Modelling the runoff-sediment yield relationship using a proportional function in hilly areas of the Loess Plateau, North China

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Geomorphology 93 (2008) 288 – 301 www.elsevier.com/locate/geomorph

Modelling the runoff-sediment yield relationship using a proportional function in hilly areas of the Loess Plateau, North China Zheng Mingguo a,b , Cai Qiangguo a,⁎, Cheng Qinjuan a,b a

Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China b Graduate School of the Chinese Academy of Sciences, Beijing 100039, China Received 9 November 2006; received in revised form 27 February 2007; accepted 1 March 2007 Available online 12 March 2007

Abstract Based on data observed at the 12 small watersheds in hilly areas of the Loess Plateau, North China, the relationship between event runoff volume and sediment yield is examined. The results reveal that the runoff-sediment yield relationship at the inter-event timescale is mainly determined by the runoff-sediment concentration relationship at the intra-event timescale. In the study area, the sediment concentration tends to be stable when the flow discharge exceeds a certain critical value. Many factors that are important for determining the characteristics of low-magnitude events, such as flow discharge, particle size of fluvial sediment, and accumulation of loose material on land surfaces prior to a rainstorm, appear to have little importance for high-magnitude events. Consequently, mean sediment concentration tends to be stable for large flood events, suggesting a strong similarity between the two flow-sediment relationships at inter-and intra-event temporal scales. Furthermore, a proportional function is proposed to predict event sediment yield, and the correspondence between the predicted and observed sediment yields is examined. The performance of the model is good for high-magnitude events, especially extreme events. The applicability of the proposed model at the annual timescale is also discussed. © 2007 Published by Elsevier B.V. Keywords: Flow-sediment relationship; Sediment yield; Temporal scale; Loess Plateau of China

1. Introduction Sediment yield is defined as the amount of eroded soil that is transported by water to a certain point in a landscape or a river system, such as the catchment outlet, over a specified timescale (Lu et al., 2005). As a net result of erosion and deposition processes within a basin, sediment yield is dependent on all variables that control erosion and sediment delivery (Langbein and Schumm, ⁎ Corresponding author. Fax: +86 10 64851844. E-mail address: [email protected] (C. Qiangguo). 0169-555X/$ - see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.geomorph.2007.03.001

1958; Verstraeten and Poesen, 2001), including climate, drainage area, soils, geology, topography, vegetation, and land use (Dendy and Bolton, 1976). In recent decades, many different models and relationships have been proposed to describe and predict soil erosion by water and associated sediment yield; however, these models, which are unable to describe all soil erosion and sediment transport processes, have yet to be successfully applied at the basin scale (de Vente and Poesen, 2005). Despite the development of a range of physically-based soil erosion and sediment transport equations, sediment yield prediction is achieved mainly through simple empirical or

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regression models (Verstraeten et al., 2003). Many of these empirical models purport to be applicable at sizable catchments that embrace a diverse range of catchment features, even at regional and national scales (Dendy and Bolton, 1976; Verstraeten and Poesen, 2001; Verstraeten et al., 2003; Rompaey et al., 2005; Restrepo et al., 2006); consequently, a large number of variables have to be taken into account. In addition, as these models focus on the mean annual sediment yield rather than the event sediment yield, it is difficult to determine the real physical factors responsible for the observed spatial and temporal variations in sediment yield. Event-based studies of small watersheds may give easy access to better understanding sediment yield processes. In addition, sediment yield studies for small watersheds in particular, are very important when investigating the linkages between soil erosion and sediment transport in large rivers (Verstraeten and Poesen, 2001; Restrepo et al., 2006). However, as hydrologists lack detailed processbased understanding at the scale of small watersheds, it is difficult to develop simulation models that adequately describe hydrologic responses (Lane et al., 1997). For a given small watershed in which many important environmental controls on sediment yield (e.g., soil type, geology, and topography) are approximately constant, runoff may be the dominant factor influencing the event sediment yield in certain cases. For example, for small watersheds in hilly areas of the Loess Plateau, North China, a strong runoff-sediment yield relationship is commonly observed for individual storm events (Jiang and Song, 1980; Cai et al., 1998). In many cases, excellent model performance (R2 N 0.9) is obtained when we model the relationship as a linear or power function (Jiang and Song, 1980; Mou and Xiong, 1980; Cai et al., 2004), meaning that the runoff factor alone explains more than 90% of the observed variance in sediment yield. However, this relationship has been only poorly understood, and even whether it is linear or nonlinear is not yet clear. The runoff-sediment yield relationship for different events can be regarded as a kind of the flow-sediment relationship at inter-event timescale. Likewise, the relationship between flow discharge and sediment concentration can be considered as the flow-sediment relationship at intra-event timescale. There may be a link between the two relationships at different temporal scales. Numerous previous studies undertaken in the Loess Plateau have examined the flow-sediment relationship at intra-event timescale (e.g., Gong and Jiang, 1978; Wang et al., 1982); however, little attention has been paid to the inter-event timescale and the link between the two temporal scales. The objective of the present paper is to understand the flow-sediment relationship in hilly areas of

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the Loess Plateau at inter-event timescale and examine its link with the relationship at intra-event timescale. We present sediment yield data for individual storm events observed in 12 small catchments. Firstly, the flowsediment relationships are discussed at both intra-event and inter-event timescales. Next, an event-based model for a specific watershed is established. Finally, the correspondence between the predicted and observed sediment yields is examined and the applicability of the model at the annual timescale is discussed. 2. Outline of study area and data sources The Loess Plateau in North China is located in the middle Yellow River basin (Fig. 1a), and records some of the highest erosion rates in the world (Xu, 1999a). The hilly part of the Loess Plateau, which is 236000 km2 in area, is covered by a thick loess mantle with an average depth of more than 100 m (Cai, 2001); this is one of the most severely eroded regions of the Loess Plateau. With a mean annual rate of soil loss of more than 10 000 t km− 2 (Gong and Jiang, 1978), the region is highly dissected by a dense channel network. The area shows considerable relief, and slopes of up to 70° are not uncommon (Hessel and van Asch, 2003). The climate is generally semi-arid and temperate, with approximately two-thirds of the annual precipitation occurring as short-duration, highintensity storms (Cai, 2001). Annual sediment yields are often attributed to a small number of heavy storms (Cai et al., 1998): single storms have been reported to produce 10% of annual rainfall and 40% of annual runoff and erosion (Hessel and van Asch, 2003). In most areas the loess is too thick for the entire mass to become saturated in such a climate, and runoff occurs only when rainfall intensity is greater than the infiltration capacity of the soil. Late Pleistocene loess, or Malan Loess, is dominant in hilly loess areas. The median grain size of this loess is approximately 0.04–0.06 mm, and the silt content is generally greater than 60% (Gong and Jiang, 1978). One of the reasons for intensive soil loss in this region is hyperconcentrated flow, which has very strong erosion and transport capabilities (Xu, 1999a). Hyperconcentrated flow is widely observed in the middle Yellow River basin (Xu, 1999a) and sediment concentrations in runoff of over 1000 kg m− 3 have been recorded regularly (Hessel, 2002). With the aim of collecting data for the study of erosion and sediment yield in the middle Yellow River drainage basin, some experimental stations have been established by the Yellow River Water Conservancy Commission of PRC and the Provincial Bureaus of Shaanxi and Shanxi for Water and Soil Conservation. Data from the Chabagou experimental watershed (Yellow River Water Conservancy

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Commission, 1961–1971) and the Wangjiagou experimental watershed (Shanxi Institute of Soil and Water Conservation, 1982), located in hilly loess regions, are relatively complete (Xu, 2004). These data were printed for internal use. All measurements of discharge as well as suspended sediment concentration, load and grain size follow national standards issued by Ministry of Water Conservancy and Electric Power, PRC (1962, 1975); the measurement procedures are basically the same as those used internationally. For the details of the procedures, see Yan (1984) and Sedimentation Commission of Chinese Society of Hydraulic Engineering (1992). Strict checks were carried out as part of complying with the standards; consequently, like Xu (2004), we consider the accuracy of the data to be reliable. The following points should also be noted. 1) As most of the discharge events last for just a short period of time, the events were intensively sampled, especially during heavy-discharge periods at each station. The sampling interval was generally less than 10 min for relatively small

experimental subwatersheds and less than 30 min for relatively large experimental subwatersheds. 2) The water level was observed at a staff gauge or flume, and flow discharge was obtained using previously established discharge-water level curves. The curves were calibrated according to measurements of flow discharge obtained using current meters. Samples of water and suspended sediment were taken using horizontal samplers or bottles, and the sample concentration was used as a surrogate for the cross-section concentration; this approach was used because of the approximately uniform distribution of sediment concentration throughout the cross section. 3) According to Mou and Meng (1982), the strong sediment-carrying capacity of hyperconcentrated flow and fine sediment load in this region means that almost all of the sediment (N 95%) in motion can be regarded as wash load (Xu, 1999a). Hence, bedload can be ignored and the measured suspended sediment load can be regarded as the total load. Additional information on data collection in these two experimental watersheds and the Loess Plateau

Fig. 1. Location and maps of the study area. (a) Yellow River basin (modified from Xu, 2004), the number ‘1’ represents the location of Zizhou Country, (b) Chabagou Creek, (c) Wangjiagou Creek. Gauging station numbers in (b) and (c) correspond to those in Table 1.

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Table 1 Information of the gauging stations

Stations in the Chabagou experimental watershed

Number

River

Gauging station

Area (km2)

Observation period

Number of recorded events

1 2 3 4 5 6 7 8 9 21

Shuiwanggou Heifangou Tuanshangou Shejiagou Tuoerxianggou Liujiagou Chabagou Chabagou Chabagou Wangjiagou

Shuiwanggou Heifangou Tuanshangou Shejiagou Tuoerxianggou Sanchuangou Xizhuang Dujiagoucha Caoping Wangjiagou

0.107 0.133 0.18 4.26 5.74 21 49 96.1 187 9.1

55 59 93 40 36 52 45 47 62 134

Yangdaogou Chacaizhugou

Yangdaogou Chacaizhugou

1959–67 1959–67 1961–69 1960–69 1960–67 1959–69 1959–67 1959–67 1959–69 1955–70 1977–81 1956–70 1956–70

Stations in the Wangjiagou experimental 22 watershed 23

0.206 0.193

114 89

The listed numbers correspond to those used in Fig. 1.

can be found in Xu (2004). Unless stated otherwise, all of the data used in this study are derived from these two experimental watersheds. Only those recorded events with zero runoff depth (in mm) in original data sets were excluded from data analysis. In such cases the event runoff volume was extremely low, and the runoff depth was recorded as zero. Table 1 provides basic information on the gauging stations used in the present study. Chabagou Creek (Fig. 1b) drains a basin of 205 km2 in the northwest part of Zizhou County and flows into the Dalihe River. The average annual precipitation of the basin is approximately 450 mm, with about 70% falling between July and September. The native vegetation was cleared several hundred years ago, and most of the area is used for intensive agriculture. Over the monitoring period (1959– 1969), many gauging stations were operated in this area, and the annual sediment yield observed at the most downstream Caoping station (#9 in Fig. 1b), varies from 2110 to 71100 t km− 2, with a mean of 22 200 t km− 2. Data from nine stations with a large number of recorded events are used in the present data analysis; the catchment areas range from 0.1 to 187 km2 (Table 1). Except for Heifangou (#2), all of the experimental subwatersheds above the gauging stations were cultivated without extensive soil conservation management practices. Conservation measures taken in Heifangou mainly included terraces, grassed hillslopes, and check dams. The 9.1 km2 Wangjiagou watershed (Fig. 1c) is located about 4 km north of Lishi County. Data from three gauging stations in the watershed were used in this study. At Wangjiagou Creek, the average annual precipitation is about 505.7 mm, approximately 80.6% of which falls from May to September. Since 1955, soil conservation effort has been made, and a significant reduction in soil loss has been observed. Over the monitoring period (1955–1981), the

mean annual sediment yield was 7582 t km− 2. Measures for erosion control in this area mainly involved establishing terraces and vegetation on hillslopes, and constructing check dams within channels. The Yangdaogou and Chacaizhugou experimental subwatersheds (#22 and #23 in Fig. 1c) are adjacent to each other in the upper part of Wangjiagou Creek. They were established in order to assess the beneficial effect of soil conservation measures, especially those on hillslopes. Thus, the Yangdaogou experimental subwatershed was cultivated with no conservation practices, whereas the Chacaizhu subwatershed was cultivated with intensive hillslope conservation practices but no engineering works within gully channels. 3. Flow-sediment relationship at inter-event timescale This section focuses on the relationship between water discharge and sediment concentration. In hilly loess areas, both flow discharge and sediment concentration soon after the onset of runoff are low. Once flow discharge increases markedly, a sharp increase in sediment concentration follows. However, during the recessing stage, when a significant decrease in flow discharge occurs, the sediment concentration does not exhibit a corresponding reduction; for a given flow discharge, this results in higher sediment concentrations during the recessing stage than during the rising stage. Thus, flood hydrographs are characterized by a steep rising limb and a rapid recession, and sedigraphs are characterized by a steep rising limb but a gentle recessing limb (Qin et al., 1990). It should be noted that in the study area, high sediment concentrations can be observed even when flow discharge is quite low (Wang et al., 1982; Xu, 2004). This phenomenon is commonly observed at the recession stage, and can

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be attributed to hyperconcentrated flow. Hyperconcentrated flow is a Binghamian flow rather than a Newtonian flow, and its physical properties and mechanical behavior are different from those of normal flow (Xu, 2004). In the loess regions of the middle Yellow River basin, hyperconcentrated flow can form from rain splash, and the successive processes of sheet, rill, gully, and river channel erosion proceed under the influence of the hyperconcentrated flow (Xu, 1999a). If hyperconcentrated flow occurs, increased flow strength is not always required for further increase in sediment concentration; instead, sediment transport equilibrium can be maintained even under lower flow strength and higher sediment concentration (Xu, 1999a; Hessel, 2006). In other words, low flow strength does not necessarily correspond to low conveyance capacity. Thus, hyperconcentrated flow from the upper part of a watershed can travel long distances even at very low water discharge. A high sediment concentration is thereby maintained at the watershed outlet, even when the flow discharge falls close to zero.

Many previous studies have reported that in hilly loess areas a general flow-sediment relationship is observed across a wide range of spatial scales (e.g., Gong and Jiang, 1978; Wang et al., 1982; Fig. 2): when water discharge is below a critical value, sediment concentration varies greatly; whereas, when water discharge exceeds this value, sediment concentration varies little and tends to be stable. The latter suggests a directly proportional relationship between water discharge and sediment discharge rate. For a given watershed, when sufficient detached material is provided and supplied to the sediment transport system, the sediment yield depends on the capacity of the sediment transport system (transport-limited). Conversely, when detached material is insufficient to satisfy the transport capacity, the sediment yield is determined by the amount of detached material (supply-limited). As an eolian deposit, loess has a loose structure and its grain-size composition is dominated by the silt fraction. This leads to a low resistance to fluvial erosion. Furthermore, vertical joints are well developed in the loess mantle, providing

Fig. 2. Relationship between water discharge and sediment concentration observed at (a) Tuanshangou station (#3), (b) Shejiagou station (#4), (c) Sanchuangou station (#6), and (d) Caoping station (#9). The log scale is used for the y-axis so that the same absolute difference corresponds to the different level of variation at different levels of sediment concentration. For the same reason, the log scale is also used in Figs. 3 and 4. C values are derived from Eq. (1) and can be found in Table 3.

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potential planes upon which slides and slumps can easily form (Xu, 1999a). Hence, in the loess region, sediment supply is generally abundant and non-limiting, and sediment flux is transport-limited (Xu, 1999b). Thus, the sediment concentration shown in Fig. 2 has an implication similar to the sediment transport capacity of the flow. 4. Flow-sediment relationship at intra-event timescale This section considers the relationship between runoff depth, h (mm), and the mean sediment concentration for a single event, Cse (kg m− 3). Cse is computed by dividing the area-specific sediment yield, SSY (t km− 2), by h. For a single flood event, Cse is largely dependent on the heavydischarge stage. For example, for the two events shown in Fig. 3, Cse closely approximates the sediment concentration during the heavy-discharge stage. As shown in Fig. 2, the heavy-discharge stage is characterized by a stable sediment concentration; thus, if the events are large enough, Cse is expected to remain relatively constant and approximate the stable sediment concentration shown in Fig. 2.

Fig. 3. Relationship between water discharge and sediment concentration for (a) July 1, 1959 storm event recorded at the Caoping station (#9), and (b) June 27, 1962 storm event recorded at the Shejiagou station (#4).

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The relationships between h and Cse for all stations listed in Table 1 are similar to examples shown in Fig. 4. The flow-sediment relationship at the inter-event timescale is similar to that at the intra-event timescale: when h is low, Cse varies greatly, whereas when h is high, Cse varies little and tends to be stable. Even for many of the low-intensity events with h values of a few mm, Cse is close to the stable value (Fig. 4) because the peak flows are higher than the critical value needed to achieve the stable sediment concentration shown in Fig. 2. The sediment transport capacity in channels is determined by many factors, including flow discharge (flow depth), channel slope, cross section shape, and the physical properties of the sediment particles (Fei and Shao, 2004). Within the study area, low-magnitude flood events usually occur as a result of low-intensity rainfall. For these events, most of the flow discharge may be lower than the critical value shown in Fig. 2. In this case, the transport capacity varies with flow depth, leading to a wide variation in the range of transport capacity for different events. Meanwhile, observations undertaken at hillslope plots in Chabagou Creek (Wang et al., 1982) have revealed that when rainfall intensity is low, eroded sediment is characterized by fine particles, and the median grain size of sediment increases with increasing rainfall intensity. This implies that considerable variation can be expected in the particle size of fluvial sediment delivered to gullys. In addition, for low-magnitude flood events the accumulation of loose material on the land surface prior to a rainstorm contributes significantly to the total sediment discharge. If abundant loose material exists prior to the rainstorm, the energy expenditure of stream flow is reduced and a high value of Cse is expected. Otherwise, more energy will be required to detach soils and a low value of Cse is expected. Consequently, even for the same flow event, differences in land surface conditions will result in a variation in Cse. Generally speaking, for low-magnitude flood events, almost all factors affecting transport capacity, together with the accumulation of loose material prior to a rainstorm and other low-magnitude disturbances, will affect Cse, leading to a wide variation in Cse. Flow discharge exerts dominant influence on sediment transport capacity when flow discharge is low; however, within the study area its significance decreases with increasing flow discharge (Fei and Shao, 2004). Moreover, in Chabagou Creek, when rainstorm intensity is sufficiently strong (N 0.3 mm min− 1), all grain-size fractions of loess on a hillslope are eroded without sorting (Wang et al., 1982; Xu, 2004). This indicates a smaller difference in sediment size for highmagnitude events. For example, at the Tuanshangou station (#3), a wide variation is observed in the median grain size of suspended sediment for small flow events;

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Fig. 4. Relationship between runoff depth (h) and event mean sediment concentration (Cse), based on data from the (a) Tuanshangou station (#3), (b) Shejiagou station (#4), (c) Sanchuankou station (#6), and (d) Caoping station (#9). C values are derived from Eq. (1) and can be found in Table 3.

however, the median size remains largely unchanged when the runoff depth is greater than 1 mm (Fig. 5). In addition, river channels in the middle Yellow River basin are generally deep and narrow (Jing et al., 1993), and a lower width-depth ratio is expected for small watersheds in the study area. For this type of channel, the influence of the

cross section shape of the channel on the sediment transport capacity of hyperconcentrated flow is invariable with flow depth (Fei and Shao, 2004). In general, many of the factors that are important for low-magnitude events appear to have little effect on Cse for high-magnitude flood events, and the significance of loose material that accumulated prior to the rainstorm decreases with increasing event sediment yield. Despite the occurrence of low flow discharge during the early period of the flow rising stage and the late period of the recessing stage, this contributes little to the total runoff and sediment discharge, and thus, scarcely contributes to Cse. Therefore, for a specific watershed, Cse remains relatively constant for high-magnitude flood events. 5. Model development

Fig. 5. Relationship between the median grain size of suspended sediment (D50) and runoff depth (h) for recorded events at the Tuanshangou station (#3) during the period 1967–68.

As noted above, hilly loess areas often show a good agreement between event sediment yield and event runoff volume (Jiang and Song, 1980; Cai et al., 2004), and regression models, whether linear (Wang and Zhang, 1990; Cai et al., 2004) or power (Mou and Meng, 1981), commonly yield determination coefficients over 0.9.

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Similar results were obtained in the study area. Linear equations, i.e., y = ax+ b, were found to explain the observed variance better than power equations (y =axb) for all stations listed in Table 1. Especially for larger events, the linear equation substantially outperformed the power equation, which is obviously due to the stability of Cse for high-magnitude events. However, the linear equations have the problem that for low flows they predict either negative or positive sediment yield for zero flow. Therefore, a proportional function was used to predict the area-specific sediment yield: SSY ¼ Ch

ð1Þ

where C is the regression coefficient. The C value represents the mean sediment yield per unit runoff, or mean sediment concentration for all of the events under consideration, Cae (kg m− 3), which is equal to the ratio of total sediment discharge to total runoff discharge of all events for each monitoring station. In addition, as mentioned above, sediment concentration is directly related to the conveyance capacity of flow in the study area; thus, C can be considered to be representative of the mean sediment transport capacity per unit runoff during storm events. As C is a variable rather than a constant when we deal with many monitoring stations, C is written in Italic, C, in the following discussion. Table 2 lists some of the important characteristic statistics of h and Cse for events with values of h greater than 1 mm or 5 mm. For all events with h greater than 1 mm, dozens-fold variations in h were accompanied by only minor variations in Cse, suggesting that most of the variation in the event sediment yield is caused by h rather than Cse. Compared to the mean sediment concentration for events with h greater than 1 mm (computed by dividing the total sediment discharge by the total runoff discharge), Cse for about 80% of these events have values within 30% apart from the mean (E30% in Table 2). The corresponding variation coefficients in Table 2 are approximately 25%, which implies that a mean error of approximately 25% is expected if the runoff-sediment yield relationship for events with h greater than 1 mm is modeled using a proportional function. Moreover, when only events with h greater than 5 mm are considered, less variation in Cse is observed, suggesting that higher model performance is expected for larger flood events. The regression results derived from Eq. (1) are shown in Table 3 for all stations listed in Table 1; two of them are illustrated in Fig. 6. All events, including those with runoff depths of less than 1 mm, were used in the regression analysis. The determination coefficients for all equations are N0.9 (Table 3), suggesting a strong explanatory power of Eq. (1); however, the C value is strongly dependent on

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high-magnitude events, assuring a good estimation of sediment yield only for high-magnitude events. Similarly, Cae, the mean sediment concentration for all events, is largely determined by high-magnitude events. Therefore, in Fig. 4 almost all of the points defined by large flood events correspond to values of Cse that are close to the derived values of C. Thus, as expected, the value of C also closely approximates the stable sediment concentration shown in Fig. 2. For low-magnitude flood events, it is possible that the stable sediment concentration in Fig. 2 may not be reached for most of the flow discharge; hence, the use of Eq. (1) in such a case would be inappropriate. However, one or several single extreme events in the study area may be responsible for the majority of the annual sediment yield, and this ensures the practical applicability of the model. For example, of the 50 runoff events recorded at the Tuanshangou station (#3) in 1964, five contributed more than 99% of the annual sediment yield. These five events, with runoff depths ranging from 2 to 12.8 mm, correspond to all of the five hyperconcentrated flow events recorded during the year (see Figs. 11 and 12 of Xu, 2004). The mean sediment concentrations of these five events (ranging from 525 to 713 kg m− 3), and even the maximum sediment concentrations (ranging from 649 to 828 kg m− 3) are close to the C value (742.2). Consequently, Eq. (1) produces reasonable results for these five events, with errors ranging from 4 to 42%. Although the other small events are predicted less well, they hardly contributed to yearly sediment yield. 6. Model validation 6.1. Comparison of observed and predicted sediment yields In view of the significant difference in model performance for events with different magnitudes, model validation was performed separately for three groups: low-magnitude, medium-magnitude, and highmagnitude groups. All events with runoff depths of less than 1 mm are considered as low-magnitude events, while all events with runoff depths greater than 5 mm are considered as high-magnitude events, and other events fall into the medium-magnitude group. The mean error, E (%), is calculated as follows:   1X 1 XSSYpi −SSYoi  E¼ ð2Þ ei ¼  n i n i  SSYoi where n is the number of recorded events, ei is the calculated error for the individual event i, SSYpi represents

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Table 2 Characteristic statistics of runoff depth (h, N1 mm or N5 mm) and mean sediment concentration (Cse) Number

Events with a runoff depth greater than 1 mm h

1 2 3 4 5 6 7 8 9 21 22 23 Average

Events with a runoff depth greater than 5 mm h

Cse

Cse

Cv

max/min

Cv

max/min

E10% (%)

E20% (%)

E30% (%)

Cv

max/min

Cv

max/min

E10% (%)

E20% (%)

E30% (%)

1.2 1.3 1.1 1.1 1.4 1.1 1.5 1.3 1.1 1.9 1.4 1.2 1.3

36.9 25.6 27.8 31.3 39.0 38.1 48.0 53.4 27.8 77.1 74.0 33.6 42.7

0.30 0.32 0.22 0.19 0.27 0.27 0.21 0.22 0.19 0.33 0.31 0.25 0.26

17.7 4.2 3.9 2.6 4.1 5.6 3.2 3.2 2.8 11.0 18.4 3.7 6.7

41.7 23.5 31.3 38.2 39.1 36.8 56.4 52.4 50.9 31.6 36.9 25.6 38.7

54.2 52.9 59.4 67.6 56.5 57.9 74.4 69.0 67.3 49.1 53.8 66.7 60.7

79.2 70.6 81.3 91.2 73.9 76.3 79.5 78.6 85.5 64.9 72.3 79.5 77.7

0.80 0.39 0.55 0.61 1.05 0.82 0.99 0.97 0.72 1.14 1.09 0.71 0.82

8.12 2.67 4.50 6.26 7.22 8.06 9.26 10.68 6.69 15.42 14.80 6.72 8.37

0.16 0.12 0.20 0.17 0.20 0.24 0.08 0.18 0.18 0.28 0.24 0.22 0.19

1.98 1.34 2.48 1.93 2.34 2.60 1.30 2.34 2.37 3.68 6.91 2.74 2.67

46.2 50 41.7 53.8 36.4 50 90 55 70.6 52.9 42.9 35.7 52.1

84.6 100 83.3 76.9 72.7 64.3 100 75 76.5 58.8 65.7 64.3 76.8

92.3 100 91.7 92.3 90.9 78.6 100 75 88.2 70.6 85.7 92.9 88.2

The listed numbers correspond to those used in Fig. 1 and Table 1. Cv refers to the coefficient of variation, which is defined as the ratio of the standard deviation to the mean. Max/min refers to the ratio of the maximum value to the minimum value. E10%, E20%, and E30% are the proportions of events with Cse within 10%, 20%, and 30% from mean, respectively.

the predicted sediment yield for event i, and SSYoi represents the observed sediment yield for event i. Table 4 lists the sediment yield contributions and mean errors for all of the studied subwatersheds, as based on the three groups listed above. No significant differences are observed among subwatersheds with different sizes and even, between non-managed and managed subwatersheds (i.e., the Heifangou, Wangjiagou, and Chacaizhugou subwatersheds: #2, #21, and #23). As expected, the model performance is rather poor for the low-magnitude group; however, the sediment yield contribution of this group is insignificant relative to the total yield. For the moderate-

magnitude group, a significant increase is observed both in the sediment yield contribution and model performance compared to the low-magnitude group. With a sharp increase in sediment yield contribution, the highmagnitude group shows satisfactory model performance. Especially, for extreme events, sediment predictions are fairly accurate. For example, for the event with the highest runoff volume occurred at every studied subwatershed, the calculated errors range from 0.6 to 18.2%, with a mean of 2.3%. When the high-magnitude group of all studied subwatersheds are considered (Fig. 7b), the relationship

Table 3 Proportional regression models for all stations Station number

Regression equation

R2

1 2 3 4 5 6 7 8 9 21 22 23

SSY = 722.2h SSY = 575.8h SSY = 742.2h SSY = 690.5h SSY = 722.2h SSY = 714.1h SSY = 803.03h SSY = 774.4h SSY = 762.2h SSY = 475.8h SSY = 611.03h SSY = 558.5h

0.986 0.984 0.976 0.975 0.961 0.929 0.989 0.984 0.979 0.984 0.959 0.956

The numbers correspond to those used in Fig. 1 and Table 1.

Fig. 6. Relationship between runoff depth (h) and area-specific sediment yield (SSY) based on data from the Xizhuang (#7) and Wangjiagou (#21) stations.

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Table 4 Model performance and contribution of different event groups to sediment yield Station Sediment yield contributions Mean error for specific watershed number Low-magnitude (%) Medium-magnitude (%) High-magnitude (%) Low-magnitude (%) Medium-magnitude (%) High-magnitude (%) 1 0.8 2 4.8 3 2.5 4 0.5 5 1.4 6 5.3 7 0.4 8 0.6 9 0.5 21 2.7 22 1.4 23 3.4 Mean for specific group

7.6 20.5 16.4 21.5 13.4 29.3 31.7 18.8 31.8 21.0 11.5 22.4

91.6 74.7 81.1 78.0 85.2 65.4 67.9 80.6 67.7 76.3 87.2 74.3

2794 1447 3561 6149 1747 292 295 106 326 1340 2732 1998 1899

266.2 94.0 41.4 26.1 76.3 40.9 33.6 26.5 22.1 82.3 121.7 34.2 61.8

14.2 10.7 18.3 15.5 23.0 24.5 7.2 22.2 14.3 32.9 27.2 21.2 21.18

The station numbers correspond to those used in Fig. 1 and Table 1. The sediment yield contributions represent the sediment yield of each group relative to the total recorded events for each watershed.

between the predicted sediment yield value, SSYp (t km− 2), and observed value, SSYo (t km− 2), can be expressed as: SSYp ¼ 0:977 SSYo

ðR2 ¼ 0:959Þ

ð3Þ

The superior model performance for the highmagnitude group is due to: 1) less variation in Cse for high-magnitude events; and 2) the predominant influence of high-magnitude events on the value of C when sediment yield is predicted according to Eq. (1). For the medium-magnitude group (Fig. 7a): SSYp ¼ 1:081 SSYo

ðR2 ¼ 0:653Þ

ð4Þ

In this case, overestimates were made for many points, especially for small SSY values (Fig. 7a). For these events, peak flow may have been still lower than the critical value necessary for the stable sediment concentration shown in Fig. 2. The rainfall intensity associated with these events may also have been low, and thus soil particles detached by rainfall splash is insufficient and hyperconcentrated flow may not have occurred (Xu, 2004), resulting in a relatively rapid decline in sediment concentration during the recession stage. In general, the model does not provide an accurate prediction if the flow-sediment relationship at the intra-event timescale is significantly different from that shown in Fig. 2. With the increase in observed SSY shown in Fig. 7a, a greater number of points are close to the line of x =y; however, in the upper right part of Fig. 7a, many points are underestimated. For these events, abundant loose material may have accumulated prior to the rainstorm, leading to an unusually high value of Cse. With a further increase in sediment export, more cohesive

soil is progressively exposed and more energy is needed for soil detachment. Consequently, as shown in Fig. 8, high-magnitude events do not necessarily correspond to high values of Cse and the highest value of Cse should be observed during medium-magnitude events. 6.2. Prediction of the annual sediment yield When annual runoff volume is known, one may expect that Eq. (1) can be applied to the prediction of annual sediment yield; however, Eq. (1) cannot be used to model the runoff-sediment yield relationship during inter-storm periods, i.e., baseflow periods. Thus, the application of Eq. (1) may be inappropriate for perennial streams; whereas, a good prediction is expected for intermittent streams that only flow in direct response to precipitation. In Wangjiagou Creek, runoff only occurs as a result of rainfall (Hu, 2005). Therefore, annual sediment yield can be calculated using the established equations in Table 3 and the annual runoff volume observed at the Yangdaogou, Chacaizhugou, and Wangjiagou gauging stations (#21–23). Compared to the observed annual sediment yield, except several extremely dry years, an error of less than 100% is observed for most years. Heavystorm events occur more frequently during wet years, leading to more runoff with sediment concentrations close to the stable sediment concentration shown in Fig. 2. Therefore, the calculated error decreases with increasing annual runoff volume; for example, when the annual runoff volume exceeds 10 mm, the calculated error is less than 20%. In the Loess Plateau, sediment yield generally occurs only during the flood season. Thus, if the baseflow

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Fig. 8. Relationship between Cse and SSY for the medium- and highmagnitude groups, based on data from all gauging stations listed in Table 1. The log scale is used at the y-axis for a clear presentation of data.

flood season (June, July, and September). First, the mean annual proportion of runoff during the flood season, β¯, is calculated as: SSYa =C ¯ha b¯ ¼ ¯

Fig. 7. Observed versus predicted SSY for (a) the medium-magnitude group, and (b) the high-magnitude group.

during the inter-storm period is sufficiently low, the runoff volume during the flood season can be used to predict the annual sediment yield for perennial streams. If the mean sediment yield per unit runoff during the flood season is close to the value of C, the annual sediment yield, SSYa (t km− 2), can be calculated as follows: SSYa ¼ bCha

ð5Þ

where ha (mm) is the annual runoff depth and β is the proportion of runoff during the flood season relative to the entire year. Clearly, a higher prediction accuracy is expected in wet years than in dry years, because of the higher proportion of base flow during the inter-storm period during dry years. The annual sediment yield was predicted using annual and monthly observed data from the Shejiagou, Tuoerxianggou, Sanchuangou, Xizhuang, Dujiagoucha, and Caoping stations (#4–9) in the Chabagou watershed, for the years 1962, 1963, 1965, 1966, and 1967. In Chabagou, the stream flows throughout the year, although most of the sediment yield occurs during the

ð6Þ

where h¯a (mm) is the mean runoff depth of the five  annual records, and SSYa (t km− 2) is the mean sediment yield for the same records. Table 5 lists the predicted and observed values of β¯. Underestimates are observed for all six stations, meaning that the C value derived from Eq. (1) is always higher than the true mean sediment yield per unit runoff during the flood season, because of the effect of the base flow during the inter-storm period; however, β¯ is generally predicted accurately, suggesting that over a relatively long timescale, the mean sediment concentration or mean sediment yield per unit runoff during storm events can be approximated by the C value of Eq. (1). The annual sediment yield was then calculated according to Eq. (5), and β is obtained from monthly recorded data. Calculated errors are shown in Table 6. As expected, much worse predictions are observed than in the Wangjiagou watershed, especially in dry years; however, prediction accuracy generally increases with increasing annual runoff volume. Especially in 1966, the wettest year Table 5 Comparison of predicted and observed values of β¯ Station number

4 (%)

5 (%)

6 (%)

7 (%)

8 (%)

9 (%)

Predicted value Observed value

43.2 58.2

50.6 62.6

46.8 56.2

57.2 64.4

58.7 68.2

55.2 59.3

The station numbers correspond to those used in Fig. 1 and Table 1.

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299

Table 6 Annual runoff depth and calculated error of annual sediment yield Station 1962

1963

1965

1966

1967

Calculated error of ha Calculated error of ha Calculated error of ha Calculated error of ha Calculated error of ha (mm) SSYa (%) (mm) SSYa (%) (mm) SSYa (%) (mm) SSYa (%) (mm) SSYa (%) 4 5 6 7 8 9

28.6 33.8 38.9 30.8 37.6 29.2

98.9 110.2 51.0 56.5 43.2 61.9

35.8 63.6 47.3 39.6 56.2 44.9

78.3 − 17.5 10.1 45.7 29.6 16.8

26.7 29.9 26.6 28.1 29.2 27

5234.4 64.8 731.7 266.3 106.7 176.7

114.6 10.8 84.5 25.7 96 4.0 145.6 6.2 143.7 2.5 117.4 4.2

58.1 47.2 43.6 55.3 70.3 59.2

51.5 50.1 76.3 53.9 47.9 56.1

Station numbers correspond to those in Fig. 1 and Table 1.

of the observed period, the annual sediment predictions are reasonably accurate with most of calculated errors less than 10%. It is expected that during 1966 the runoff produced during storm events made up the vast majority of the total runoff volume of the flood season and most of them attains sediment concentrations close to the C value derived from Eq. (1). Thus, it is clear that the good predictions of β¯ are due to the heavy weighting of wet years in determining β¯. 7. Discussion Although the proposed approach of modelling the runoff-sediment yield relationship using a proportional function is somewhat contrary to the usual belief, our Chinese case is not expected to be an unique example in the world. For example, in the Walnut Gulch Experimental watershed in southeastern Arizona, USA, the relationship between event sediment yield and event runoff volume for eight runoff events can be fitted with a power function with an exponent of 1.07 and a determination coefficient of 0.99 (Lane et al., 1997), suggesting that sediment yield is approximately directly proportional to runoff volume. There are a number of similarities between the present study area and the Walnut Gulch Experimental watershed. For example, the soils in the Walnut Gulch Experimental watershed are derived mostly from highly erodible soft fan deposits and lake beds (Osterkamp and Toy, 1997); consequently, sediment availability is generally high (Lane et al., 1997) and sediment yield is transport-limited as in the Loess Plateau. Moreover, hydrographs are flashy, also implying that most of the runoff and sediment discharge are produced during the heavy-discharge stage. Normally, for a given sediment transport system, the maximum transport capacity or the upper limit of sediment concentration is expected to exist and remain constant to some degree under the local control of specific gully landforms, sediment properties, and other factors, leading to a degree of stability in the sediment concentration when the flow discharge further increases. For a given

watershed, if sediment supply is sufficient and thus sediment yield only depends on the capacity of the sediment transport system, and the stream is characterized by a flashy regime, sediment yield is largely determined by the sediment transport capacity at times of heavy flow. Thus, it is likely that most of the event runoff volume can attain the limit value of sediment concentration, and the runoff-sediment yield relationship can be modeled using a proportional function. Among the subwatersheds investigated in the present study, three (Heifangou, Wangjiagou, and Chacaizhugou: #2, 21 and 23) have been subjected to intensive soil management; in particular, engineering works have been installed within channels in the Heifangou and Wangjiagou subwatersheds. High model performances are still observed, implying that the mean sediment concentration is also approximately constant, at least for large flood events, even in these managed subwatersheds. It should be noted that the implication here is not the inefficacy of conservation measures. In fact, a significant reduction in sediment yield has been observed for these three experimental subwatersheds, which can in large part be attributed to the reduction in the number and magnitude of large runoff events. For example, over the 15-year monitoring period, the sediment yield of the Chacaizhugou subwatershed (#23) decreased by 59.1% and runoff volume decreased by 55.9% relative to the neighboring non-managed Yangdaogou subwatershed (#22). Although small runoff events occur frequently, their contribution to the annual sediment yield at the watershed outlet can be ignored; however, this does not mean that their role in geomorphological processes can also be ignored. In the hilly part of the Loess Plateau, relatively coarse fractions of sediment derived from hillslopes may temporarily be deposited and stored in gully channels during low-magnitude events. The following highmagnitude event may set the stored sediment in motion to release it from the gully channel (Xu, 2004). By virtue of this ‘preparation’ of sediment sources for subsequent

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events, the low-magnitude events may also play a role in the overall continuum of geomorphological activity. 8. Conclusions In the study area, at the intra-event timescale, sediment concentration tends to be stable when the flow discharge exceeds a critical value. For low-magnitude events, many factors, such as flow discharge, the particle size of fluvial sediment, and the accumulation of loose material on land surfaces prior to a rain storm, play important roles in determining event mean sediment concentration. However, these factors appear to have little effect for high-magnitude events and consequently the event mean sediment concentration also tends to be stable, suggesting a strong similarity between the two flow-sediment relationships at inter- and intra-event timescales. The proposed proportional model expresses a general runoff-sediment yield relationship for large flood events; thus, a good model performance is observed for highmagnitude events, especially extreme events. Despite the poor model prediction for low-magnitude events, one or several single extreme events may be responsible for the vast majority of the annual sediment yield in the study area. Hence, the model can be effectively used as a management tool. It should be noted that high-magnitude events, especially extreme events, exert the dominant influence on C values in Eq. (1); consequently, it is not necessary to exclude any low-magnitude events from the regression analysis when establishing a proportional model. The C value in the proposed model represents mean sediment yield per unit runoff, mean sediment concentration for all events under consideration, or mean sediment transport capacity per unit runoff during storm events. Especially, C value can be representative of stable sediment concentration when water discharge exceeds a critical value for a specific watershed. This implies that if the relationship between flow discharge and sediment concentration, i.e., the flow-sediment relationship at the intra-event timescale is known, then the runoff-sediment yield relationship, i.e., the flow-sediment relationship at inter-event timescale will also be known. In this way, the present study bridges the gap between the two timescales; it can therefore be considered as a case study on temporal up-scaling. Acknowledgements Two anonymous referees and Professor T. Oguchi are greatly acknowledged; their comments and suggestions are invaluable in the improvement of this paper. The financial support from the National Natural Science

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