Dams induced stage–discharge relationship variations in the upper Yangtze River basin

The relationship between stage and discharge is of considerable significance to understanding river behaviors (Sudheer & Jain 2003; AI-Abadi 2014). A reliable stage–discharge relationship (also known as rating curve) is the fundamental component for stream-flow estimation and forecasting. Such information is vital for coping with extreme events, such as floods and droughts. Over the past century, significant variations in river hydrology and morphology have been reported around the world as a result of climate change and human activities, which further affect the relationship between water level and river flow (Dai et al. 1998; Dettinger & Diaz 2000; Labat et al. 2004; Milly et al. 2005; Milliman et al. 2008; Naik & Jay 2011). In such a situation, the former rating curves that were free from outside interferences are no longer feasible. Consequently, there is a need to re-evaluate the stage–discharge relationship by taking account of environmental changes, especially human activities.

A number of techniques have been applied to model river stage–discharge relationships (Tawfik et al. 1997; Birkhead & James 1998; Jain & Chalisgaonkar 2000; Kisi & Cobaner 2009). The conventional approaches, including power-law function and multiple linear regression equation, approximate the best fitting curve for a particular gauging station through the observed water level and the passing discharge (Kisi & Cobaner 2009). It is noteworthy that the traditional methods link the measured water level unequivocally to a discharge, which disregard the hysteretic behavior due to effects of unsteadiness and back water (Tawfik et al. 1997; Wolfs & Willems 2014). To overcome significant unsteadiness effects, Jones's formula and its variations are recommended (Birkhead & James 1998; Perumal et al. 2004; Petersen-Øverleir 2006). However, these approaches neglect variable backwater effects. In recent years, a number of computing techniques have been proposed for constructing rating curves, including artificial neural network (ANN), Bayesian technics, genetic programming and fuzzy theory (Jain & Chalisgaonkar 2000; Moyeed & Clarke 2005; Guven & Aytek 2009; Shrestha & Simonovic 2010). As compared to the conventional approaches, these computing techniques produce quite satisfactory results and allow for back water, unsteadiness, and channel modification effects.

Although great attempts have been made to effectively relate the stage to discharge, few works address the impacts of dam regulations on stage–discharge relationships. Recently, Gordon & Meentemeyer (2006) examined the rating curves for a stream system in northern California, and indicated significant changes in channel morphology between the pre- and post-dam periods. Wang et al. (2013) established yearly stage–discharge rating curves for the Three Gorges Dam's (TGD) downstream during 2004–2012, and suggested that channel geometrics reshaped stage–discharge rating curves. More recently, Zhang et al. (2015) reconstructed stage–discharge relationships for the Pearl River Delta, and pointed out that water stages became lower in terms of the same amount of discharge due to sand excavation. Most previous works linked the water level measurements unequivocally to discharge records when investigating the influence of dam on stage–discharge relationships, which disregarded hysteresis of rating curves.

Over the past century, around 97,000 dams have been constructed in China, with a total storage of 810.410 billion m³, which makes China the world's largest dam builder (MWR 2013). Combined with climate change, this hydraulic engineering suggests significant effects on river behaviors over the country (Lu 2005; Chen et al. 2009; Yang & Tian 2009; Jiang et al. 2011; Zhang et al. 2012; Zhao et al. 2013). The Yangtze River basin is the most prominent example of intensive hydraulic engineering under the scenario of climate change, and thus has attracted considerable concern (Zhang et al. 2008a). The modifications in water resources have been documented in terms of discharge (Dai et al. 2008; Xu et al. 2008), water level (Zhang et al. 2006a; Wang et al. 2013), base-flow (Dai et al. 2010), sediment (Xu et al. 2006b; Yang et al. 2006; Zhang et al. 2006b; Dai & Liu 2013), and rating curves of discharge versus sediment (Xu & Milliman 2009). In spite of considerable research on hydrology changes in the Yangtze River basin, most of the previous works focused solely on an individual hydrological component, which failed to examine the effects of changing environment on integrated index, such as stage–discharge relationship.

Thereafter, the aims of this research include: (1) to set up stage–discharge rating curves for Yichang station in various flow scenarios based on the most advanced ANN theory; (2) to detect changes of stage–discharge relationship over the period 1950–2013, during which Gezhouba Dam (GD) and TGD were constructed; (3) to link the rating curve variations to human activities and climate change in the river basin, including dam regulation, sand exploitation, and precipitation variation; and (4) to quantify the effects of individual factors (sand mining, GD operation, and TGD operation) on rating curves.

The Yangtze River (91°E–122°E, 25°N–35°N) is the third longest river in the world and the longest in Asia, with a length of over 6,300 km. It originates from the Qinghai-Tibet Plateau, and reaches the East China Sea near Shanghai. The Yangtze River covers 20% of China with a total drainage area of 1.8 million km². Generally, the Yangtze River is partitioned into three sub-reaches (upper, middle, and lower reaches) according to its hydrologic and geomorphologic characteristics (Xu et al. 2006a). The three terms are referred to as the reaches above Yichang, from Yichang to Hukou, and from Hukou to the estuary, respectively.

The Yangtze River is controlled by around 50,000 reservoirs, among them the most notable examples being GD and TGD from the upstream basin (Yang et al. 2005). GD is the first dam that crosses the main stream of the Yangtze River. As a part of the Three Gorges project, GD aims to re-regulate the tail water from the TGD and improve the navigation condition between the two dams. GD was put into use in 1981 and was completed in 1988. TGD is the largest hydroelectric engineering project in the world. Three major functions of TGD are flood control, navigation, and hydropower generation. The TGD dam began to retain water and sediment in June 2003 and was completed in 2009. Characteristics of the two dams are provided in Table 1.

Yichang hydrometric station, located about 6 km downstream of GD and 44 km downstream of TGD, is the outflow control station of the upper Yangtze River. Yichang station covers an area of 1.1 × 10⁶ km², with a mean yearly water discharge of 439 × 10⁹ m³ (Dai et al. 2014).

Daily records of discharge, water level, and sediment load from 1950 to 2013 at Yichang hydrometric station are collected from the Changjiang Water Resources Commission (CWRC), China (www.cjh.com.cn). In addition to the above hydrological data, the precipitation records of 60 meteorological stations during 1950–2013 over the upper Yangtze River basin have been collected from the China Meteorological Administration. The measurements related to the Yichang cross section during 1970–2013 are collected from CWRC.

In statistical data analysis, change tests (trend test and abrupt change test) are necessary and critical steps. The purpose of trend test is to determine whether a data series has a gradual increase or decrease with time, whereas the purpose of abrupt change test is to detect if there is a time at which a sudden jump occurs in a set of data. In the present study, the Mann–Kendall (MK) test is applied for analyzing trend while the standard normal homogeneity (SNH) test is used for detecting abrupt change in the hydrological time series, and these are described in detail by Yue et al. (2002) and Khaliq & Ouarda (2007), respectively.

ANN, originating from the idea of human brain processes, has strong learning, reserving, and concluding abilities. It is an efficient tool for modeling and forecasting the complicated nonlinear relationship between input and output of a system (Hsu et al. 1995; Bourquin et al. 1998). Compared with the simple rating curve approach, ANN is less sensitive to the error term assumptions. However, despite their satisfactory performances in the reported studies, ANN models are prone to uncertainties due to their ‘black box’ nature and random construction of training set (Talebizadeh et al. 2009). Therefore, it is necessary to validate ANN models and check their accuracies prior to their implementation.

For the purpose of stage–discharge relationship analysis, change tests are applied to the individual water level and discharge series first, including annual minimum discharge (Q_min), annual mean discharge (Q_mean), annual maximum discharge (Q_max), annual minimum water level (h_min), annual mean water level (h_mean), and annual maximum water level (h_max).

From the MK test results, it is noted that all data series for the period 1950–2013 exhibit significant downtrends at a 0.05 significance level, except for Q_min which presents an upward trend (Table 3).

The results of the SNH test are also listed in Table 3, and indicate abrupt changes for all data sets at a significant level of 5%. It is shown that change points are located in two time intervals. For Q_min, Q_mean, Q_max, h_mean, and h_max, the shifts occurred around 2003, while for h_min, h_mean, and h_max significant changes were indicated around 1981. It is worth noting that the h_max and h_mean series detect two mutations, respectively, around 1981 and 2003.

For evaluating the effectiveness of ANN model on rating curves generation at Yichang station, daily discharge and associated water level are divided into two sets according to DUPLEX data splitting method (Snee 1977). One set is employed for training, while the other one is used for verification. The performance of ANN model during the training and validation stages are presented in Table 4. Two goodness-of-fit measures, correlation coefficient (R), and root mean square error (RMSE) are used to evaluate the capability of the predictions over the observations. The calculated R values between predictions and observations range from 0.88 to 1 during the validation period as well as training period, which show statistically significant correlation (p < 0.001). Therefore, the ANN model is capable of capturing good simulation performance at Yichang station. Moreover, the RMSE values are located in the range of 84–2,288 m³/s and 101–1,854 m³/s for training and validation stages, respectively.

The rating curves established for different phases demonstrate significant and sudden shifts in each scenario. It is shown that the obtained curves present upgrade tendencies since GD and TGD were put into practice. The rating curves of Phase 3 lie on the top of the plots. However, the tendencies do not appear to be the same for all sets. Details are as follows.

The rating curves in the normal flow scenario indicate equilibrium state with almost the same slopes (Figure 4(b), 4(e), and 4(h)). In this case, the rating curves of Phase 3 and Phase 2 are relatively parallel to the one under natural conditions. For different amounts of discharge, the net differences between Phase 1 and Phase 2 are stable at 1.34 m, 0.95 m, and 0.88 m in dry year, normal year, and wet year, respectively. On the other hand, the calculated differences between Phase 2 and Phase 3 corresponding to dry year, normal year, and wet year are around 0.31 m, 0.67 m, and 0.79 m, respectively. Obviously, the variations between Phase 1 and Phase 2 show a decreasing trend while that between Phase 2 and Phase 3 display an upward trend with annual discharge.

In the low flow scenario, the intercepts between Phase 1 and Phase 2, Phase 2 and Phase 3 are variable at different discharge level. In real terms, at 5,000 m³/s discharge level, GD induces 1.31 m, 0.97 m, and 1.09 m reduction of water level in dry years, normal years, and wet years, respectively, while TGD results in 0.34, 0.64, and 0.46 m of water level decline (Figure 2(a), 2(d), and 2(g)). When discharge increases to 6,500 m³/s, the water level differences between Phase 1 and Phase 2 in dry years, normal years, and wet years are 1.38, 1.01, and 0.81 m while those between Phase 2 and Phase 3 are 0.41, 0.73, and 1.12 m (Figure 2(a), 2(d), and 2(g)).

The high flow scenario is characterized by mixed rating curves at intersection points. For the present study, the water level difference with respect to different amounts of discharges between Phase 1, Phase 2, and Phase 3 are random without order and can present either a positive or negative value. Specifically, in dry years, the curves of Phase 1 and Phase 2 converge at around 42,700 m³/s (Figure 4(c)). In normal years, the curve of Phase 3 goes across that of Phase 2 and Phase 1 at about 42,700 m³/s and 52,200 m³/s, respectively (Figure 4(f)). In wet years, the curves of Phase 2 and Phase 3 intersect at around 42,100 m³/s (Figure 4(i)).

Taken altogether, the rating curves constructed at different phases present significant upward shifts for low and normal flow scenarios, indicating that water level becomes lower corresponding to the same amount of discharge. On the other hand, rating curves for high flow scenario have no regular pattern. It is noted that the rating curves for both low and high flow scenarios present hysteretic behaviors.

The variations of stage–discharge relationships can be explained by changes in river discharge as well as water level. Here, precipitation, dam regulation, sand exploitation, and channel erosion, the possible indicators that may affect the relations between water level and discharge are discussed.

For a stable cross section, the variation of water level is likely to follow that of discharge. However, in this study, the patterns of water level series are significantly different from that of discharge. For instance, during GD regulation period (1981–2002), the water levels dramatically reduced whereas the river discharge was relatively stable (Figure 6(d)–6(f)). The variation in riverbed morphology at Yichang station is a possible reason for this phenomenon, which can be caused in two ways: sand exploitation and channel erosion.

According to Rao et al. (1999), around 10.5 million m³ bed material (sand and gravel) was exploited from Zhenchuanmen to Huyatan, a 17.94 km stretch below GD, for the construction of GD over the period 1972–1981, which resulted in significant riverbed degradation. Sand mining continued until 1987, when another 14.26 million m³ of bed material was exploited.

As Figure 8 indicates, channel erosion at Yichang cross section mainly occurs in the area below 45 m bed elevation, which corresponds to the high flow scenario. Therefore, water levels corresponding to 20,000 m³/s at different time periods are calculated to distinguish the impacts of various anthropogenic activities on rating curves (Table 5). Over the past five decades, the water level under the 20,000 m³/s scenario presented 2.01 m degradation (from 47.39 to 45.38 m). From 1972 to 1981, the changes in cross section were fully due to sand mining, which led to a 0.31 m water level decrease. In the following 6 years (from 1981 to 1987), Yichang cross section experienced both sand mining and dam regulation, and presented a 0.57 m water level reduction. From 2002 to 2012, TGD regulation was the main reason for bed elevation scour, which resulted in 1.07 m of water level decrease. To distinguish the effects of sand mining and GD regulation on riverbed incision during 1981–1987, this study assumes that sand mining from 1981 to 1987 occurred at the same place with the same mining patterns as that of 1972–1981. Therefore, sand mining-induced water level change during 1981–1987 can be estimated based on the ratio of sand mining quantity over the two periods and the water level decrease between 1972 and 1981. During the study period, Yichang cross section experienced 2.01 m bed erosion with respect to 20,000 m³/s discharge. The relative contributions of sand mining, GD, and TGD amount to 36%, 53%, and 11%, respectively (Table 5).

The upper Yangtze River is characterized by intensive river engineering. In addition to the course of climate change, it is valuable to assess the influence of dam regulation on river stage–discharge relationships. This study focuses on the rating curve variations at Yichang station, the first control station downstream of GD and TGD reservoirs. The main findings are summarized as follows:

1. There are clear abrupt changes around 1981 and 2003 for water level and discharge at Yichang station when GD and TGD were constructed. Meanwhile, from 1950 to 2013, annual maximum and mean discharge, annual maximum, mean and minimum water level show decreasing trends while annual minimum discharge presents an upward trend.

2. The long-term relationship of stage to discharge is drastically altered by human activities over the period 1950–2013, and can be classified into the following three types: (a) normal flow: the rating curves present similar slopes and reach equilibrium state; (b) low flow: the reduction in water level changes with water discharge; and (c) high flow: the rating curves cross each other without observable regularity.

3. Sand mining, GD regulation, and TGD regulation are responsible for rating curve variations at Yichang station. Among them, TGD regulation is the leading cause (53%), sand mining is second (36%), and GD regulation has the smallest effect (11%).

This study is supported by the Ministry of Science and Technology of China (SKLEC: 2010RCDW03) and NSFC (41076050). We are grateful to Editor Chong-Yu Xu and two anonymous reviewers for their constructive comments and suggestions that improved the article.