Suspended sediment transport response to upstream wash-load supply in the sand-bed reach of the Upper Yellow River, China

Journal of Hydrology 528 (2015) 562–570

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Suspended sediment transport response to upstream wash-load supply in the sand-bed reach of the Upper Yellow River, China Wanquan Ta ⇑, Haibin Wang, Xiaopeng Jia Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Institute, Chinese Academy of Sciences, Donggang West Road 260, Lanzhou, Gansu Province, China

a r t i c l e

i n f o

Article history: Received 22 March 2015 Received in revised form 19 May 2015 Accepted 22 June 2015 Available online 27 June 2015 This manuscript was handled by Andras Bardossy, Editor-in-Chief, with the assistance of Purna Chandra Nayak, Associate Editor Keywords: Suspended sediment concentration Upstream wash-sediment supply Sand-bed river Yellow River

s u m m a r y Wash load is a major component of suspended sediment transport in the sand-bed reach of the Upper Yellow River, China. This wash load sediment originates from the Loess region, with the high runoff mainly originating from the rock mountains of its upstream basin. These characteristics result in a mismatch between water and sediment sources and a low probability of high runoffs meeting high suspended sediment concentration (SSC) flows. As a result, higher runoff with lower SSC levels (HR-LS) and lower runoff with higher SSC values (HS) occur, whose SSCs do not follow the typical power form for flow discharges, Ci = aQb, where Ci and Q are SSC and flow discharge, respectively. Here, we modify the traditional power form with an upstream wash-load supply function C1b to satisfy the relation between the water and wash load sediment concentrations in water–sediment mismatched cases, Ci = aQbC1b, where C is an input flow’s SSC. Using the daily flow discharges and SSCs of nine typical HR-LS flows and 18 HS flows in our study reach from 1960 to 2012, we find that b changes in response to input flow conditions and downstream transport distances. When the downstream transport distance is between 360 and 663.5 km, b varies between 0.3 and 0.6 in a HS input flow condition, while in the HR-LS input flow case, b tends to be greater than 0.6 (between 0.74 and 0.65). The entrainment rate of an HR-LS flow and the deposition rate of an HS flow appear to be asymmetrically balanced, establishing a primary mechanism for channel aggradation and upward fining of floodplains in our study reach. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Suspended sediment is a major component of sediment transport in many lowland sand-bed rivers. Suspended sediment contains silt and clay (i.e., wash load (Asselman, 2000)), and has important effects on the morphology, flood characteristics, and ecology of downstream channels and estuaries, the prediction of which has long been the goal of engineers, hydrologists, sedimentologists, and other earth scientists (Leopold et al., 1964). A river’s suspended sediment load is source dependent, with sediment supply, stream discharge, and grain size among the basic driving factors (Bennett and Nordin, 1977; Milliman and meade, 1983; Vansickle and Beschta, 1983; Walling and Moorehead, 1989; Trimble, 1997; Inman and Jenkins, 1999; Asselman, 2000; Hicks et al., 2000; Lenzi and Marchi, 2000; Syvitski et al., 2000, 2005; Topping et al., 2000; Rubin and Topping, 2001; Lave and Burbank, 2004; Maria et al., 2007; Warrick and Rubin, 2007; Yang et al., 1996; Yang and Simoes, 2005). For instance, if a flow’s ⇑ Corresponding author. Tel.: +86 931 4967539. E-mail address: [email protected] (W. Ta). http://dx.doi.org/10.1016/j.jhydrol.2015.06.051 0022-1694/Ó 2015 Elsevier B.V. All rights reserved.

suspended sediment has a small grain size and is dominated by wash materials, the suspended sediment concentration (SSC) will be highly variable in response to upstream runoff changes and available wash load supply in a highly sensitive and nonlinear fashion. Although suspended sediment transport is complex in a large sand-bed river and is difficult to model and predict, a number of studies have exploited long-term hydrological monitoring data from a single stream gauge station to establish statistical relationships between SSC and stream discharge (Vansickle and Beschta, 1983; Syvitski et al., 2000, 2005). This relationship commonly follows the power law of stream discharge and indicates that the majority of the sediment load is transported during infrequent periods of high runoff via turbulent entrainment (Hunt, 1954; Smith and McLean, 1977; VanRijn, 1984; Coleman, 1986; Garcia and Parker, 1991; McLean, 1992; Nelson et al., 1993; Rubin and Topping, 2001; Nezu and Azuma, 2004; Nielsen and Teakle, 2004; Wright and Parker, 2004; Winterwerp, 2006). However, this function only applies to rivers where the water and sediment originate from the same source; in cases where the water and sediment sources are mismatched, there is a lack of correlation

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between SSC and stream discharge using the power law. Rating curves are unsuitable for modeling wash load transport when wash load transport is mismatched between water and sediment sources, and the appropriate model for changes in SSC in response to the upstream wash load supply in a large sand-bed river (several hundreds of kilometers) has yet to be determined. Wash load can be transported for long distances downstream in suspension, and primarily contains silt and clay resistant to deposition in stream beds (Church, 2006). Due to large variations in upstream wash load supply, the relationship between SSC and flow discharge will show complex hysteresis during a runoff event. Here, we propose that the traditional rating curve can successfully be used to quantitatively describe wash load transport in water– sediment mismatched cases by the addition of an upstream wash load supply function. Even if the upstream wash load supply rate is given, it is still difficult to describe downstream SSC changes in a large sand-bed river using a dynamic model alone, since suspended sediment transport is a very complex entrainment and deposition process. A statistical model based on long-term monitoring data might be a better way to estimate and predict wash load sediment transport in a large sand-bed river. The Upper Yellow River represents a typical water–sediment mismatched river. The sediment primarily contains wash loads originating from tributaries of the Loess Plateau, from whose upstream rock mountains the primary runoff is generated. This mismatch results in a low probability of peak discharge meeting peak SSC, leading to high runoff with low SSC levels or low runoff with high SSC levels. This phenomenon is also observed in the lower Yellow River, thus ‘‘the more it comes, the more it goes; or the less it comes, the less it goes’’ (Wu et al., 2008a). In this study, we provided a long-term field evidence of the upstream wash load supply that regulates the downstream SSC levels in the sand-bed reach of the Upper Yellow River. Our objective was to establish an upstream wash load supply function that could be used to modify the traditional rating curve to establish an SSC model in a water–sediment mismatched sand-bed river. 2. Theory analysis We considered a flow primarily carrying wash loads and passing through a low gradient sand-bed stream channel. Since the wash load is fine in grain size, it is resistant to deposition in the main stream bed but easily deposit on bar tops and floodplain surfaces due to shallow water. In our study reach, the input flow is characterized by higher runoff with lower SSC levels and lower runoff with higher SSC levels (Fig. 1). This will cause no correlation between SSCs and flow discharges for different flow events, or the SSC-discharge hysteresis in rising and falling limbs for a given flow. Despite no correlation or the hysteresis between SSCs and flow discharges at a given site, Fig. 1b suggests that the SSC to flow discharge ratio, an upstream sediment supply coefficient or an important indicator of changes in the relationship between SSCs and flow discharges (Stubblefield et al., 2007; Wu et al., 2008b; Ma et al., 2012), shows a definite relationship between the input and output flows:

  Ci C ¼f Q Qi

ð1Þ

where C and Q are the SSC and stream discharge of the flow at the input site, and Ci and Qi are the SSC and stream discharge of the flow at the output site. This spatial relationship shows no obvious change in rising and falling limbs of peak flows and provides a method to establish a SSC model in water–sediment mismatched river. We propose that the relationship (Ci/Qi  C/Q) may be nonlinear and its pattern may change with different input–output

distances and different longitudinal bed slopes. For a given HR-LS or HS flow event, this relationship may show a similar pattern on both rising and falling limbs. If the input–output distance is small enough, Ci/Qi may equal C/Q; however, if the input–output distance is large enough, it may follow a power law. Since the channel gradient S determines the rate of flow energy expenditure, we used SQ and SiQi to replace Q and Qi according to the suggestion by Lane (1955):

 b Ci C ¼a SQ Si Q i

ð2Þ

where S and Si are the channel gradients of the input and output stream reaches, and a and b are the coefficient and the exponent and may be related to factors such as channel morphology, gradient, hydraulic geometry, and the distance between two sites. If the bed slope is the same (Si  S) and the stream discharge is assumed to change little during downstream transport (Qi  Q), Eq. (2) can be expressed as:

 b1 Ci C ¼a SQ C

ð3Þ

where a and b  1 can be estimated through the log–log regression model proposed by Ferguson (1986):

log

  Ci C þ ei ¼ log a þ ðb  1Þ log SQ C

ð4Þ

where e is the independent additive normally distributed errors with mean zero and variance r2. Using a simple correction factor exp(2.65s2) of the normal least square method (Ferguson, 1986), we can make an unbiased estimate of the parameters of a and b  1. Thus, the suspended sediment concentration can be expressed as a power law of the stream discharge, which is modified to include an upstream wash-load supply function:

C i ¼ aQ b C 1b

ð5Þ ei

1b

1b

where a equals a10 S , b equals 1  b, and C is defined as an upstream wash load supply function that expresses the relative change in SSC due to the upstream wash load supply. This supply function differs from the supply washout function proposed by Vansickle and Beschta (1983), who argued that the suspendable sediments may be stored in stream channels and their supply rates may increase with stream discharge and decrease with time. Instead, we propose that the suspended sediment load primarily originates from the upstream wash load supply, which enters the channel through a high runoff with low-SSC levels or a low runoff with high-SSC levels. 3. Study area and method 3.1. Study area The Yellow River flows through the Hetao plain and develops a typical sand-bed stream channel. This sand-bed channel is a braided (Shizuishan–Sanhuhekou) and meandering (Sanhuhekou–Toudaoguai) channel of 663.5 km with an average gradient of 0.00015 (Fig. 2). Data from three gauge stations (Shizuishan, Sanhuhekou, and Toudaoguai) in this reach indicate that, on average, 82–85% of the total suspended sediment is clay and silt (Table 1), which plays an essential role in suspended sediment transport in the Upper Yellow River. This wash load primarily originates from tributaries of the Loess region between the Xiaochuan and Qingtongxia stations, but most of the runoff originates from tributaries of the rock mountain area upstream to the Lanzhou station (Figs. 2 and 3). The runoff and sediment primarily result from heavy rainfall in the summer and autumn. Since the

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Fig. 1. A higher runoff with lower-SSC levels and two higher SSC flows with lower runoffs from July 7 to September 14, 1964, in the sand-bed reach of the Upper Yellow River. (a) Blue lines represent flow discharge curves, orange lines represent suspended sediment concentrations (SSC) curves; (b) C0/Q0 is the ratio of SSCs to flow discharges at the Shizuishan station, Ci/Qi is the ratio of SSCs to flow discharges at the Bayangaole, Sanhuhekou and Toudaoguai stations. Shi, Bay, San and Tou are Shizuishan, Bayangaole, Sanhuhekou and Toudaoguai stations, respectively.

Fig. 2. The Upper Yellow River and our study sand-bed reach (from the Shizuishan station to the Toudaoguai station). The thicker red dashed line is the dividing line between the Upper Yellow River basin and the Middle Yellow River basin; Black circles with black dots are the gauge stations in the Yellow River. YR is the Yellow River; Da is Dari station; Ma is Maqu station; Tang is Tangnaihai station; Gui is Guide station; Xun is Xunhua station; Xiao is Xiaochuan station; Lan is Lanzhou station; Xia is Xiaheyan station; Qin is Qingtongxia station; Shi is Shizuishan station; Bay is Bayangaole station; San is Sanhuhekou station; Tou is Toudaoguai station; Wu is Wubao station; Long is Longmen station; Tong is Tongguan station; Hua is Huayuankou station; Li is Lijin station.

Table 1 Estimates of averaged median grain sizes (D50) and wash material contents of the total suspended sediments in three gauge stations in the sand-bed reach of the Upper Yellow River, China. Period

Silt and clay (<0.063 mm; %)

D50 (mm)

Shizuishan

1966–1968 1969–1986 1987–1999 2000–2012 1966–2012

86.1 83.1 83.2 76.6 82.3

0.017 0.021 0.019 0.026 0.022

Bayangaole

1959–1968 1969–1986 1987–1999 2000–2012 1959–2012

87.6 82.0 80.9 74.8 82.7

0.019 0.023 0.018 0.022 0.021

1961–1968 1969–1986 1987–1999 2000–2012 1961–2012

87.8 84.9 84.3 80.6 85.4

0.018 0.019 0.014 0.018 0.017

Toudaoguai

water and sediment sources are mismatched in the upstream basin, this study reach experiences a higher runoff with lower SSC levels or a lower runoff with higher SSC levels.

This channel also shows coarser-grained beds (>0.08 mm), whose sediments primarily originate from wind-blown sand inputs from the Ulan Buh Desert, hyper-concentrated floods (sediment concentration: 1600 kg m3) from the ten tributaries crossing the Kubq Desert and bank erosions of the stream channel (Ta et al., 2008, 2011, 2013). As a consequence, although the channel shows a high lateral channel shift and bank erosion rate, its SSC levels only minimally increase in our study reach. A flow’s SSC in our study reach primarily depends on the upstream sediment supply rather than on its stream discharge alone. 3.2. Method To establish a statistical SSC function in response to the upstream wash load supply, we selected three gauge stations (Shizuishan, Sanhuhekou and Toudaoguai) in the sand-bed reach of the Upper Yellow River (Fig. 2) and compiled their daily SSCs and daily flow discharges of high runoffs and high-SSC flows from 1960 to 2012. The daily SSCs and flow discharges were the averaged cross-section values in the three gauge stations, whose measurements and calculations followed the criteria of GB 50159-92 and GB 50179-93, respectively, issued by the Ministry of Water Resources of the People’s Republic of China. The Shizuishan station

W. Ta et al. / Journal of Hydrology 528 (2015) 562–570

Fig. 3. Annual flow discharges (FD), sediment transport (ST), and suspended sediment concentrations (SSC) from 1952 to 2007 of eleven gauge stations indicating the water and sediment sources in the Upper Yellow River. WS is the water source, which yields the runoffs from rock mountain tributaries between the Tangnaihai and Lanzhou station; SS is the sediment source that delivers wash material from loess tributaries between the Xiaochuan and Qingtongxia stations; SBR is our study sand-bed reach. The abbreviations for the gauge stations are shown in Fig. 2.

565

was considered the input site and the other stations the output sites. These two input–output site pairs result in two study reaches: Shizuishan–Sanhuhekou and Shizuishan–Toudaoguai, which are about 360 and 663.5 km in length, respectively. Although the Bayangaole station is also an important station in our study reach, it was unsuitable for this study because it lies about 1500 m downstream of the Sanshengong barrage gate, which regulates the water for the Hetao irrigation district (Ta et al., 2008) and influences SSC levels. These two selected reaches are long enough for a flow from which the balance between entrainment and deposition rates can be approximated. According to the monitoring data, this study reach experienced 13 high runoffs (discharge peak >3000 m3 s1and SSC levels <10 kg m3 at both the Shizuishan and Toudaoguai stations) and 29 high SSC flows (Peak SSC > 15 kg m3 at the Shizuishan gauge station) over 62 years. High runoffs that showed high SSC values at the Toudaoguai station were excluded due to influences by hyper-concentrated flows from the ten cross-desert tributaries in the Ordos Plateau. High SSC flows that were transported downstream and decreased their peak SSC values too low to be identified at the Toudaoguai station were also excluded. Thus, nine high runoffs with low-SSC levels (HR-LS) and 18 high SSC flows (HS) were selected for study (Figs. 4–6). Using these data and Eqs. (4) and (5), an unbiased estimate of the parameters of a and b were calculated, from which a and b in Eq. (5) were also estimated to provide a modified rating curve for the wash load concentration in our study reach.

Fig. 4. The daily flow discharges and SSCs of nine typical high runoffs with low SSCs (HR-LS flows) in the sand-bed reach in the Upper Yellow River. Blue lines represent flow discharges as in (a); orange lines represent SSCs as in (b). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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4. Results The upstream wash load supply played an essential role in regulating the downstream SSCs in our study reach. SSC peaks (20.2–74.1 kg m3) observed at the input site at the Shizuishan station passed through the output site at the Toudaoguai station about 5–7 days later, with SSC peaks decreasing to between 6.3 and 30.3 kg m3 (Table 3). This wash load supply was higher than transport capacity and regulated the downstream SSCs through deposition in our study reach. Although a higher runoff has higher transport capacity for suspended sediments, the nine selected HR-LS flows had low SSC levels during their passage through our study reach, with values of 1.74–7.00 kg m3 at the Shizuishan station and 1.65–9.64 kg m3 at the Toudaoguai station (Table 2). These low SSC values at both the input and output sites also suggested that suspendable sediments such as wash materials were minor bed components, which inhibit a flow’s entrainment rate and is a primary reason for a high runoff with low SSC levels in our study reach. Plots of Ci/C and C/SQ in the nine HR-LS flows (Fig. 7) and the 18 HS flows (Fig. 8) showed a power Ci/C to C/SQ relationship and tested that our hypothesis of Eq. (2) is right. Using the method of Eq. (4) and the data of Figs. 4–6, we can make an unbiased estimate of the parameters of a and b in Eq. (5) in an HR-LS or HS flow case, and provide its related SSC model, respectively (Table 4). These results indicated that if an HR-LS flow entered the reach through the Shizuishan station, its SSC level at the downstream sites of

the Sanhuhekou and Toudaoguai stations obeyed the following equations:

C Qs ¼ 0:024Q 0:74 C 0:26 h l

ð6aÞ

C Qt ¼ 0:027Q 0:65 C 0:35 h l

ð6bÞ

where Cl and Qh are the SSC and the stream discharge of the HR-LS flow at the Shizuishan station, and CQs and CQt are the SSCs at the Sanhuhekou and Toudaoguai stations, respectively. These two equations indicated that b was closely related to the downstream transport distance, which decreased from 0.74 to 0.65 as the downstream transport distance increased from 360 to 663.5 km. In addition, as an HS flow appeared at the Shizuishan station, its SSC level at the Sanhuhekou and Toudaoguai stations responded to show:

C Cs ¼ 0:15Q 0:34 C 0:66 l h

ð7aÞ

0:4 C Ct ¼ 0:04Q 0:6 l Ch

ð7bÞ

where Ch and Ql are the SSC and the stream discharge of the HS flow at the Shizuishan station, and CCs and CCt are the SSCs at the Sanhuhekou and Toudaoguai stations, respectively, showing that b increased from 0.3 to 0.6 with increased downstream transport distance from 360 to 663.5 km in the HS input flow case. These results suggested that if the HR-LS and HS flows at the input site (the Shizuishan station) have equal flow discharges

Fig. 5. The daily flow discharges and SSCs (>40 kg m3 peak SSCs at the Shizuishan station) of the 18 typical high SSC flows (HS flows) in the sand-bed reach in the Upper Yellow River. Blue lines represent flow discharges as in (a); orange lines represent SSCs as in (b). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 6. The daily flow discharges and SSCs (<40 kg m3 peak SSCs at the Shizuishan station) of the 18 typical high SSC flows (HS flows) in the sand-bed reach of the Upper Yellow River. Blue lines represent flow discharges as in (a); orange lines represent SSCs as in (b). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 Flow discharge peaks and their suspended sediment concentrations of the selected 9 high runoffs (discharge peak > 3000 m3 s1 at the Shizuishan and Toudaoguai stations) in the sand-bed reach of the Upper Yellow River, China from 1960 to 2012. Peak-discharge flows with SSC levels (discharge peaks/SSC levels, m3 s1/kg m3) Shizuishan

Sanhuhekou

Toudaoguai

Date

FD/SSC

Date

FD/SSC

Date

FD/SSC

4 October 1963 15 September 1967 12 September 1976 18 September 1978 20 September 1981 23 August 1983 2 August 1984 17 September 1989 31 August 2012

4140/4.19 5240/4.87 3940/3.31 4210/5.64 5660/3.16 3660/4.09 4030/7.00 3340/4.43 3360/1.74

8 October 1963 19 September 1967 15 September 1976 19 September 1978 23 September 1981 25 August 1983 4 August 1984 21 September 1989 3 September 2012

3460/8.31 5380/9.64 3770/8.93 3960/8.07 5460/7.73 3660/8.05 3770/9.10 2900/6.55 2830/5.87

12 October 1963 20 September 1967 18 September 1976 23 September 1978 26 September 1981 27 August 1983 10 August 1984 24 September 1989 7 September 2012

3170/6.59 5310/4.99 3640/7.05 3770/5.93 5150/3.06 3460/8.74 3890/9.64 3020/6.56 3010/1.65

Note: SSC is suspended sediment concentration; FD is flow discharge.

(Qh = Ql), their SSC levels at the output site (the Toudaoguai station) primarily depend on their SSC levels at the input site. In addition, as the two input flows have equal SSC levels (Ch = Cl), their SSC levels at the output site will respond to increase with increased flow discharges at their input site. This model also provided a criterion suggesting that the HR-LS and HS flows at the Shizuishan station can ultimately reach similar SSC values at the Toudaoguai station via net entrainment and deposition, respectively, when the 0.6 power of their stream discharge ratios approximate the 0.4 power of their SSC ratios:

 0:6  0:4 Qh Ch  Ql Cl

ð8Þ

This criterion indicates that there is an inherent tendency for wash loads to settle easily on floodplain surfaces due to shallow water but to entrain difficultly by high runoffs due to separation from the mainstream. As a result, there is an asymmetric balance between the entrainment rate of an HR-LS flow and the deposition rate of an HS flow, which is a primary mechanism of channel aggradation and upward fining of floodplains in our study reach (Fig. 9).

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Table 3 Suspended sediment concentration peaks and their flow discharges of the selected 18 high-SSC flows (SSC peak > 15 kg m3 at the Shizuishan station) in the sand-bed reach of the Upper Yellow River, China from 1960 to 2012. Peak-SSC flows with flow discharges (SSC peaks/flow discharges, kg m3/m3 s1) Shizuishan

Sanhuhekou

Toudaoguai

Date

SSC/FD

Date

SSC/FD

Date

SSC/FD

10 June 1963 23 August 1964 26 August 1968 31 August 1973 9 August 1977 18 July 1978 30 June.1986 10 August 1988 14 August 1992 13 August 1994 9 August 1995 6 September 1995 30 July 1996 13 Aug. 1996 2 Aug. 1997 10 Aug. 1999 18 Oct. 1998 30 Sep. 2012

28.9/963 61.5/3620 20.2/2260 49.8/1950 24.6/2160 35.6/851 74.1/1580 22.0/990 33.9/1520 26.1/1920 37.8/1270 41.1/1140 57.3/1590 32.6/1220 48.1/1190 47.7/1170 29.9/568 23.1/1570

16 June 1963 26 August 1964 30 August 1968 5 September 1973 12 August 1977 22 July 1978 4 July 1986 14 August 1988 18 August 1992 16 August 1994 13 August 1995 9 September 1995 4 August 1996 15 August 1996 7 August 1997 13 August 1999 22 October 1998 3 October 2012

9.17/352 32.1/3020 14.3/968 33.8/1770 14.2/1840 19.6/545 36.1/1140 15.4/1230 14.2/1620 15.2/1910 22.5/916 18.6/1450 21.3/914 18.8/1530 14.1/704 21.2/1250 12.3/563 11.7/1270

22 June 1963 28 August 1964 3 September 1968 5 September 1973 14 August 1977 25 July 1978 7 July 1986 17 August 1988 21 August 1992 18 August 1994 16 August 1995 11 September 1995 7 August 1996 18 August 1996 10 August 1997 17 August 1999 27 October 1998 5 October 2012

6.35/359 20.6/3020 12.3/942 28.1/1790 14.1/1730 10.8/364 30.3/1260 10.9/1210 6.48/1460 8.42/1650 15.8/972 13.0/1410 13.1/976 12.3/1040 7.21/795 8.55/877 6.73/318 6.3/1000

Note: SSC is suspended sediment concentration; FD is flow discharge.

Fig. 7. Relationship between Ci/C and C/SQ for the nine typical high runoffs with low SSCs (HR-LS flows) in the Shizuishan–Sanhuhekou reach (olive) and the Shizuishan–Toudaoguai reach (blue), respectively.

gradient channel. Especially in a reach with a wide floodplain, the channel adjustment resulting from quickly increased flow was very limited, and hence increased flow should lead to a wash load deposition by shallow water over the wide floodplain and consequently to a downstream decrease in the SSC level. Syvitski et al. (2000) argued that suspended sediment load should be an integration of the river basin characteristics above the measurement site. They proposed that the suspended sediment load can be predicted using the power law form of stream discharge where the water and sediment sources are similar but not where the water and sediment sources are mismatched. Although they did not provide a SSC function for the mismatched case, they recognized the importance of upstream flows’ SSC levels on downstream SSC changes in large sand-bed rivers. Vansickle and Beschta (1983) provided a revised power SSC function of stream discharge that included a supply depletion or washout function. They proposed that the suspendable sediment may be stored in stream channels and their supply rates may increase with stream discharge and decrease with time. Our analysis suggests that their model is based on the bed-sediment supply but cannot

5. Discussions In our study reach, the suspended sediment originates from the loess region but the high runoff is mainly from the rock mountain of its upstream basin. This water–sediment mismatch leads to a low probability of high runoffs meeting high-SSC flows and, therefore produces high runoffs with low SSC levels or low runoffs with high-SSC values. These two flows transport most of suspended sediment as wash loads and, once entering the channel, their SSC levels depend on their input water–sediment relationship rather than stream discharge alone. We hypothesize that the wash load supply from high SSC flows not only regulates downstream suspended sediment levels, but also deposits finer sediments on upper banks and floodplain surfaces rather than in the mainstream bed to alternately inhibit the SSC level of a high runoff. This was confirmed in the nine HR-LS flows in our study reach, examination of which also indicated that the coarser bed sediments (>0.08 mm) cannot be transported as suspended loads for long distances by high runoffs in such a low

Fig. 8. Relationship between Ci/C and C/SQ for the 18 typical high SSC flows (HS flows) in the Shizuishan–Sanhuhekou reach (olive) and the Shizuishan–Toudaoguai reach (blue), respectively.

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Table 4 Relationship between Ci/C and C/SQ for the nine typical high runoffs with low suspended sediment concentrations (HR-LS) and the 18 typical high-SSC flows (HS) in the Shizuishan–Sanhuhekou reach and the Shizuishan–Toudaoguai reach, respectively. Eei

Ordinary least square fitting equations HR-LS

HS

Exp(2.65s2)

C ¼ 0:8558  0:7425 logðSQ Þ; ðR ¼ 0:89; P < 0:0001Þ

0.0000

1.020

C 0:8859  0:6486 logðSQ Þ; ðR ¼ 0:69; P < 0:0001Þ

0.0020

1.060

C Þ; ðR ¼ 0:64; P < 0:0001Þ log CCCs ¼ 0:41  0:34 logðSQ

0.0018

1.056

log CCCt

0.0005

1.074

C log CQs C log CQt

¼ 0:82 

C 0:59 logðSQ Þ;

ðR ¼ 0:80; P < 0:0001Þ

2 . ðn  2Þ. Notes: ei is an independent additive error with expectation Eei and variance r2, s2 is an unbiased estimator of r2: s2 ¼ i¼1 log CCm  log^ CCm where C and Q are the SSC and stream discharge of the flow at the input site; m represent Qs, Qt, Cs, and Ct, respectively. CQs and CQt are the SSCs of the flows at the Sanhuhekou and Toudaoguai stations in response to HR-LS input flows, and CCs and CCt are the SSCs of the flows at the Sanhuhekou and Toudaoguai stations in response to HS input flows, respectively. Pn 

impacts, parameters a and b will change greatly in different sand-bed rivers. Since a and b are very important for predicting the wash load sediment transport in a large sand-bed river, their functions deserve further consideration and study. 6. Conclusions

Fig. 9. Schematic of a downstream decay of a high SSC flow in SSC levels by deposition and a downstream increase of a high runoff in SSC levels by entrainment, suggesting an asymmetric balance between the entrainment rate of an HR-LS flow and the deposition rate of an HS flow in a sand-bed river. L is a downstream distance; Ct is the suspended sediment concentration.

accurately predict a flow’s SSC change in response to the high upstream wash load supplies normally found in minor quantities in the stream bed. We provide an upstream wash load supply function C1b that was used to modify the traditional rating curve and establish an SSC model in a water–sediment mismatched river, Ci = aQbC1b. Like the rating curve, our model is a simple, statistical SSC model with only two parameters and that can be easily and reliably calibrated and validated with limited data sets from many given rivers. In our study reach, b was between 0.3 and 0.6 in an HS input flow condition, and between 0.74 and 0.65 in an HR-LS input flow case. Our results also suggest that b was closely related to downstream transport distance. If the downstream transport distance is long enough to balance the entrainment rate and the deposition rate in the flow, its SSC level will tend to approximate a constant value, even at its downstream site. For a given discharge flow, we suggest that although input flows with different SSC levels can finally reach a similar SSC level, their entrainment-deposition balance distance is likely to be different and increase with increased SSC levels at the input site. This effect will cause net deposition and is a primary mechanism of channel aggradation and upward fining of floodplains in our study reach. Although our results indicated that the coefficient a and the exponent b are closely related to the channel bed slope (a10eiS1b) and the downstream transport distance, respectively, they actually also depend on several other basic factors such as the input flows’ water–sediment relationship, confluence of tributaries, channel morphology, bank erodibility, which combined to determine wash load sediment transport. Since these factors are highly variable in many natural rivers due to nature and human

Here, we report a modified rating curve for wash load sediment transport in the sand-bed reach of the Upper Yellow River, China. Our model includes an upstream wash load supply function C1b and describes the wash load concentration in cases where water and sediment sources are mismatched and in which the traditional rating curve is unsuitable. In this supply function, the parameter b changed in response to input flow conditions and downstream transport distances. Using daily flow discharges and SSCs of nine typical HR-LS flows and 18 HS flows in our study reach between 1960 and 2012, we established that when the downstream transport distance is between 360 and 663.5 km, b changed between 0.3 and 0.6 in the HS input flow condition. In an HR-LS input flow case, b tends to be larger than 0.6, varying between 0.74 and 0.65. This result also suggests that the entrainment rate of an HR-LS flow and the deposition rate of an HS flow are asymmetrically balanced, establishing a primary mechanism of channel aggradation and upward fining of floodplains in our study reach. Acknowledgements This work was supported by the Natural Science Foundation of China (No. 41171011), the National Basic Research Program of China (No. 2011CB403302) and the One-Hundred Talents Project of CAS ‘‘Desert Surface Processes and Mechanisms’’. The authors acknowledge Prof. Andras Bardossy and two anonymous reviewers for their reviews of the manuscript, which helped to improve the article. The authors also thank Nextgenediting (www.nextgenediting.com) for editorial help. References Asselman, N.E.M., 2000. Fitting and interpretation of sediment rating curves. J. Hydrol. 234, 228–248. Bennett, J.P., Nordin Jr., C.F., 1977. Simulation of sediment transport and armoring. Hydrol. Sci. Bull. 4, 555–570. Church, M., 2006. Bed material transport and the morphology of alluvial river channels. Annu. Rev. Earth Planet. Sci. 34, 325–354. Coleman, N.L., 1986. Effects of suspended sediment on the open-channel velocity distribution. Water Resour. Res. 22, 1377–1384. Ferguson, R.I., 1986. River loads underestimated by rating curves. Water Resour. Res. 22, 74–762. Garcia, M., Parker, G., 1991. Entrainment of bed sediment into suspension. J. Hydraul. Eng. 117, 414–435. Hicks, D.M., Gomez, B., Trustrum, N.A., 2000. Erosion thresholds and suspended sediment yields: Waipaoa River basin, New Zealand. Water Resour. Res. 36, 1129–1142.

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