removal by water flow. Sediment and woody debris both remain on the slopes, and are transported by streamflow in the channels. The microtopography near channel head varies with the steepness, as described in the next subsection.
[16] Thirty‐four channel heads in this area (Figure 3a) were surveyed, in November 2000, October 2001, and from June to July 2003. The locations of channel heads were verified in the field with an altimeter, and plotted on a base map of the 1:25,000 topographic map “Shimotsuke‐Ohgaki” issued by the Geographical Survey Institute of Japan. Drainage area was measured on the base map using graphics software. The local head slope, Sh, from the channel head to a point about 10 m upslope, and the local channel gradient, Sc, from the channel head to a point about 10 m downstream, were measured with a hand compass or a slope meter.
[17] The distribution of channel heads, unchanneled valleys and source areas in the chert area are identified in Figure 3b. At three channel heads the source areas were not determined, because they were too small to express topographic convergences on the base map. We could not measure Sh and/or Sc at seven channel heads because of their great steepness or dangerous position. This inability to sample steep channel heads could provide a possible bias in the subsequent analysis. Full data were available at 24 channel heads (Table 1).
| Number | Type | Sh | Scaa
Abbreviation n/a indicates data are not available.
|
A, m2 |
|---|---|---|---|---|
| C1H | G | 0.53 | 0.50 | 4700 |
| C3H | S | 1.22 | 0.78 | 810 |
| 11 | G | 0.58 | 0.36 | 6630 |
| 12 | G | 0.75 | 0.53 | 1400 |
| 14 | G | 0.70 | 0.63 | 680 |
| 15 | G | 0.55 | 0.53 | 3140 |
| 16 | G | 0.42 | 0.36 | 7200 |
| 17 | G | 0.51 | 0.45 | 6910 |
| 18 | S | 0.75 | 0.71 | 3690 |
| 21 | G | 0.70 | 0.65 | 5250 |
| 23 | ⋯ | 0.93 | n/a | 1340 |
| 24 | S | 1.07 | 0.86 | 1490 |
| 25 | S | 1.07 | 0.98 | 710 |
| 27 | G | 0.70 | 0.67 | 6240 |
| 30 | ⋯ | 0.93 | n/a | 880 |
| 31 | G | 0.84 | 0.67 | 2060 |
| 33 | ⋯ | 0.75 | n/a | 1470 |
| 35 | S | 0.84 | 0.86 | 530 |
| 36 | S | 1.19 | 0.82 | 580 |
| 51 | G | 0.50 | 0.49 | 9900 |
| 52 | S | 0.67 | 0.81 | 2650 |
| 53 | G | 0.55 | 0.40 | 4210 |
| 54 | S | 0.93 | 0.70 | 990 |
| 55 | G | 0.49 | 0.47 | 16900 |
| 60 | S | 0.81 | 0.70 | 2250 |
| 61 | S | 0.97 | 0.78 | 1020 |
| 62 | S | 0.78 | 0.75 | 1740 |
- a Abbreviation n/a indicates data are not available.
[19] Features in microtopography transitionally change when Sc is close to 0.70, thus we classified channel heads into two types (Figure 5), according to Sc: type G (Sc < 0.70) and type S (Sc > 0.70). Detailed land surveys in two first‐order watersheds clarify the microtopographic difference in two types of channel heads (Figure 6). A type‐G channel head (C1H) in the watershed C1 has a large hollow, which appears to be filled with gravels. Bedrock is exposed in only 3% of the source area. Small ephemeral channel banks are gradually formed along the hollow axis (shown as the dashed line in Figure 6), and the gradient also changes gradually from slope to channel. In the other type‐G channel heads, large hollows appear to be filled with gravels. Gravels are supplied from the bedrock outcrops and steep slopes behind the hollows. Shallow landslides are not directly related to the location of type‐G channel heads.
[20] In contrast, bedrock is exposed in 29% of the source area of a type‐S channel head (C3H) in the watershed C3 (Figure 6). Many bedrock outcrops were also found in the other type‐S channel heads. Shallow‐landslide scars are not common even in type‐S channel heads, probably a result of the coarse particle size derived from the chert bedrock. Five type‐S channel heads have shallow‐landslide scars, which are relatively small in size (<5 m in width). Although the channel head C3H has a small landslide scar, the scale of this landslide is much smaller than that in granitic hillslopes (10–20 m in width) where frequent shallow landslides are dominant geomorphic processes [e.g., Iida and Okunishi, 1983; Onda, 1992, 1994]. Hattanji and Onda [2004] observed rockfall and bed load transport at the watershed C3 underlain by chert, and indicated that coarse sediment supplied by rockfall from bedrock outcrops must be transported as bed load in storm runoff at the steep channel head (C3H).
4. Hydrogeomorphic Observations
4.1. Spatial Distribution of Spring Discharge
[21] Discharge from springs was measured manually at 12 first‐order channels in the basin designated CL, having a drainage area 0.128 km2 (Figure 3a). Nine total observations were made from January to October in 2002, including two cases of stormflow. A single observation at all 12 springs took from 2.0 to 3.7 hours. Some spring locations varied along the channel in response to runoff conditions. Narrow and sloping bedrock channels immediately below the springs were selected for observation so as to reduce the leakage of water into the channel bed. Flowing water was captured with a vinyl bag in a given time, and the amount was measured with cylinders. This method is available for a range of discharge rates from 10–6 to 10–2 m3/s.
[22] Spring discharge varied with runoff conditions. On low‐flow stages in the dry winter (January to April), eight first‐order channels had no springs. Minor flows of 10–6–10–5 m3/s were observed at only four springs, which were located from 20 to 100 m downstream of the channel heads. On low‐flow stages in the humid summer (May to September), springs with flows of 10–6–10–4 m3/s were observed at nine first‐order channels; the remaining three had no springs. The springs were located from 5 to 40 m downstream of the channel heads. During stormflow immediately after rainfall events exceeding 100 mm (11 July and 2 October in 2002), all 12 first‐order channels had springs with flows ranging between 10–4–10–2 m3/s. The distance between springs and channel heads fell between 0 and 25 m. Since the spring locations were observed a few hours after the runoff peak, springs must have been closer to the channel heads just at the runoff peak of these events.
4.2. Rainfall‐Runoff Response at Channel Heads
[23] Intensive hydrogeomorphic observations were undertaken in the two first‐order watersheds: C1 and C3 (Figures 3a and 6). Observation sites denoted C1L and C3U were located approximately 30 m downstream of the channel heads C1H and C3H, respectively. Site C3U has the steeper channel gradient, with a smaller drainage area than site C1L (Table 2). The stream discharge at sites C1L and C3U was observed using Parshall flumes and capacitive water depth probes. Rainfall was observed with tipping bucket gages at the sites R and R' (Figure 6). These observations were conducted from 11 June 2000 to 3 November 2002, and were suspended during the dry winter (essentially November to May). Rainfall events in winter were small in frequency and magnitude. Discharge and rainfall were recorded every 5 min in 2000, and 10 min from 2001 to 2002.
| Site | C1L | C3U |
|---|---|---|
| Drainage area, m2 | 7200 | 1700 |
| Local channel gradientaa
Channel gradient between an observation site and the point 10 m upstream.
|
0.384 | 0.758 |
| Ratio of bedrock outcrop, % | 5 | 19 |
- a Channel gradient between an observation site and the point 10 m upstream.
[24] A total of 59 rainfall events were observed at sites C1L and C3U over three years (2000–2002). Figure 7 shows hydrohyetographs in four rainfall events. The streamflow did not respond to small events of total rainfall <10 mm. In a rainfall event >50 mm (event A), distinct runoff peaks could be identified at both channel heads. In large events with total rainfall >100 mm (events B–D), the peak discharge of an event was clearly affected by the peak rainfall intensity rather than the total rainfall of the event. For example, although event D has less total rainfall than event B, event D had a larger peak runoff than event B at both sites. The maximum discharge over the three years (2000–2002) was observed at both sites during event C, which has the largest rainfall intensity and largest total rainfall of the four events.
4.3. Bed Load Transport
[25] Bed load transport was measured at sites C1L and C3U from 11 June 2000 to 4 May 2003. A plastic container was installed 3 m downstream of the C1L flume. A wire net having 1 cm mesh was installed about 10 m downstream of the C3U flume with anchor bolts fixed on the bedrock channel. The channel at site C3U is very steep (37°) and has gravelly sediment with no fine‐grained particles. Trapped bed load at both sites was collected every month or immediately after large storm events. Leaves and woody debris were removed from samples, as much as possible. Bed load samples at site C1L were dried in an oven at 110 °C for 24 hours and then weighed in the laboratory with an electric balance. Bed load samples at site C3U were weighed in the field with a spring balance or in the laboratory with an electric balance without oven drying, since the water content of gravels >1 cm is negligible.
[26] Figure 8 shows the temporal change in cumulative transported bed load from 11 July 2000. Bed load transport occurred mainly in the summer, from May to October. Three large rainfall events triggered the large bed load yield at site C3U from 5 August to 1 September 2001. Although the bed load trap at site C3U was partly torn by debris, the flume as well as the trap at this site captured bed load exceeding 200 kg. In contrast, the bed load yield at site C1L was only 1.1 kg during the same period. The second largest event (event C in Figure 7) triggered a bed load yield of 7.9 kg at site C1L and 6.8 kg at site C3U.
[27] Rockfalls were occasionally trapped at site C3U in winter, when intensive rainfalls were seldom observed (Figure 8). A small rockfall occurred immediately upslope of the C3U trap from February to April in 2003, contributing to the accumulation of substantial rock fragments at this trap (53.4 kg). The rockfall was probably triggered by freeze‐thaw action. Since winter rainfall was rare during the observation period (2000–2002), bed load transport by storm runoff did not contribute to the sediment yield at site C3U in winter.
5. Analysis
5.1. Prediction of Peak Discharge
[28] To test the applicability of the linear area‐discharge relation with the form of equation (1) to the investigated area, the spring discharge at the 12 sites was plotted against the drainage area for differing runoff conditions (Figure 9). Although the area‐discharge plots for low‐flow stages were relatively scattered (Figures 9a and 9b), the discharge increases proportionally with drainage area during stormflow (Figures 9c and 9d), in spite of statistical errors arising from the time required for measurements. The coefficient in the area‐discharge relation increases with increasing antecedent precipitation index, API30 [Mosley, 1979]. Hattanji and Onda [2004] have reported the generation of subsurface stormflow on the bedrock‐regolith boundary along the slope segment C–C' in watershed C3 (Figure 6). The topography of the bedrock‐regolith boundary, which controls the amount of subsurface stormflow at a given point, would approximate to the surface topography in the case of shallow regolith [Hutchinson and Moore, 2000]. The effect of topography on subsurface stormflow should yield a more accurate area‐discharge relation in springs during stormflow (Figure 9). This result indicates spring discharge is strongly controlled by drainage area during stormflow, rather than in low‐flow stages. Thus we assume a linear relationship between source area and peak discharge in the subsequent analysis.
5.2. Critical Discharge for Bed Load Transport
[30] The bed load yield at sites C1L and C3U was plotted against the peak discharge for each sampling period in the rainy seasons (Figure 11). Figure 11 indicates bed load yield increased abruptly, at both C1L and C3U sites, when the peak discharge exceeded a critical value. The critical discharges for bed load transport, Qcr, were estimated to be 0.035 m3/s for site C1L, and 0.007 m3/s for site C3U. One overscaled event of bed load transport at site C3U also occurred in response to a peak discharge exceeding the critical discharge.
[31] The relationship between critical discharges, Qcr, at sites C1L and C3U, versus the local channel gradient, Sc, from the observation site to the point 10 m upstream is highlighted in Figure 12. As described in the section of empirical model, Qcr is in proportion to Sc to the power of −7/6. Substitution of Qcr and Sc values into equation (4) gives γ values of 0.0115 m3/s for site C1L and 0.0051 m3/s for site C3U. Thus we adopt the average and range of the observed two γ values, i.e., γ = 0.0083 ± 0.0032 m3/s, in the following discussion.
5.3. Area‐Slope Thresholds for Bed Load Transport
[32] We calculate area‐slope thresholds for bed load transport for two rainfall conditions with different recurrence interval of 1 year and 100 years. In the case of 1‐year rainfall (R4 = 38 mm), equation (8) predicts kpIR = 1.65 ± 1.32 μm/s with 95% prediction interval. Substituting kpIR = 1.65 ± 1.32 μm/s and γ = 0.0083 ± 0.0032 m3/s into equation (5), critical ASc7/6 value for bed load transport with statistical uncertainty ranges 1710–34,700 m2. For 100‐year rainfall (R4 = 171 mm), kpIR with 95% prediction interval is 10.9 ± 1.43 μm/s. Thus critical ASc7/6 value for bed load transport caused by 100‐year rainfall ranges 410–1210 m2 when γ = 0.0083 ± 0.0032 m3/s.
[33] Figure 13 shows the relationship between source area and channel gradient at 24 channel heads, with the critical zones of bed load transport under the two rainfall conditions. These critical zones include statistical uncertainties derived from the rainfall‐runoff relationship and the Qcr–Sc relation of bed load transport. The critical zone of bed load transport drops with increasing rainfall intensity of storm events. Although the critical conditions for bed load transport have wide statistical uncertainties, many channel heads fall inside or between the zones of 1‐year and 100‐year rainfalls.
6. Discussion
[34] Almost all channel heads are plotted above or in the critical zone for 100‐year rainfall (Figure 13). Although the calculated threshold has a large statistical uncertainty, two thirds of all channel heads are plotted above the critical zone for 100‐year rainfall. This fact supports the hypothesis that many channel heads are located where the peak discharge produced by frequent rainfall is sufficient to transport bed load. Actually, we also observed bed load transporting events in some ungaged channel heads. On 30 November 2000, a recent removal of bed sediment was identified immediately below the channel head No. 19 (Figure 3). We also found a recent sediment yield below the channel head No. 54 on 22 September 2001. These observations support the notion of frequent bed load transport in ungaged channel heads as well as the observation sites.
[35] Shallow landslide scars were observed 0–10 m upstream of five channel heads (e.g., the channel head of site C3U in Figure 6). All of these five channel heads are plotted in the zone of 100‐year rainfall (the open diamonds in Figure 13), and may not be explained by bed load transport in a frequent rainfall (<100 years) because of the wide statistical uncertainty. Thus shallow landslides may affect the location of channel heads, particularly in higher gradient locales. The shallow landsliding may also affect the steeper trend of area‐slope relationship at all channel heads than calculated thresholds for bed load transport.
[36] We could not find any channel heads retreating successively during the observation periods of three years (2000–2002). The location of all channel heads appears to be stable on a timescale of a few years. However, channel heads must migrate on the longer timescales of more than a few years. Forest plantations in the 1960s or climate change might facilitate the migration of channel heads. Microtopography around channel heads provides qualitative evidences for the migration of channel heads. The presence of hollows filled with gravels can be interpreted as the past downstream migration of type‐G channel heads. In contrast, bedrock cliff and shallow landsliding imply the upstream retreat of type‐S channel heads. In terms of mass balance approach, exposed bedrock on most slopes above type‐S channel heads must be attributed to the larger capacity of sediment transport than sediment production. The result of the bed load observation also indicated greater bed load yield at a type‐S channel head (C3U) than a type‐G channel head (C1L, Figure 8). Thus two distinct types of channel heads must be originated from different long‐term trend of channel‐head migration.
[37] Hydrogeomorphic processes vary with lithology in humid forested mountains [Onda, 1992, 1994; Hattanji and Onda, 2004]. Climatic conditions as well as mechanical and hydrological properties also affect magnitude and frequency of landslide initiation processes. Thus the relative importance of shallow landslides on channel initiation changes site by site. Effect of shallow landsliding on channel‐head location must be more distinct in landslide‐prone areas, such as granitic areas [Onda, 1992, 1994], where the finer sediment facilitates more frequent landslide initiation. The coarser sediment in the investigated chert area than the other lithologies may reduce the frequency of landsliding, and bed load transport can have a strong influence on channel‐head location. Although shallow landsliding is actually one significant process for channel initiation, bed load transport plays another important role on channel‐head locations by maintaining the “channel” features, at least in a mountain where shallow landslides are not frequent.
7. Conclusions
[38] We examined the effect of bed load transport on channel‐head locations in the eastern Ashio Mountains, a chert area, where shallow landslides are not frequent. Empirical area‐slope thresholds for bed load transport were estimated from three types of hydrogeomorphic data: (1) spring distribution in storm runoff, (2) rainfall‐runoff relation, and (3) critical discharge for bed load transport at two channel heads of differing gradient. The discharge at 12 springs in storm runoff indicated an increase of spring discharge in proportion to drainage area. Regression analyses for rainfall and runoff data revealed peak discharge per unit area can be predicted from peak 4‐hour rainfall with a minimal statistical uncertainty. The bed load transport at both channel heads increased abruptly when the peak discharge exceeds a critical discharge. These critical discharges can be explained by a power function of channel gradient.
[39] Comparing the calculated area‐slope threshold with the observed area‐slope relation at channel heads, two thirds of all channel heads are plotted above the critical zone of bed load transport for a 100‐year rainfall. This main finding indicates that many channel heads are located where peak discharge produced by a frequent rainfall with the recurrence intervals of less than 100 years can transport bed sediment. In humid forested mountains, shallow landsliding is considered to be dominant processes for channel initiation and landform evolution. However, frequency of shallow landsliding depends on lithologic condition as well as climatic condition. Infrequent landsliding alters the dominant channel initiation processes to bed load transport. Ongoing bed load transport can be a primary geomorphic process affecting the location of channel heads if shallow landslides are not frequent.
Acknowledgments
[40] This study was supported financially by the Japan Society for the Promotion of Science Research Fellowship for young scientists, and the Foundation of River and Watershed Management (FOREM) of Japan, 12–1–1–2. We thank Yuki Matsushi, Sachi Wakasa, and Tetsushi Itokazu for their help with field work. We also thank Thad Wasklewicz for his technical support of the manuscript. We are also grateful to Mike Kirkby, and Leonard Sklar for constructive review comments.
