Hydrologic data analysis for pre-and post-dam construction in China

Mei Xuefei 1, P.H.A.J.M. van Gelder 2 and J.K.Vrijling 3

1 Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands; email: [email protected]

2 Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands; email: [email protected]

3 Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands; email: [email protected]

Abstract Hydrologic data analysis at Yichang in central China is investigated under the impact of the Gezhouba project and the Three Gorges project in the present study. Four methods, including two methods (Mann-Kendall test and Spearman’s rho test) for detecting trend, and two methods (the Pettitt test and the Standard Normal Homogeneity Test) for detecting changes are applied to initial data. It was shown that little change is observed in flow series in terms of various indices, but significant changes are found in water levels due to the construction of the Gezhouba dam, which indicates that the water level is much more sensitive to the impact of dam construction than stream flow. The small change in extreme flows could be explained by the small ratio (0.0035) of reservoir capacity to the total annual runoff and the special function of the Gezhouba project (mainly for hydropower and channel regulation). Finally, we compare the influence of the Gezhouba project and the Three Gorges project on the hydrologic regime of the Yangtze River at Yichang hydrological station. Our research suggests that Three Gorges project indeed exerts more influences, but a detailed process of change could not be identified yet because of information shortage.

Keywords—hydrological data analysis,dam impact, statistics

1 Introduction It is widely conceived that dams have major impacts on river hydrology, especially to the extreme events. A general tendency towards increases of minimum flows and decreases of maximum flows following impoundment has been detected in many cases over the world (Onema et al, 2006; Francis et al, 2003). However, the degree of influence depends on the actual situation. Williams and Wolman (1984) suggest that the effects of a given reservoir on flow regime will depend on its capacity in comparison with river runoff, its purpose (e.g. irrigation diversions, hydroelectric generation, flood control), and its operating rules. For example, dam impacts are especially obvious in countries like the US where the dams have a storage capacity that is only slightly less than a full year’s runoff (Wang et al, 2008). In the case of dam built for flood control, we could expect a consistent relationship between degree of impoundment and change in flow variables. However, for the dam built for comprehensive benefit, the relation may be more complicated. Moreover, the effect of dam may be variance followed by the change of climate conditions and seasons. Generally, the effects of dams are more pronounced in drier climates and early in the season (Ramon et al, 2004). The objective of this study is to determine how extreme river flows and water levels of the Yangtze River at the Yichang hydrological station have changed with the construction of the Gezhouba Dam (GZD) and the Three Gorges Dam (TGD). In Sect. 2, we will briefly introduce our study area and the data used. Description of the dada analysis methods used in the study will be presented in Sect. 3. Related results are reported in Sect. 4, followed by a draft comparison after TGD construction in Sect. 5. Finally, some conclusions and discussions are given in the last section.

2 Study area The Yangtze River arises in southwestern China and flows 5500 km across the country to reach the East China Sea near Shanghai. It is the third largest river in the world and the longest in Asia (with a length of more than 6300 km), draining nearly 2 million km 2 (19 percent of China’s total area), with a run-off volume of nearly 1 billion m 3 (38 percent of China’s total). GZD, 4 km upstream of Yichang city, Hubei province, was the first dam constructed on the main stream of the

WATER 2010 Changjiang River. It is a low-head, run of the river hydroelectric project. GZD was completed in January 1981 and impounded in May 1981. The project creates a reservoir with a length of 110-180 km and an area of 79.3 km 2. TGD, the largest hydroelectric engineering project in China, located about 40 km upstream of Yichang City. Three major functions of TGD are flood control, navigation and hydropower generation. Although the project will not be completed until 2009, the dam began to retain water and sediment in June 2003. Yichang hydrological station is located about 2 km downstream of GZD. The mean annual discharge and mean full year runoff in Yichange station of the river is about 14300m3/s and 4510 ×10 8 m3 respectively, while the maximum discharge is 71100m 3/s. The period June to October is the flood season when about 72% of the annual runoff occurs, with peak flows concentrated in July and August. Detailed information and geographic position are shown in Table 1 and Figure 1.

Table 1. Main technical parameters of study station. River dam Dam Dam Reservoir Reservoir Initial C/R Height Length Areas Capacity Operation 2 6 3 (m) (m) (km ) (10 m ) year Changjiang Gezhouba 70 2606 79.3 1580 1981 0.0035 TGD 185 3035 1084 39300 2003 0.0871 Note: C denotes the capacity of the reservoir; R denotes annual runoff.

Figure 1. Location of the study region and hydrological station

Daily discharge and water level records are available from 1950 to 2007 at Yichang hydrological station. Here, we divide the data sample into three groups according to the construction of GZD (1981) and TGD (2003). Taking the short time series of post-TGD (2003-2007) into account, we choose 1950-2002 as our major object of analysis.

3 Methods for data analysis In statistical data analysis, change tests (trend test and abrupt change test) are necessary and critical steps. The purpose of a trend test is to determine whether the value of a series have a general increase or decrease with time (Van Gelder et al, 2008), whereas the purpose of abrupt change test is to determine if there is a jump term in the components of the time series. As different methods may lead to different conclusions, we employed two methods for each test in this paper to reduce the uncertainty of the results. In the present study, 4 methods will be applied, including two methods (Mann-Kendall test(MK)and Spearman’s rho(SR)) for detecting trend, two methods (the Pettitt test(TPT) and the Standard Normal Homogeneity Test (SNHT)) for detecting abrupt change in the hydrological time series 1950-2002.

3.1 Test of trend 3.1.1 Mann-Kendall test The MK test is based on the test statistic S defined as follows: n−1 n = − S∑ ∑ sgn( xj x i ) i=1 j = i + 1

WATER 2010 Where x i are the sequential data values, n is the length of the data set, and  1if θ > 0  sgn()θ= 0if θ = 0 −1if θ < 0  Mann (1945) and Kendall (1975) have documented that when n ≥ 8 , the statistic S is approximately normally distribution with the mean and variance as follows:

E(S) =0; n − +− − + nn( 1)(2 n 5)∑ tti ( i 1)(2 t i 5) = Var(S)= i 1 18 Where t i is the number of data points in the i th tied group. The standardized test statistic Z is computed by −  S 1 >  S 0  Var( S ) = = ZMK  0 S 0  S +1  S < 0  Var( S ) 

The null hypothesis that there is no trend is accepted at significance level of 0.05 if the standardized MK statistic Z is less than 1.96. In this study, the discharge series are suggested to have no trend. For water levels there is a significant decreasing trend because ZMK turned to be negative and its absolute value is larger than T* . The results are shown in Table2.

Table 2. Mann-Kendall trend test on hydrologic data

Qmax Qmin Qmean hmax hmin hmean

ZMK -1.84 -0.44 -0.62 -2.33 -6.03 -5.01 T* 1.96 1.96 1.96 1.96 1.96 1.96

Note: Q max denotes the annual maximum flow; Q min denotes the annual minimum flow; Q mean denotes the annual mean flow. Hmax denotes the annual maximum water level; h min denotes the annual minimum water level; h mean denotes the annual mean water level. 3.1.2 Spearman’s rho test

Given a sample data set {X i, i=1,2,…,n}, the null hypothesis H 0 of the SR test against trend tests is that all the X i are independent and identically distributed; the alternative hypothesis is that X i increase or decrease with i, that is, a trend exists. That test statistic is given by (Sneyers, 1990). n − 2 6∑ [(R Xi ) i ] D =1 − i=1 2 − n( n 1) th Where R(Xi) is the rank of i observation X i in the sample of size n. Under the null hypothesis, the distribution of D is asymptotically normal with the mean and variance as follows (Lehmann, 1975; Sneyers, 1990): E(D)=0 1 Var(D)= n −1 The P-value of the SR statistic (D) of the observed sample data is estimated using the following standardization, D Z = SR V( D )

The standardized statistic Z follows the standard normal distribution Z∼ N (0,1) . Table 3 exhibits the results. Again we notice no trend for the discharge, but a strong negative trend for the water level data.

WATER 2010 Table 3. Spearman’s rho trend test on hydrologic data

Qmax Qmin Qmean hmax hmin hmean

ZSR -1.94 -0.46 -0.65 -2.31 -5.64 -4.75 T* 1.96 1.96 1.96 1.96 1.96 1.96

3.2 Test of abrupt change 3.2.1 The Pettitt test

Consider a sequence of random variables X1, X2,…, XT , then the sequence is said to have a change point at τ by TPT if X t for t=1, …,τ have a common distribution function F1(x)and Xt for t= τ+1,τ+2,…,T have a common distribution function F2(x) and F 1(x) ≠ F2(x). Take the null hypothesis of “no-change” H 0: τ=T against the alternative hypothesis of “change” H 1: 1 ≤ τ ≤ T, a non-parametric statistic KT for testing that the two continuous samples X1, X2,…, X τ and Xτ+1 ,…, X T come from the same population is defined as (Pettitt, 1979): = KTmax U t, T 1≤t ≤ T t T = − UtT, ∑∑ sgn( X ij X ) i=1 j = 1

The approximate significance probability POA associated with KT is given by = −2 3 + 2 → ∞ POA 2exp[6 kTT /( )] For T Choosing a level of significance α and we shall reject the hypothesis of no change has occurred in the time series if POA is smaller than α. Here we set α as 0.05. Related outcomes are shown in Table 4.

Table 4. the Pettitt change test on hydrologic data

hmax hmin hmean

POA 0.14 2.68*E-8 7.38*E-5 Change point 1968 1977 1977 3.2.2 The Standard Normal Homogeneity Test

SNHT uses a statistic T0 to compare the mean of the first a years of the record with that of the last n-a years. T0 will be smaller than the critical value if the null hypothesis H0 is true, whereas large value of T0 makes the hypothesis HA more probable.A possible shift is located at the year A when T0 reaches a maximum at the year a=A. The test statistic T0 is defined as: (Alexandersson and Moberg, 1997) = =2 +− 2 = T0max T ()a max( az 1 ( naaz ) 2 ) With a1,2,..., n 1≤

a (Y− Y ) n (Y− Y ) = 1 i = 1 i z1 ∑ , z2 ∑ ai=1 s n− ai= a + 1 s Where Y is the mean of the sample; s is the standard deviation of the sample; n is the sample size. The critical values corresponding to different levels are given for sample sizes ranging from 10 to 50000 by Knaliq and Ouarda (2007). In this study, we define our significance level as 5% and the critical value corresponding to it is 8.48.

Table 5. the Standard Normal Homogeneity Test on hydrologic data

hmax hmin hmean Change point 1968 1977 1977 T0 6.03 34.86 19.34 T* 8.48 8.48 8.48 Change point 1981 1981 1981 T0 2.57 30.46 17.99 T* 8.48 8.48 8.48

WATER 2010 4 Results of the analyses From the trend analysis, it is noticed that the series of water level, especially the minimum level of the Changjiang River for the period 1950-2002 at the Yichang hydrological station exhibit significant downtrend. Meanwhile, no obvious trend is present in the flow indices at a 0.05 significance level, which is in agreement with the research results of Zhang et al (2006). The change test did not find any obvious change in peak water level but detected significant change in minimum and mean water level around 1977. That is, the decrease of the peak water level is not as statistically significant as minimum and mean series. SNHT was also applied to the new time series of mean and minimum water level divided by 1981 to further test whether or not the year 1981 is a potential change point. The answer is in the affirmative. In fact, the conclusion is foreseeable as 1977 is located in the regulation period of GZD. Usually, annual water levels in river systems increase with annual precipitation and water discharge. When we combine Becker et al’s (2006) finding (no significant trends were detected in the precipitation at Yichang hydrological station) with the above research, we get the conclusion that the water level balance was broken by human activity (dam construction) in Yichang. In fact, good correlations exist between annual flow discharge and water level before the construction of Gezhouba Dam in 1981, but the situation changed a lot after 1981.

Maximum time series before 1981 Maximum time series after 1981

y=0.00016x+44.65 54 y=0.00020x+41.99 55 r=0.91 n=32 r=0.89 n=26

53 54

52

53

51 Water level (m) 52 Waterlevel(m)

50

51

49

50

3.5 4 4.5 5 5.5 6 6.5 7 3.5 4 4.5 5 5.5 6 3 4 3 4 Discharge(m /s) x 10 Discharge(m /s) x 10 Mean time series before 1981 Mean time series after 1981

45.4 y=0.00031x+39.83 44.5 y=0.00038x+38.11

45.2 r=0.88 n=32 r=0.69 n=26 44 45

44.8 43.5 44.6

44.4 43

44.2 Water level (m) Waterlevel(m) 42.5 44

43.8 42

43.6 41.5 43.4

1.2 1.3 1.4 1.5 1.6 1.7 1.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 3 4 3 4 Discharge (m /s) x 10 Discharge (m /s) x 10 Minimum time series before 1981 Minimum time series after 1981

40 y=0.00092x+36.38 y=0.00053x+36.91 39.2 r=0.80 n=32 39.8 r=0.49 n=26

39 39.6

38.8 39.4

39.2 38.6 Water level (m) Waterlevel (m)

39 38.4

38.8 38.2

2800 3000 3200 3400 3600 3800 4000 2800 3000 3200 3400 3600 3800 4000 3 3 Discharge(m /s) Discharge (m /s) Figure 2. Changes in water level-discharge relation between per- and post-dam for different situations

WATER 2010 Figure 2 give us a clear description of the change in water level-discharge relation for maximum, mean and minimum situations. Good linear regressions are detected in all of the situations before the construction of GZD. Their R-square values are 0.91, 0.88 and 0.80 respectively. However, the balance was broken since 1981. A rate reduction in R-square values certified this argument. The clear variation in minimum water level-discharge and relatively small change in maximum water level-discharge are in agreement with the result of the preceding tests. To further explain the influence, we draw the water level hydrograph under a fixed discharge (5000 m 3/s) because the water level under 5000 m 3/s at Yichang hydrological station is closer to the minimum water level.

41.5

41

40.5

40 water level water (m)

39.5

39 1960 1965 1970 1975 1980 1985 1990 1995 2000 Year Figure 3. Annual water level under the discharge of 5000 m 3/s at Yichang station

As Fig.3 shows, the water level under the discharge of 5000 m 3/s is divided into two phases by 1981. While the water level is relatively stable between 1960 and 1981, a significant negative trend was observed since 1981. This further shows the prominent influences of the GZD reservoir on the minimum water level.

5 Comparison to TGD construction TGD began to retain water as its reservoir reached the water level of 135m in June 2003, and 139 m in November 2003 (Yang et al., 2006). As a mere five-year period (2003-2007) for the post-TGD could not provide sufficient information to establish a robust series, we just present the changes in mean and compare the difference brought by the two dams.

Table 6. compare of changes in mean value after dam construction

Time Qmax Qmin Qmean hmax hmin hmean 1950-1980 50962 3374 13861 52.67 39.50 44.17 GZD(1981-2002) 50883 3382 13793 52.24 38.78 43.38 Difference -0.16% 0.24% -0.49% -0.82% -1.82% -1.79% TGD(2003-2007) 46814 3650 12487 50.94 38.57 42.54 Difference -8.14% 8.18% -9.91% -3.28% -2.35% -3.69%

Table 6 suggests that the construction of TGD and GZD have decreased the annual maximum flows and increased the annual minimum flows, which is consistent with the conclusion from Magilligan (2005). It is foreseeable that TGD will cause much larger change to the river regime than GZD for its huge storage capacity, but its relatively small ratio (0.0871) of reservoir capacity to the total annual runoff suggests the influence might be limited. In the present state, the difference is especially obvious to flow discharge. This could be interpreted from the dam function of TGD, which is mainly built for flood control.

6 Conclusions Our research on stream flow and water level series at Yichang hydrological station demonstrates that the construction of GZD in 1981 exerts much more influence on water level than on stream flow. The reason of the significant change in minimum water level might be a combined effect of cross-section enlarging and flow velocity increase due to GZD construction. The small change in water flows could be explained by two reasons. Firstly, dam impacts are normally obvious in dams that have a huge storage capacity comparable with a full year’s runoff. In the case of GZD, the ratio of

WATER 2010 reservoir storage capacity to the total annual runoff is only 0.0035, which is too small to react on the river discharge. The special function and operating rules of GZD is another decisive factor. GZD is mainly built for hydropower and channel regulation. With restriction of shipping, it cannot play the function of flood peak reduction and flood regulation. Our research also suggests that the TGD indeed exerts some influences on the river regimes of the Yangtze River at the Yichang hydrological station, which exceeds by far GZD. However, detailed trends still need further investigation because of the current information shortage.

Acknowledgements The authors acknowledge the Changjiang Water Resources Commission, China for providing the data which was used in this study.

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