Decreasing trend of sediment transfer function of the Upper Yellow River, China, in response to human activity and climate change

Abstract

An index (F_s) for sediment transfer function is introduced, based on the sediment budget at the channel scale. The purpose of this study is two-fold: to gain a deeper insight into how F_s is influenced by natural and human factors, and to provide some new knowledge for decision making in the management of the Upper Yellow River, China. Since 1960, the F_s of the Lanzhou to Toudaoguai reach of the Upper Yellow River shows a decreasing trend. At the drainage basin level, the decreased F_s can be explained by changes in precipitation and air temperature, as well as by a number of variables describing human activity, such as reservoir regulation, water diversion, and soil and water conservation. The higher temperature reduces the transfer function, while the larger runoff coefficient increases it. At the channel level, the decreased F_s can be explained by a number of variables of flow and sediment input. Three countermeasures for restoration of the F_s are suggested.

Editor Z.W. Kundzewicz

Résumé

Un indice F_s du transfert de sédiments a été défini, basé sur le bilan des sédiments à l’échelle du chenal d’écoulement. L’objectif de cette étude recouvre deux aspects : développer une connaissance plus approfondie de la façon dont l’indice F_s est influencé par des facteurs naturels et humains, et fournir de nouvelles connaissances pour la prise de décision dans la gestion de la partie supérieure du fleuve Jaune, en Chine. Depuis 1960, l’indice F_s du tronçon du fleuve Jaune amont compris entre Lanzhou et Toudaoguai, indique une tendance à la décroissance. A l’échelle du bassin versant, la diminution de l’indice F_s peut être expliquée par les modifications des précipitations et la température de l’air, ainsi que par un certain nombre de variables décrivant l’activité humaine, telles que la régularisation par des réservoirs, la dérivation de l’eau, et la préservation des sols et de l’eau. La température plus élevée réduit le transfert alors que le coefficient d’écoulement plus élevé l’augmente. Au niveau du chenal, la diminution de l’indice F_s peut s’expliquer par un certain nombre de variables d’entrée de débit et de sédiments. Nous proposons trois contre-mesures destinées à la restauration de l’indice F_s.

Key words:

• Upper Yellow River, China
• sediment transport
• human activity
• reservoirs
• changing hydrological regime

Mots clefs:

• cours supérieur du fleuve Jaune
• Chine
• transport des sédiments
• activité humaine
• réservoirs
• modification du régime hydrologique

1 INTRODUCTION

The river system is an open system and has multiple functions including ecological, water resources, flood release, sediment transfer, navigation and environmental functions (Xu 2008). For a heavily sediment-laden river like the Yellow River, the study of sediment transfer function (STF) is particularly important. The STF of a river depends on its sediment carrying capacity and is closely related to the water and sediment combinations of the river controlled by natural and human factors in the drainage basin, and also on the processes at reach scales. When these factors change, the STF will also change.

Source-to-sink relationships that characterize catchment sediment cascades have been effectively measured using the sediment budget approach (Walling 1983). This approach has been widely used throughout the world (e.g. Trimble 1983, Olive et al. 1994, Fryirs and Brierley 2001). Although most of the studies established this approach at basin scale, it may also be used at reach scales (e.g. Kesel et al. 1992, McLean and Church 1999). Based on the sediment budget at reach scales, the sediment delivery ratio (SDR) for a river reach can be calculated (Jiongxin 2003). In our earlier study (Xu 2008), the SDR at reach scales is used as an index for STF referred to as F_s (Xu 2008). Sediment delivery varies with time when the river basin is influenced by climate change or human activity. Reservoir construction is a major factor that changes sediment storage in a river system. Lima Neto et al. (2011) studied the sediment redistribution at basin scale due to a dense reservoir network in a large river basin and Tena et al. (2012) studied the suspended sediment balance at reach scale downstream from dams in a large Mediterranean river.

In Xu (2008), we dealt with the STF in the Lower Yellow River, using the F_s index. In this paper, the F_s of the Upper Yellow River is studied with the following objectives: to improve the method by introducing more quantitative indices of the influencing factors that better reflect the physical reality; and, to reveal the cause of the decreasing trend of F_s in the Upper Yellow River and to propose some countermeasures for better drainage basin management aimed at the restoration of F_s. As the upper part of the river basin is the ‘water tower’ of the Yellow River contributing most runoff to the river, it is greatly different from the middle part, which is the major sediment source area producing much less runoff. The human activity is also different. The Upper Yellow River is an important base for hydro-electric generation in northwest China. Although the reservoirs trap a large quantity of sediment, the sedimentation in the Upper Yellow River has shown an increasing trend since the 1980s, greatly increasing the risk of flood disaster, especially during ice-induced floods. This implies that the STF becomes weakened after dam construction. Much research has been devoted to the variations in sediment load and river flow and channel sedimentation in response to the impact of the Liujiaxia and Longyangxia Reservoirs, the two largest on the Upper Yellow River (Hou et al. 2007, Shen et al. 2007, Ta et al. 2008, Liu et al. 2009, Ran et al. 2010, Wang et al. 2010, Xu 2013). The purpose of this study is to answer the question of why the STF becomes weakened when the dams trap large quantities of upstream sediment, and thereby to provide some new knowledge for decision making in sediment management. The Ningxia-Inner Mongolia reach of the Upper Yellow River and the Lower Yellow River are two major alluvial reaches. A comparative study of the F_s between the two reaches is not only important for river management, but also interesting for river science.

2 STUDY AREA

The dividing point between the upper and middle reaches of the Yellow River is located at Hekouzhen. The most downstream hydrometric station is Toudaoguai, located 10 km above Hekouzhen (Fig. 1) and draining an area of 367 898 km². According to the hydrometric data from 1950 to 2008, the mean annual runoff (river flow) at Toudaoguai is 214.6 × 10⁸ m³, and the mean annual suspended sediment load (SSL) is 1.06 × 10⁸ t. The major sediment source areas in the Yellow River basin do not coincide with the major water source areas. The majority of runoff comes from the upper basin above Hekouzhen, and the majority of suspended sediment comes from the middle drainage basin between Hekouzhen and Longmen. The drainage area of the Upper Yellow River accounts for 51.3% of the total area of the Yellow River, the annual water yield for 55.0%, but the annual sediment yield accounts for only 8.7%. In contrast, the annual water yield from the Middle Yellow River basin from Hekouzhen to Sanmenxia accounts for only 40.2% of the total of the Yellow River, but the annual sediment yield accounts for 89.7% of the total (Ye 1994).

Fig. 1 (a) Location of study area showing Jingyuan and Quanyanshan stations. (b) Schematic relationship between sediment input and output. Q_s,L, Q_s,T, Q_s,Z, Q_s,Q, Q_s.K and Q_s,KD are annual suspended sediment load (SSL) at Lanzhou, Toudaoguai, Jingyuan (on Zulihe River), Quanyanshan (on Qingshuihe River) and from Kushuihe and 10 kondui, respectively. The sediment division (Q_s,div) with irrigation water is not shown.

The Upper Yellow River basin can be separated into two parts. The drainage area above Lanzhou is located in high mountain areas in the northeast part of the Qinghai-Tibet Plateau with a cold sub-humid climate. Annual precipitation ranges from 200 to 400 mm and evapotranspiration is low due to low air temperatures. River runoff is relatively abundant and this is the major source area of runoff for the Yellow River. As the surface material on the Qinghai-Tibet Plateau is bedrock with little loess (Ye 1994), the specific sediment yield is low compared with other parts of the Yellow River basin.

The area from Lanzhou to Hekouzhen is located in an area of temperate semi-arid or arid climate. Water erosion is relatively weak compared to that on the Loess Plateau, while wind erosion is intensive. Although, on average, erosion intensity is low, some tributaries have high specific sediment yields, such as the Zulihe and Qingshuihe River basins where a considerable part of the land surface is mantled by loess. There are 10 small creeks located in the southern bank of the Yellow River, originating from the northern edge of the Erdos Plateau, crossing the desert and flowing into the Yellow River. The total drainage area of these is 7385 km² and the specific sediment yield is in excess of 2680 t km^-2 year^-1. In Mongolian language, the 10 creeks are called ‘10 konduis’, so hereafter we refer to these rivers as 10 konduis (Zhao et al. 2008).

Since the 1960s, soil and water conservation measures have been undertaken in some tributary basins where soil erosion is strong, and erosion has been controlled to some degree. Since 1960, 13 reservoirs have been built on the trunk stream of the Upper Yellow River, among which Longyangxia, Liujiaxia, Qingtongxia and Sanshenggong exert a considerable influence on the water and sediment regime. The Longyangxia Reservoir, with total capacity of 247 × 10⁸ m³, regulates river flow on a multi-annual basis, while the Liujiaxia Reservoir, with a total capacity of 57.1 × 10⁸ m³, is used for seasonal regulation of river flow. The main objective of these two reservoirs is hydro-electric generation resulting in great changes to the hydrological regime of the river. Other reservoirs are much smaller in storage capacity, aimed at raising water level to divert water for irrigation, and therefore have a smaller influence on the hydrological regime (Zhao et al. 2008).

Due to the differing physiography and geographical settings between the two sub-drainage areas, i.e. the area above Lanzhou and the area between Lanzhou and Toudaoguai, the major source areas for water and for sediment do not coincide in the Upper Yellow River basin. According to data from 1955 to 1967, before the completion of the Liujiaxia Reservoir, the mean annual SSL at Lanzhou station was 1.10 × 10⁸ t, and the mean annual river flow was 322 × 10⁸ m³. Below Lanzhou, the main tributaries are Zulihe and Qingshuihe rivers. The mean annual SSL and river flow for Zulihe was 0.773 × 10⁸ t and 1.63 × 10⁸ m³, respectively, and the mean annual SSL and river flow for Qingshuihe was 0.206 × 10⁸ t and 4.67 × 10⁸ m³, respectively. The increase in river flow due to the two tributaries was 3.1 × 10⁸ m³, accounting for only 0.96% of the annual river flow at Lanzhou station; however, the increase in SSL by the two tributaries was 1.07 × 10⁸ t, accounting for 97.3% of the annual SSL at Lanzhou station (Xu 2013). The total SSL of 10 konduis was estimated as 0.22 × 10⁸ t (Zhao et al. 2008). The sediment supply from the tributaries between Lanzhou and Toudaoguai was 1.29 × 10⁸ t. It is thus clear that the drainage area between Lanzhou and Toudaoguai supplies little runoff but a large amount of sediment to the Yellow River. Of the total runoff, more than 95% comes from the drainage area above Lanzhou, and less than 5% from the tributaries between Lanzhou and Tougaoguai; however, of the total sediment, 46.0% comes from the drainage area above Lanzhou, and 54.0% from the tributaries between Lanzhou and Tougaoguai (Xu 2013).

The present study involves the river reach from Lanzhou to Toudaoguai, 1342 km in length. This river reach is basically located in the Ningxia-Inner Mongolia alluvial plain, and about 1000 km of it crosses deserts, such as the Tengger, Ulanbuh and Kubiq deserts. Thus, most of the river reach is alluvial channel. The channel slope decreases downstream; it is 0.79‰ from Lanzhou to Qingtongxia, 0.25‰ from Qingtongxia to Bayangaole and 0.12‰ from Bayangaole to Toudaoguai.

3 METHOD AND DATA

3.1 Index of sediment transfer function

Different from the concept of sediment carrying capacity, the sediment transfer function for a natural river is at a larger scale, relating to a long river reach over a certain period of time (say, a year or longer). The condition of sediment transport equilibrium is not necessarily needed because a natural river reach always has a sediment transfer function, whether it is in equilibrium or not. The hydraulic behaviour of rivers is highly dynamic, not only in different seasons, but also during a flood event. Hence, it is difficult to describe the sediment transfer function of rivers using hydraulic variables. In geomorphology, a force or a process itself may be described by the effect that the force or process has caused. Thus, the sediment transfer function of rivers is defined using the concept of sediment budget at river reach scales (Xu 2008). Assuming that there is a river system that consists of a trunk stream and a few tributaries, the annual sediment input at the inlet of the trunk stream is Q_s,i, the annual sediment output at the outlet is Q_s,o, and the inflow of sediment from the tributaries are Q_{s, t1}, Q_{s, t2}, …, totalled as ΣQ_s,t. The F_s is defined as the sediment output from a certain reach divided by the total sediment input to this reach:

(1)

The F_s index reflects the ‘load’ of the river relative to its ‘force’. The ‘load’ is sediment supply from the drainage basin, which the river has to carry downstream. The ‘force’ is the ability of the river to carry sediment, depending on flow strength as a function of water discharge and its time distribution. If F_s > 1, then the force of the river exceeds its load, and it may be in the condition of scour or degradation. If F_s = 1, then the force of the river matches its load, and it may be in the condition of sediment transport equilibrium (non-scour, non-fill). If F_s < 1, then the load of the river exceeds its force, and it may be in the condition of fill or aggradation.

The inlet control of the Lanzhou-Toudaoguai river reach is Lanzhou station; the outlet control is Toudaiguai station; the tributaries in between are the Zulihe, Qingshuihe, Kushuihe rivers and the 10 konduis; sediment supply from other tributaries is negligible. Some sediment is diverted with irrigation water from the trunk stream, which may be regarded as a reduction in sediment input. Thus, according to equation (1), the following can be written:

(2)

where Q_s,L, Q_s,T, Q_s,Z, Q_s,Q, Q_s,K and Q_s,KD are annual suspended sediment load (SSL) at Lanzhou, Toudaoguai, Jingyuan (on the Zulihe), Quanyansha (on the Qingshuihe) stations and from Kushuihe and 10 konduis, respectively, and Q_s,div is the annual sediment amount diverted from the trunk stream with irrigation water. The units are 10⁸ t year^-1. The relationship between sediment input and output is shown schematically in Fig. 1(b). The Q_s,div was calculated as the annual amount of water diversion from the studied reach (mainly for the Qingtongxia Reservoir and Sanshenggong Reservoir irrigation districts) multiplied by annual mean sediment concentration of the diverted water.

To calculate F_s using equation (1), the sediment input and output should include all sediment loads, namely, both suspended load and bed load. However, just like most large rivers of the world, systematic bed load measurement is not carried out in the Upper Yellow River. However, bed load measurements were taken at Toudaoguai station in 1964,1965 and 1966, with annual bed load transports of 0.376, 0.291 and 0.317 × 10⁶ t (cf. Hydrological Bureau et al. 1967), respectively, representing only 1.27‰, 3.55‰ and 1.69‰, respectively, of the annual SSL in each year. Therefore, bed load is not significant in terms of total sediment transport. Due to the lack of bed load data for most of the relevant stations, it was impossible to include the bed load element and only suspended sediment is considered in this study, so the established sediment budget is a suspended sediment budget. Since most of the river bed from Lanzhou to Toudaoguai is made up of fine sand—e.g. the median size of bed material at Baotou station 38 km upstream from Tougaoguai is 0.104 mm (Zhao 1996)—it is implicit that sediment transport is dominated by suspended sediment, and the percentage of bed load is rather low.

3.2 Indices of influencing factors at channel and drainage basin levels

3.2.1 Influencing factors at drainage basin level

Both natural and human factors influence variations in runoff and sediment yield. Annual precipitation and temperature are taken as climate variables. Due to the marked difference in runoff generation between the drainage area above Lanzhou and that between Lanzhou and Toudaoguai, the area-weighted annual precipitation over the drainage area above Lanzhou (P_L), between Lanzhou and Toudaoguai (P_LT) and that above Toudaoguai (P_T) are used as precipitation indices. The area-weighted annual air temperature (T_L) over the drainage area above Lanzhou and that (T_T) above Toudaoguai are used as temperature indices.

There are three categories of human activity in the study area, namely reservoir construction, water diversion, and soil and water conservation. So far 13 dams have been built on the trunk stream of the Upper Yellow River, greatly regulating the time distribution of runoff and sediment transport and thereby changing the sediment degradation and aggradation processes of the river channel. Reservoir regulation on annual water and sediment regimes depends not only on the storage capacity of the reservoir, but also on the annual flow of the river. Thus, the ratio (R_ra) of total storage capacity (ΣC_re) of all reservoirs on the trunk stream to the annual runoff (river flow) (Q_w) measured at Toudaoguai station is used as an index: R_ra = ΣC_re/Q_w, where R_ra may be called the regulation coefficient of reservoirs on annual flow (Xu and Yan 2010). The ratio (R_hr) of the high-flow-season flow (Q_w,H) to the annual flow (Q_w) downstream of the reservoir is also used: R_hr = Q_w,H/Q_w, to quantify the flow regulation by the reservoir. The Ningxia-Inner Mongolia Irrigation District, the most well-known irrigation district in China, is located in the study area, and the amount of water diversion is large. The index of net water diversion (Q_w,div) is used, defined as the annual amount of actual water diversion minus the amount of water returning to the river after use. To assess the relative amount of net water diversion, the ratio (R_div) of net water diversion (Q_w,div) to natural runoff (Q_w,n) is used: R_div = Q_w,div/Q_w,n. The Q_w,n is calculated as Q_w,n = Q_w,m + Q_w,div, where Q_w,m is the measured runoff. Soil and water conservation measures including land terracing, tree planting and grass planting, may be indexed by the area (A_tfg) covered by such measures. Another measure is check-dam building for trapping sediment from gullies, the effect of which is usually indexed by the area (A_c) of the land created by the trapped sediment above the check-dam (Wang and Fan 2002). In essence, the effect of sediment reduction of soil and water conservation measures results from runoff regulation on hillslopes and gullies, which reduces the runoff to precipitation coefficient during rainstorms. Thus, the natural runoff coefficient (C_nr) is also used as an index for soil and water conservation measures: C_nr = Q_w,n/P, where Q_w,n is annual natural runoff and P is annual precipitation, both above Toudaoguai.

3.2.2 Influencing factors at channel level

Due to a lack of data on channel shape and its variation, river flow and suspended sediment load are considered. The scour and fill behaviour of the river is controlled by the combination of river flow and sediment load. If sediment supply is large relative to river flow, the relative ‘load’ of the river is heavy, then it is incapable of carrying all the sediment downstream, and sediment deposition occurs. On the other hand, if sediment supply is not sufficient relative to river flow, the relative ‘load’ of the river is light, and then apart from carrying all the sediment downstream, the river has some surplus capability to scour the riverbed. The relative ‘load’ of a river can be expressed by the ratio of sediment load to its sediment carrying capability. As an approximation, we use the following two indices to reflect the river’s relative ‘load’ (Xu 2013):

(3)

(4)

where Q_s,H and Q_w,H are, respectively, suspended sediment transport rate and water discharge during high-flow (July–October) seasons. In this study, Q_s,H and Q_w,H are, respectively, the total July–October river flow and SSL to the downstream channel below Lanzhou, calculated as the sum of river flow and SSL at Lanzhou station, from Zulihe River (represented by Jingyuan station) and Qingshuihe River (represented by Quanyanshan station).

Based on data for all variables, time series analyses and statistical analyses are performed, with the Mann-Kendall method (Kendall 1975) being used to detect the trend and jump change points.

4 RESULTS AND DISCUSSION

4.1 Temporal variation in F_s and the influencing variables

The temporal variation in F_s is shown in Fig. 2(a), where a linear regression equation is given with the squared correlation coefficient (also called determination coefficient) R² at a level of p < 0.01, where p is probability of significance. This indicates that the decreasing trend in F_s is significant. The decreased F_s may result in channel sedimentation and reduces the flood releasing capacity of the river, increasing the risk of flood hazard. Thus, it is necessary to discover the causes for the decreased F_s, which will help in enhancing F_s by drainage basin management measures including reasonable river flow regulation by reservoir operation. From 1960 to 1986 the inter-annual fluctuation around the average (F_s = 0.556) is large. After 1986 a step-like decrease occurs and the averaged F_s declines to 0.168. An analysis using Mann-Kendall’s U is performed to further detect the trend in F_s, and the result is shown in Fig. 2(b). The Mann-Kendall U was calculated for the forward statistic sequence and the reversed statistic sequence of F_s, referred to as UF_k and UB_k, respectively. The curve showing temporal variations in UF_k can be used to reflect the trend of variation. The UF_k has an overall decreasing trend, with two turning points at 1974 and 1986: UF_k decreased from 1960 to 1974, and then increased; after 1986, it decreased again. If the intersection point of the curves of UF_k and UB_k occurs within the confidence interval of −0.05 < α < 0.05, then it indicates a jump-change point (Demaree and Nicolis 1990; Moraes et al. 1998). Figure 2(b) shows that the curves of UF_k and UB_k intersect at 1986 and the intersection point is located within the confidence interval; therefore, the year 1986 is a jump-change point. The year 1974 was when the Liujiaxia Reservoir was completed and all five groups of hydro-electric generators started electricity generation; 1986 was the year when the Longyangxia Reservoir was completed and used for water storage. Hence, the change in F_s is closely related to reservoir construction and operation, which is discussed in more detail later.

Fig. 2 Temporal variation in F_s: (a) variation in F_s and (b) variations in UF_k and UB_k of F_s. Confidence interval between −0.05 < α < 0.05.

Fig. 3 Temporal variation in influencing variables at (a) and (b) basin and (c) channel-reach levels.

The temporal variations in influencing variables at basin level are shown in Fig. 3(a) and (b) and those at channel-reach level in Fig. 3(c). There is a significant increasing trend in T_L, especially since the early 1980s, but no increasing or decreasing trend in P_L. The linear correlation coefficient between annual precipitation and annual temperature is only 0.168, with p = 0.225. Therefore, there is no significant correlation between the two climate variables. The R_ra and R_div increase and the C_nr decreases; the trends of all the three variables are significant at level of p < 0.01. The three variables related to dam regulation on streamflow show significant decreasing trends, with abrupt declines in 1968 and 1986. The former corresponds to the closure of the Liujiaxia Dam and the latter to the completion of the Longyangxia Dam, which has much greater impact on the river.

Fig. 4 Plots of F_s against annual precipitation (P_L) and air temperature (T_L) for the drainage area above Lanzhou.

4.2 Relationship between F_s and drainage basin factors

As previously mentioned, the drainage basin factors influencing F_s include climate variables such as P_L, P_LT, P_T, T_L and T_T, and variables of human activity such as R_ra, A_tfg, A_c, Q_w,div and C_nr. Figure 4 shows the plots of F_s against annual precipitation (P_L) and air temperature (T_L) over the drainage area above Lanzhou; regression equations, R² and p are also shown. The correlation between F_s and P_L is very low (p = 0.343). However, the negative correlation between F_s and T_L is high (p < 0.001). This is because a higher temperature may enhance evapotranspiration that reduces runoff and therefore the sediment carrying ability of the river. The very low correlation between F_s and precipitation may be explained by the two-fold effects of the changed precipitation. If precipitation increases, both runoff and sediment supply may increase. The increased runoff means an increased ‘force’ for sediment transfer, but an increased sediment supply means an increased ‘load’ of the river. Because F_s reflects the ratio of ‘load’ to ‘force’, when both the ‘load’ and ‘force’ are increased, the ratio may show little variation, and the correlation between the variations in F_s and precipitation might be low. Furthermore, the time series analysis shows a very low correlation between annual lnP_L and time (R² = 0.010). Thus, it is obvious that the decreasing trend of F_s with time cannot be caused by the variation in precipitation.

Figure 5 shows plots of F_s against R_ra, C_nr and R_div, with regression equations and R² and p also given. It may be seen that F_s is negatively correlated with R_ra and R_div, but positively correlated with C_nr, all significant at a confidence level of p < 0.001. The negative correlation of F_s with R_ra means that, after reservoir regulation, F_s decreased (Fig. 5(a)). The effects of reservoir regulation on F_s are two-fold. Sediment trapping by dams may reduce the ‘load’ in the downstream channel, an effect that increases F_s. Flow regulation by dams may reduce water discharge during high-flow seasons and thereby the force to carry sediment, an effect that reduces F_s. If the former effect exceeds the latter, the F_s may increase; if the latter exceeds the former, F_s may decrease. The drainage area below Lanzhou supplies a large quantity of sediment but a small quantity of water to the trunk stream. As noted earlier, more than 95% of the total runoff of the Upper Yellow River comes from the drainage area above Lanzhou, while 54% of the total sediment supply to the Upper Yellow River is from the tributaries below Lanzhou. The Liujiaxia and Longyangxia Reservoirs above Lanzhou can control 46% of the total sediment to the Lanzhou-Toudaoguai river reach at most, but cannot control the remaining 56% that comes in below Lanzhou. Thus, the effect of the two reservoirs to reduce sediment input to this river reach is limited (Xu 2013). However, the reservoirs, especially the Longyangxia Reservoir, have a strong ability to regulate the flow above Lanzhou, which accounts for more than 95% of the total flow input to the Lanzhou-Tougaoguai reach. Capable of performing multi-annual regulation on flow for hydro-electric generation, the Longyangxia Reservoir stores huge quantities of water during high-flow seasons, greatly reducing the July–October water discharges of the Langzhou-Toudaoguai river reach and therefore reducing its sediment carrying ability. The runoff from below Lanzhou, which is only 5% of the total, cannot increase the sediment carrying ability. Hence, after the construction of the Liujiaxia and Longyangxia reservoirs, especially the latter, the relative ‘load’ of the Langzhou-Toudaoguai reach does not decrease, but increases, and this can be regarded as the major cause for the decreased F_s. In an overall declining trend (Fig. 5(a)), the points are distributed in three sub-groups: the left contains the points from the period before the Liujiaxia Reservoir was completed, the middle contains the points from the period after Liujiaxia Reservoir was completed but before completion of Longyangxia Reservoir, and the right contains points from the period after the Longyangxia Reservoir was completed. The points in the middle and right sub-groups show a declining trend with the increased R_ra, reflecting the influence of varying annual water discharge on F_s. Therefore, for a given reservoir capacity, the higher the annual water discharge, the lower the R_ra, and then the higher the F_s.

Fig. 5 Plots of F_s against variables of human activity. (a) F_s versus R_ra; (b) F_s versus R_div; and (c) F_s versus C_nr.

With an irrigated area of 985 000 ha, the Ningxia-Inner Mongolia Irrigation District is the most important in China. The annual mean net water diversion above Toudaoguai is 114.6 × 10⁸ m³, and the annual ratio R_div of net water diversion to natural runoff ranges from 18.2 to 62.1%. Diversion of large amounts of water will reduce river flow and the sediment carrying ability and, thus, F_s decreases. Figure 5(b) indicates a negative correlation of F_s with R_div, with R² = 0.6679 and p < 0.001. As mentioned previously, C_nr can be used to index the effect of soil and water conservation measures. Figure 5(c) shows a positive correlation of F_s with C_nr, with R² = 0.6035 and p < 0.001. Soil and water conservation measures reduce F_s in two ways: firstly, July–October runoff is reduced due to enhanced infiltration and thus the ‘force’ of the river to carry sediment is reduced, and secondly, sediment yield declines due to the reduced soil erosion, which lowers the ‘load’ of the river. The negative correlation of F_s with C_nr means that the former exceeds the latter, and then a decreasing trend in F_s occurs.

Based on data from the period 1960–2005, the correlation matrix between F_s and a number of drainage basin influencing variables is shown in Table 1. The result of a t test shows that the correlation of lnF_s with lnP_L is low (p = 0.34), and the correlations of lnF_s with other variables are all significant (p < 0.001). To assess the relative contribution of these influencing variables to the variation in lnF_s, we compared, as shown in Table 1. A comparison of the correlation coefficients of lnF_s with all influencing variables, shows that the three variables related to human activity, i.e. lnR_div, lnC_r,n and lnR_re rank first, second and third, respectively, and the two climate variables, i.e. lnT_L and lnP_L rank fourth and fifth. Therefore, the variation in human activity plays a major role in the decreasing trend of F_s, with the role of the precipitation and temperature variations secondary.

Table 1 Correlation matrix between F_s and a number of drainage basin influencing variables, all converted to logarithmic values. The last row shows the rank of the correlation coefficients of lnF_s with each influencing variable.

	lnPL	lnTL	lnRre	lnCr,n	lnRdiv	lnFs
lnPL	1.00	0.09	−0.06	0.04	−0.13	0.14
lnTL	0.09	1.00	0.59	−0.71	0.70	−0.70
lnRre	−0.06	0.59	1.00	−0.55	0.70	−0.77
lnCr,n	0.04	−0.71	−0.55	1.00	−0.67	0.78
lnRdiv	−0.13	0.70	0.70	−0.67	1.00	−0.82
lnFs	0.14	−0.70	−0.77	0.78	−0.82	1.00
Rank	5	4	3	2	1

4.3 Relationship between F_s and water and sediment inputs to the river channel

Drainage basin factors on the river channel influence the amount and time distribution of flow and sediment inputs, and thereby control sediment transfer and shape-forming processes at channel level. Hence, we need to discuss the relationship between F_s and water and sediment inputs to the river channel. A number of variables influencing the F_s of the Lanzhou-Toudaoguai river reach have been introduced: (i) July–October flow (Q_wh), (ii) ratio (R_rh) of July–October flow to annual flow, (iii) ratio (C_vr) of standard deviation of monthly flow to monthly mean, (iv) annual amount of water diversion (Q_w,div), (v) the average (C_mean,H) of suspended concentration and (vi) the ratio (ξ_H) of C_mean,H to average water discharge. Variables (i), (ii) and (iii) are at Lanzhou station, (iv) is at Toudaoguai station, and (v) and (vi) are for the Lanzhou-Toudaoguai river reach. Table 2 shows the correlation matrix of F_s with these influencing variables; all correlation coefficients are significant (p < 0.01). To assess the relative contribution of these influencing variables to the variation in lnF_s, we compared the ranking of the correlation coefficients of lnF_s with all influencing variables. lnQ_wh, lnR_rh and lnC_v,r are ranked first, second and third. They are all related to reservoir regulation, especially from Longyangxia Reservoir. lnξ_H and lnC_mean,H are ranked fourth and fifth, and are influenced by reservoir regulation and soil and water conservation measures. lnQ_w,div reflects the influence of human water diversion. Hence, all six variables reflect the influences of human activity, which plays a major role in the decreasing trend of F_s.

Table 2 Correlation matrix between F_s and a number of influencing variables at channel level, all converted to logarithmic values. The last row shows the rank of the correlation coefficients of lnF_s with each influencing variable.

	lnCmean,H	lnξH	lnQwh	lnRrh	lnCvr	lnQw,div	lnFs
lnCmean,H	1.00	0.90	−0.35	−0.36	−0.32	−0.01	−0.51
lnξH	0.90	1.00	−0.72	−0.69	−0.63	0.12	−0.79
lnQwh	−0.35	−0.72	1.00	0.93	0.86	−0.26	0.89
lnRrh	−0.36	−0.69	0.93	1.00	0.93	−0.17	0.82
lnCv,r	−0.32	−0.63	0.86	0.93	1.00	−0.20	0.80
lnRdiv	0.17	0.52	−0.84	−0.67	−0.65	0.69	−0.84
lnQw,div	−0.01	0.12	−0.26	−0.17	−0.20	1.00	−0.43
lnFs	−0.51	−0.79	0.89	0.82	0.80	−0.43	1.00
Rank	5	4	1	2	3	6

Figure 6 shows the plots of F_s against Q_w,H, R_hr and C_vr at Lanzhou station. All the three correlations are highly significant (p < 0.001). Since the flow at Lanzhou station accounts for 95% of the total flow to the Lanzhou-Toudaoguai river reach, Q_w,H at Lanzhou is the major factor controlling the sediment carrying ability of the reach. The variation in R_hr may reflect the effects of reservoir regulation and soil and water conservation on flow regime. Figures 6(a) and (b) show significant positive correlations, indicating that increases in Q_w,H and R_hr are reflected in higher F_s values. C_vr reflects seasonal variations in flows, with a high C_vr indicating a relatively uneven distribution of monthly flows. Hence, this index can reflect the regulation of reservoirs on flow regime. When C_vr is high, the frequency of occurrence of large water discharges is high, and then the sediment-carrying capability is strong, because the latter is in direct proportion to the square of water discharge (Q²) in the Yellow River (Chien and Zhou 1965). Thus, a positive correlation occurs between F_s and C_vr (Fig. 6(c)).

Fig. 6 Plots of F_s against flow variables. (a) F_s versus Q_w,H; (b) F_s versus R_hr; and (c) F_s versus C_vr.

Figure 7 shows the plots of F_s against two water-sediment variables, ξ_H and C_mean,H, indicating negative significant correlation (p < 0.001). As mentioned earlier, ξ_H and C_mean,H reflect the ‘load’ (sediment transport rate, Q_s) of the river relative to its ‘force’ (water discharge, Q) to carry the ‘load’. Since Q_s is roughly in proportion to Q² in the Yellow River (Chien and Zhou 1965), the ξ_H, which is defined as Q_s/Q², may better reflect the ‘load’ of the river relative to its ‘force’. If ξ_H and C_mean,H are high, then F_s would be low. The correlation coefficient for ξ_H is much higher than that for C_mean,H, indicating that ξ_H can better explain the variation in F_s.

Fig. 7 Plots of F_s against (a) ξ_H and (b) C_mean.

4.4 Causes for the decreasing trend of F_s

To determine the trends of the influencing variables, their correlation coefficients with time (the year) have been calculated as shown in Tables 3 and 4, at drainage basin and channel scales, respectively. It can be seen that, apart from annual precipitation whose correlation coefficient with time is not significant, all other influencing variables have trending variations, decreasing or increasing, significant at a confidence level of p < 0.01. The correlation coefficients of lnF_s with the logarithmic value of each influencing variable are also shown, and according to the sign (positive or negative) of the correlation coefficients, the direction in which lnF_s is influenced by each variable can be determined. Taking lnR_re for example, because the correlation coefficient of lnR_re with time is positive, it has an increasing trend of variation; because its correlation coefficient with lnF_s is negative, the increase in lnR_re may make lnF_s decrease, and this is shown in the fourth row of the table. From Table 3 we can see the increased air temperature might be the cause of the decreased F_s. Other causes for the decreased F_s may include the increase in the regulation coefficient (R_ra) of reservoirs on annual flow, the increase in the ratio (R_div) of net water diversion to natural runoff, and the increase in the natural runoff coefficient (C_nr) resulting from soil and water conservation. Table 4 shows the decrease in July−October flow (Q_w,h), the increases in C_mean,H and ξ_H, all due to the reservoir regulation, might be the cause for the decreased F_s, as well as the increase in net water diversion (Q_w,div). In drainage basin management, we cannot change precipitation and air temperature, but by changing the variables related to human activity, the unfavourable decreasing trend in F_s can be eased to some extent.

Table 3 Influence of drainage basin variables on the trend of F_s.

	lnPL	lnTL	lnRre	lnCr,n	lnRdiv	lnFs
Correlation coefficient with time	0.10	0.73	0.88	−0.55	0.66	−0.70
Trending with time	Not significant	Increasing	Increasing	Decreasing	Increasing	Decreasing
Correlation coefficient with Fs	0.14	−0.70	−0.77	0.78	−0.82
Direction in which Fs is influenced by each variable	No influence	Make Fs decrease	Make Fs decrease	Make Fs decrease	Make Fs decrease

Table 4 Influence of flow and sediment variables on the trend of F_s.

	lnCmean,H	lnξ	lnQwh	lnRrh	lnCv,r	lnQw,div	lnFs
Correlation coefficient with time	0.24	0.48	−0.66	−0.73	−0.73	0.40	−0.75
Trending with time	Increasing	Increasing	Decreasing	Decreasing	Decreasing	Increasing	Decreasing
Correlation coefficient with Fs	−0.51	−0.79	0.89	0.82	0.80	−0.43
Direction in which Fs is influenced by each variable	Make Fs decrease	Make Fs decrease	Make Fs decrease	Make Fs decrease	Make Fs decrease	Make Fs decrease

4.5 Effect of reservoirs on F_s

In the foregoing sections, the effect of the reservoirs on F_s has been discussed, using R_ra index. However, this index is rough and cannot differentiate between the influences of different reservoirs. Of the 13 reservoirs that have been built on the trunk stream of the Upper Yellow River, the Longyangxia and Liujiaxia Reservoirs have the largest storage capacities and exert the greatest effect on sediment transport. The Liujiaxia Dam is located 99 km upstream of Lanzhou, and its total storage capacity at normal level of water storage is 57 × 10⁸ m³, of which the regulation storage capacity is 41 × 10⁸ m³. With the help of the Soviet Union, construction of the reservoir started in 1958, and dam closure occurred in 1960. Later, construction stopped due to deterioration in the Sino–Soviet relationship. In 1964, construction re-started, and in 1968, the reservoir was completed and used for water storage. In 1974, all hydro-electric generating units were put into operation. The primary objective of Liujia Reservoir is hydro-electric generation, as well as flood protection, irrigation and ice flood protection (Xu 2013). Longyangxia dam is located 333 km above Liujiaxia Dam, 432 km upstream of Lanzhou. The project was started in 1977, dam closure occurred in 1979, and the reservoir was completed and used for water storage in 1986. The total storage capacity at normal level of water storage is 247 × 10⁸ m³, of which the regulation capacity is 193.5 × 10⁸ m³. Capable of performing multi-annual regulation on river flow, the primary objective of the reservoir is hydro-electric generation, and other objectives include flood protection and irrigation etc. (Xu 2013). The regulation of the two reservoirs on flow and sediment regime is different. For the purpose of electricity generation, the Longyangxia Reservoir stores a large quantity of flow during high-flow seasons to raise the water level, while the Liujiaxia Reservoir has much less effect on flow, but a larger effect on sediment load. The major water source area is located above the Longyangxia Dam, but the major sediment source area is located below the Longyangxia Dam and above the Liujiaxia Dam. Data from 1956 to 1967, before the construction of the two dams, show that Longyangxia Dam controls only 1.1 × 10⁷ t of sediment, but the sediment supply from the drainage area between the two dams is 1.03 ×10⁸ t which can only be controlled by the Liujiaxia Dam. The Longyangxia Dam controls 200.02 × 10⁸ m³ of water, and the inflow water between the two dams is 133.15 ×10⁸ m³. Hence, Longyangxia Dam controls most of the runoff above Lanzhou, and Liujiaxia Dam controls most of the sediment above Lanzhou. With a much larger storage capacity, Longyangxia Reservoir is capable of performing multi-annual regulation, while the Liujiaxia Reservoir is capable of performing seasonal regulation only. The regulation of the former is mainly on the flow regime, while the regulation of the latter is on the sediment regime. Moreover, the completion dates of the two dams were different. Controlled by the above factors, the response of the sediment transfer function of the downstream channel to the regulations of the two reservoirs is different.

The regulation of flow and sediment regimes has affected the F_s of the downstream channel in two ways. Sediment trapping by a reservoir may reduce the ‘load’ of the downstream channel, and intercepting a large quantity of flow during high flow seasons may reduce the sediment carrying ability. Whether the F_s increases or decreases depends on which of the two aspects is dominant. After 1974, all electric generators of the Liujiaxia Reservoir were operational, and a large quantity of sediment was trapped, causing serious sedimentation within the reservoir. From 1973 to 1988, 7.92 × 10⁸ t of sediment was deposited, and annual sedimentation was 5.28 × 10⁷ t (Zhang et al. 2008). As a result, annual SSL at Lanzhou decreased markedly. In the meantime, the reservoir also intercepted flow during high-flow seasons, but the proportion of the intercepted flow of the total is relatively small because the storage capacity of the reservoir is small (Xu 2013). Hence, after 1974, F_s increases and the curve of UF_k rises (see Fig. 2(b)). However, after 1986 when the Longyangxia Reservoir was completed and used for water storage, the situation became quite different. Although this reservoir trapped most of the input sediment, the absolute amount is small because the sediment input to the reservoir is small. From 1986 to 2005, the sediment deposited within the reservoir was 4.0 × 10⁸ t, and the annual sedimentation was 2.0 × 10⁶ t. Hence, the resultant decrease in annual SSL at Lanzhou is small. As the sedimentation in the Liujiaxia Reservoir increased, its storage capacity decreased, and the sediment trapping effect attenuated. From 1988 to 2003, the trapped sediment was 5.10 × 10⁸ t, and the annual sedimentation was 3.4 × 10⁷ t (Zhang et al. 2008), indicating a decreased effect of SSL reduction at Lanzhou station. Furthermore, the Longyangxia Reservoir intercepted larger quantities of July−October flow after 1986, and thus July−October flow at Lanzhou significantly decreased. Therefore, an abrupt decrease in F_s occurred in 1986 (see Fig. 2(b)).

The above discussion implies that the variation in F_s is nonlinear, although the linear correlation coefficient of F_s with time is significant (see Fig. 2(a)). The variation in F_s can also be fitted by a quartic parabolic regression equation (see Fig. 8(b)). Due to reservoir regulation, the variation of flow and SSL combination indexed by ξ_H at Lanzhou station was complicated and can also be fitted by a quartic parabolic regression equation (see Fig. 8(b)). The curves of F_s and ξ_H show a ‘mirror image’ relationship. When the ξ_H curve goes up, the F_s curve goes down, and vice versa. This indicates that the nonlinear variation in ξ_H due to reservoir regulation resulted in nonlinear variation in F_s.

Fig. 8 Temporal variations in ξ_H and F_s: (a) scatter plots, and (b) curves fitted by quartic parabolic regression equations.

Both the variations shown in Figs 2(a) and 8(b) can be used for sediment management purposes. Figure 2(a) is simpler and shows that a step-like change occurred in 1986, after which the average F_s decreased from 0.556 to 0.168. In Fig. 8(b) the mechanism for F_s change is shown by a comparison between the temporal variation in F_s and in ξ_H that reflects the sediment-carrying capability of the river. The variation of the two variables is in reverse, indicating that the variation in F_s is dependent on the variation in ξ_H. Therefore, both Figs 2(a) and 8(b) can provide some useful reference tools for sediment management.

5 DISCUSSION and CONCLUSION

5.1 Comparison of results with those in the lower reaches of the Yellow River

The main difference between the results from the lower reaches of the Yellow River reported by Xu (2008) and the results of the present study on the upper reaches is outlined as follows. First, in the present study, it is made clear that the factors and processes that control the variation in F_s are at two levels: the drainage basin level and the channel reach level. At the two levels, the correlation matrix between F_s and the influencing variables is established, and the correlation coefficients of F_s with all the influencing variables are calculated. On this basis, the ranking in terms of the importance of the influencing factors is made, and the influence of these trends on the the trend in F_s is discussed. The results of the latter are more quantitative than the former. Secondly, the treatment of the impact of the dam on F_s is more quantitative in the present study. In Xu’s 2008 study, the impact of the dams was indirectly reflected by dividing the temporal variation of F_s into different sub-periods based on reservoir construction and the changes in its operation mode. In the present study, a number of quantitative indices, such as R_ar and C_vr, are adopted to express the impact of dams directly, and the differing effects of different dams are discussed in detail. Under the consideration that the F_s is controlled by the ratio of the river ‘load’ to its ‘carrying force’, C_mean,H and ξ_H are adopted for this ratio and then related to F_s. In this way the physical meaning behind the phenomenon that F_s decreases may be better reflected. The effects of soil and water conservation are usually quantified by the area (A_sw) under these conservation measures (e.g. Wang and Fan 2002). In the present study, the natural runoff coefficient (C_nr) is used, considering that the main physical process of soil and water conservation measures is to reduce surface runoff by increasing infiltration. Thirdly, the consideration of climate change in the present study is better. As a very large drainage basin, climate change in the upper and middle parts of the Yellow River basin is different. In Xu (2008), only the changing precipitation was considered, but in the present study, both precipitation (P_L) and temperature (T_L) are considered. The result shows that the F_s is more closely correlated with T_L than with P_L in the upper part of the Yellow River basin. As demonstrated by the upper and lower reaches of the Yellow River, the F_s-based method may be used in other rivers in similar geographical settings to provide useful information for river management.

5.2 Suggested countermeasures for restoring the F_s

The enhanced sedimentation in the Lanzhou-Toudaoguai reach due to the decreased F_s has significantly reduced its flood-releasing capacity, especially for ice floods and the question of how to restore F_s becomes an important objective in drainage basin management. Three countermeasures are suggested.

The first is to increase the July−October flow at Lanzhou station. This may be realized by changing the operation mode of the Longyangxia Reservoir by reducing the water storage during the high-flow seasons. In so doing, the flow at Lanzhou station may be increased, and ξ_H decreased. Therefore, F_s can be increased.

The second is to reduce the amount of water diversion, thereby increasing the sediment carrying ability of the river. To avoid resulting unfavourable effects on agricultural production, water-saving techniques should be enhanced, including techniques for reducing irrigation canal seepage and for increasing the utilizing efficiency of irrigation water.

The third is to introduce some water-saving soil and water conservation measures, namely, when reducing soil erosion the water consumption measures themselves may be reduced, compared with traditional measures. Therefore, the reduction in C_nr may be eased, and the F_s can be increased.

5.3 Conclusions and discussion on countermeasures

An index (F_s) for the sediment transfer function has been introduced, based on the sediment budget at channel scales. Since 1960, the F_s of the Lanzhou-Toudaoguai reach of the Upper Yellow River shows a decreasing trend. The causes have been dealt with at drainage basin and channel levels for the purpose of providing some knowledge for river drainage management. At drainage basin level, the F_s is correlated with precipitation and air temperature and a number of variables describing human activity such as reservoir regulation, water diversion and soil and water conservation. The higher temperature, taken as a natural factor, reduces the transfer function, while the larger runoff coefficient, taken as a human factor, increases the transfer function. At the channel level, the F_s is correlated with a number of variables of flow and sediment inputs. An analysis based on a correlation matrix shows that at the drainage basin level, the three variables related to human activity rank first, second and third respectively, and the two climate variables rank fourth and fifth respectively. At the channel level, reservoir regulation and water diversion greatly changed flow and sediment inputs to the channel and the flow–sediment combination, thereby reducing F_s. Three countermeasures for restoration of F_s are suggested: increasing the July to October flow released from the Longyangxia Reservoir; reducing the amount of water diversion and enhancing water saving irrigation techniques; and introducing some water-saving soil and water conservation measures.

Acknowledgements

All hydrometric data, including precipitation data for 300 raingauges in the study area, were provided by the Yellow River Water Conservancy Commission. The SSL data for relevant hydrometric stations was provided by the Yellow River Commission of Water Conservancy. The water storage capacity of reservoirs, soil and water conservation measures and annual amount of net water diversion data were provided by the Yellow Water Conservancy, and used in the present study with their permission. Data on flows and sediment concentrations in water diversions were provided by the Yellow River Institute of Hydraulic Engineering and Water Resources. Temperature data, from 52 county meteorological stations, were provided by the Chinese State Meteorological Bureau. I am also grateful to two anonymous reviewers, whose comments and suggestions were invaluable in improving the manuscript.

Additional information

Funding

The financial support from the National Major Basic Research Programme of China (Grant no. 2011CB403305), the Natural Science Foundation of China (Grant no. 41071016) and the Chinese Academy of Sciences is gratefully acknowledged.