Changes in channel morphology along rivers and their responses to different affecting factors in alluvial rivers are key research areas of fluvial processes. The Ningxia-Inner Mongolian reach is a main reach in the upper Yellow River whose scouring and silting processes are quite complex (Wang et al., 2014a; Du et al., 2014). Recently, the water regime of this reach has changed greatly under the effect of climate change, reservoir operation and water consumption as an irrigation region (Shen et al., 2007; Shi et al., 2012; Wang et al., 2012a, 2012b; Zhou et al., 2012; Zhang et al., 2013). This obvious change has caused an increase of sedimentation rate as well as severe shrinkage of the active channel (Qin et al., 2011; Fan et al., 2012). The coastal area thus has to withstand more pressure from daily life related to production activities as the frequency of flood in low water level has increased. Therefore, a lot of works have studied the fluvial process in this river reach. Utilizing channel cross-section surveys, Shi et al. (2013) found that the Inner Mongolian reach experienced a scouring process from 1963 to 1982 and a silting process after 1982. Wang and Fan (2010) investigated the flood processes and channel responses of different channel patterns in the Inner Mongolian reach, the results showing that the channel bed erosion is mainly in the braided channel reach, the channel bed aggradation is in the meandering channel reach, and the slight aggradation or the balanced erosion-deposition is in the straight channel reach. Qin et al. (2011) constructed a time series of cross-section area and identified three different evolution tendencies for channel change in the Inner Mongolian reach. Hou et al. (2007) estimated the volumes of sediment erosion and storage in the Inner Mongolian section. Wang et al (2014b) calculated the lateral migration rate of river banks in the Yinchuan Plain reach of the Yellow River using remote sensing images. Besides, other works have studied the causes of channel deposition (e.g., Petts, 1979; Zhao et al., 1999; Yang et al., 2003; Shen et al., 2007; Wang et al., 2012b; Ta et al., 2008), change of hydraulic geometry along the river (Ran et al., 2012), and characteristics of spring flood (Feng et al., 2009). So far, few works have quantitatively studied the change rate of channel shape parameters over a flooding period. A quantitative study of channel morphology change rate over a flooding season is necessary for assessing channel stability and formulating reasonable river management measures.

The objective of the paper is to investigate the change rate of channel morphology over flooding periods under the effect of the joint operation of the Liujiaxia and Longyangxia reservoirs. The article selects the early 1990s as a time boundary when the Longyangxia and Liujiaxia reservoirs operated jointly. We also utilize every 5-year data before and after the time boundary to characterize temporal variation. Four parameters, namely cross-section area, channel width, mean water depth, and the width-to-depth rate, are used to describe the channel shape changes based on the cross-sectional data derived from four hydrological stations. This article is expected to provide evidence for the management of the Yellow River, such as flood control and disaster reduction.

The Inner Mongolian alluvial reach is located between Shizuishan and Toudaoguai gauging stations with a total channel length of 673 km and a mean annual runoff of 25.2 billion m³. The catchment of this river reach is 106°41'59"-110°06'30"E and 39°19'06"-41°18'15"N. The river flows along the northwest margin of the Ordos Plateau with a gentle channel gradient (Hu et al., 2012). As is shown in Figure 1, the reach lies at the end of the upper Yellow River and is the northernmost part of the whole basin. The reach is located in the peripheral area of the monsoon climate region and its mean annual precipitation is 150-400 mm. The intra-annual distribution of precipitation is extremely uneven with about 75% of the total occurring from July to September (Wang et al., 2014a). The water surface is covered with ice from December to March and the spring flood is serious when the ice begins to melt in late March (Yao et al., 2007).

There are some tributaries in the river reach. Ten ephemeral tributaries drain into the Yellow River on the south side of the reach, and Dukunlun and Wudanggou tributaries drain into the Yellow River on the north side. These ten ephemeral tributaries can deliver large quantities of sediment into the main channel when a rainstorm occurs. As a result, the trunk channel at the junction is partly blocked and shifts northward, and the elevation of the main channel above the junction increases (Xu, 2014).

Several major reservoirs were constructed in the upper Yellow River during the period 1968-1986. The largest two are the Longyangxia and Liujiaxia reservoirs, constructed in 1986 and 1968 and with capacities of 24.7 billion m³ and 5.7 billion m³, respectively. Qingtongxia reservoir, with a relatively small capacity of 0.61 billion m³, has suffered severe sedimentation after impoundment. Sanshenggong reservoir with a capacity of 80 million m³ is the only reservoir located in the study river reach.

To investigate the impact of the joint operation of reservoirs on the change rate of channel morphology in flooding seasons, the change rates of channel morphology both before and after the joint operation of Longyangxia and Liujiaxia reservoirs are separately estimated. Cross-sections, located at Dengkou, Bayangaole, Sanhuhekou, and Toudaoguai gauging stations, are used to calculate the channel morphological change along the Inner Mongolian reach (Figure 1). Those four stations are located in straight, braided, meandering, and straight channel reaches along the Inner Mongolian reach, respectively. Two periods before and after the joint operation of the reservoirs are adopted. The former period is from 1978 to 1982 and the latter is from 2008 to 2012. The reasons are the following. (1) Longyangxia and Liujiaxia reservoirs began to operate jointly in 1986, which led directly to the unprecedented cut off in the lower reach. So the 1990s is a key period for investigating how the joint operation of the reservoirs affects the inflow conditions. The key scientific problem is how the joint operation of the reservoirs affects the variation of shape parameters over a flooding season. (2) There are no continuous sediment and water records in the period 1990-2007. (3) Generally, the bank-full discharge of the alluvial rivers in the world appears once in 2.33 years, thus 5 years of continuous data can well contain a bank-full discharge that may occur. Because Dengkou station only measured one time in 1979 and 1981, it is impossible to compare the change of shape parameters over a flooding season, so we choose the data in 1976, 1977, 1978, 1980, and 1982 instead.

All the above data are provided by the Yellow River Conservancy Commission (YRCC, 1976-1982, and 2008-2012) and are measured according to national standards. Cross-sections are surveyed at least twice each year to acquire the topographic change before and after a flooding season. Daily discharge and suspended sediment load (SSL) are measured by rating curve method. Those records measured in each gauge span more than 50 years. Variation of these sections can well reveal the change of channel morphology in the different channel patterns.

In the present work, four parameters, namely channel cross-section area, water width, mean water depth, and the width-to-depth rate, are used to describe the channel shape changes. All parameters are calculated before and after a flooding season in each year, and the difference between corresponding parameters is considered as the change rate. The measured water levels before and after a flooding season commonly are different, and thus we choose the lower one in each year as the controlling water level to calculate the related parameters and compare the channel change. Cross-section area is defined as the area below the selected water level; water width is defined as the channel width at the selected water level; and mean water depth is defined by dividing water width into cross-section area.

The study estimated the change rates of channel shape parameters at the Dengkou, Bayangaole, Sanhuhekou, and Toudaoguai cross-sections over each flooding season in the 5-year periods before and after the joint operation of reservoirs. The main conclusions are as follows:

(1) The cross-section area, water width, mean water depth, and width-to-depth rate evidently increased after a flooding season in both periods except for some individual parameters.

(2) The change rate was greater in the early period and decreased greatly in the later period. Meanwhile, it was found that the average change rate of cross-section area, water width, and mean water depth decreased 3.4, 3.5, and 2.8 times after the joint operation of the reservoirs.

(3) The joint operation of the large-scale reservoirs caused the change rate of channel shape parameters at the Sanhuhekou cross-section to vary from the second-largest value in the early period to a minimum in the later period. The distribution pattern of the change rate along the cross-sections changed from a convex curve in the early period to an S-shaped curve in the later period.

(4) Joint operation of the reservoirs not only reduced the total runoff and SSL in the flooding season but also reduced the peak discharge and maximum flow velocity. Consequently, the ability of flood to scour the riverbed weakened and the change rate of channel shape parameters decreased accordingly. Apparently, the joint operation of the reservoirs caused channel shrinkage which will increase the potential for an extreme flood.

(5) It will be reasonable to utilize the adjustment function of the reservoirs in future. The total water and sediment discharge and the peak discharge in flooding seasons must be effectively controlled. The channel thus can avoid continuous shrinkage and be ready for potential extreme flood.