## Abstract

The identification of the water level time lag (WLTL) under the regulation processes is of great significance for environmental impact, flood control, and sediment transport of huge reservoirs. The traditional hydrodynamic method can calculate the flood inflow process and the water level change process along the river channel, but it is difficult to estimate the time difference of the reservoir water level fluctuation to the dispatching process. To quantitatively evaluate the reservoir regulation effect on the WLTL in the Three Gorges Reservoir (TGR), the daily water level data from 2011 to 2017 of five stations in the TGR are analyzed in this paper. The results revealed that there is a significant water level difference along the reservoir from April 1 to October 31. The gap between the end of the reservoir and the Three Gorges Dam (TGD) is the largest, reaching 23.67 m on July 2. The longer the distance from the TGD, the longer the time lag. Furthermore, the WLTL is also different at the four different operating periods of the reservoir in a year. During the low water level operation period and high water level operation period, the time lag is 3 days which is the greatest, while in the water level decline period and water level rise period, the time lag is within 2 days.

## HIGHLIGHTS

Wavelet analysis is as an analysis tool for the time lag in the different hydrological process.

The water level in the whole reservoir showed an obvious difference from April to October.

The water level time lag in the reservoir area is related to the distance from the dam, the river channel landform, and the annual operation process of the TGR.

The time lag is not more than 3 days under the annual operation process.

## Abbreviations

*TGD*Three Gorges Dam

*TGR*Three Gorges Reservoir

*WLTL*Water level time lag

*FJ*Fengjie

*WX*Wanxian

*ZX*Zhongxian

*QXC*Qingxichang

*CT*Cuntan

*CWT*Continuous wavelet transform

*XWT*Cross-wavelet transform

*WTC*Wavelet transform coherence

*DP*Water level decline period

*LP*Low water level operation period

*RP*Water level rise period

*HP*High water level operation period

*COI*Cone of influence

## INTRODUCTION

The construction of the Three Gorges Dam (TGD) has had the strongest anthropogenic impact on surface water in the Yangtze River, which is the third-longest river in the world and the longest river in Asia. Yangtze River stretches from the Tibetan Plateau to eastern China, spans a total length of 6,300 km, and drains an area of 1,800,000 km^{2}. The project of the TGD, located at the end of the upper Yangtze River Yichang City (Hubei province), began in 1998 and was completed in 2003. The Three Gorges Reservoir (TGR) is currently one of the largest reservoirs in the world, with a capacity of 39.3 billion m^{3} over a length of 663 km and an average width of 1.1 km (Nilsson *et al.* 2005; Yang *et al.* 2007a).

As the largest hydropower project in the world, the Three Gorges Project has brought remarkable benefits, including flood control, electricity generation, and shipping capacity improvement (Zheng 2016). Meanwhile, the impacts of the TGR on the ecosystem and environment have been widely discussed (Wu *et al.* 2003; Shen 2004; Fu *et al.* 2010; Xu *et al.* 2013). After the impoundment in 2003, the TGR was formed along the Yangtze River, starting from Chongqing to the dam site at Yichang. Approximately 40 tributaries were transformed into tributary bays and became a part of the TGR. It has dramatically changed the aquatic ecosystem from a continuous lotic ecosystem to a huge reservoir, which exhibits complex hydrodynamic processes (Zhang *et al.* 2009; Holbach *et al.* 2014; Zhao *et al.* 2016). As a consequence, increasingly serious eutrophication and algal blooms usually occurred in spring and autumn in tributary bays in the TGR, which were induced by multiple factors, including the ecological and hydrodynamic environment change (Jin 2010; Wang *et al.* 2011; Liu *et al.* 2012; Yang *et al.* 2018; Yao *et al.* 2018). While sediment deposition in the reservoir has brought about a series of environmental and ecological problems (Yang *et al.* 2007b, 2013; Wu *et al.* 2011; Wang *et al.* 2016), the decline of ecological health and ecosystem services function for river basins has become a worrying environmental problem (Chai *et al.* 2009). The reduced velocity accompanied by the increases in river depth is the primary reason for these problems. The water level scheduling of the dam may have a positive effect on solving these problems. The water level in TGR is affected by many factors, such as the runoff of the Yangtze River, channel morphology, and reservoir regulation. Therefore, understanding the water level time lag (WLTL) in the whole TGR under the regulation processes is the primary problem of water level scheduling for water environment restoration.

The TGR also has a downstream flood control function, while providing water supply, navigation, and power generation. In August 2020, the No.5 Yangtze River flood with the peak discharge of 7,500 m^{3}/s entered into the TGR, and the water level in Chongqing reached nearly 191 m, about 8 m higher than the safe water level. This requires the reservoir not only to ensure downstream safety but also to consider the security of the reservoir area through the operation process. The traditional hydrodynamic model can calculate the flood inflow process and the water level change process along the TGR river channel (Jin 2010; Kumar *et al.* 2011; Zhang *et al.* 2018), but it is difficult to estimate the response of the water level in the TGR to the dispatching process from the time perspective because of the high requirements on the amount of data and the accuracy of the calculated parameters (Taormina & Chau 2015; Alizadeh *et al.* 2017; Kargar *et al.* 2020; Shamshirband *et al.* 2020). It has a great significance for the flood control safety of the TGR to identify the time lag effect between the water level in the TGR and the water level operation process in front of the dam. Once the response time of the water level in the reservoir area is known, it is helpful for the TGR to ensure flood safety in the reservoir. Furthermore, it provides the basis for hydrological forecast and flood control of reservoirs and the management of water resources deployment in the Yangtze River basin.

In recent years, the wavelet analysis method has been widely utilized to quantify the multi-scale characteristics and periodic features of data series (Grinsted *et al.* 2004; Labat 2010; Yang *et al.* 2010; Alizadeh *et al.* 2017; Li *et al.* 2020). Wavelet analysis can reveal the local characteristics of time series from time domain and frequency domain simultaneously, and it is suitable for the study of hydrological time series with multi-time-scale characteristics and non-stationary features (Kumar & Foufoulageorgiou 1997; Torrence & Compo 1998; Vitagliano *et al.* 2017; Campozano *et al.* 2020), which has more advantages than the single cross-spectrum analysis (Yu *et al.* 2012; Sang 2013; Wu *et al.* 2015). Furthermore, it requires less data volume than machine learning models (Wu & Chau 2013; Chen & Chau 2019). Therefore, in this study, after an analysis of the water level changes, the wavelet analysis method was adopted to quantitatively analyze the changes in the time lag characteristics at different locations within the reservoir area when the TGR entered the normal operation period. In this way, it will be helpful to explore the source of this time lag feature, which is beneficial for the water resource management and channel planning of the TGR.

## STUDY AREA AND DATA COLLECTION

The TGR refers to the submerged area after the construction of the TGD, and it begins at the TGD and ends at Cuntan (CT) in Chongqing, located between 28°31′ N–31°44′ N and 105°50′ E–111°40′ E, with a total of 50,000 km^{2}. Fengjie (FJ), Wanxian (WX), Zhongxian (ZX), Qingxichang (QXC), CT five stations where the distances are 187, 315, 409, 523, and 661 km from the TGD, respectively, were chosen, and their measured water levels were collected from 2011 to 2017. The spatial distribution of stations is shown in Figure 1. The reservoir inflow and storage outflow at the TGR from 2011 to 2017 are carefully selected to explore the causes of WLTL (Figure 2). The daily data enable us to locate the scale and time of change in the signal more accurately than the monthly time series. In addition, it offers us the possibility to have a comprehensive understanding of the streamflow behavior at different temporal scales. Since there are hourly intervals of water level observation data every day, the arithmetic mean method is adopted to obtain the daily average water level. Some statistical characteristics are shown in Table 1.

Variable . | Longitude (°) . | Latitude (°) . | River bed elevation . | River width . | The distance from the TGD (km) . | Mean . | Minimum . | Maximum . | Standard deviation . | Coefficient of variation . | Skewness . |
---|---|---|---|---|---|---|---|---|---|---|---|

TGD (m) | 111.00 | 30.83 | 66 | 2,310 | 0 | 162.46 | 145.07 | 175.04 | 10.18 | 0.06 | −0.39 |

FJ (m) | 109.46 | 31.01 | 75 | 912 | 187 | 162.78 | 145.32 | 175.40 | 9.93 | 0.06 | −0.39 |

WX (m) | 108.39 | 30.81 | 96 | 1,389 | 315 | 163.03 | 145.51 | 175.70 | 9.82 | 0.06 | −0.39 |

ZX (m) | 108.05 | 30.29 | 120 | 349 | 409 | 163.06 | 140.96 | 175.77 | 9.69 | 0.06 | −0.37 |

QXC (m) | 107.46 | 29.80 | 142 | 476 | 523 | 163.58 | 146.55 | 175.85 | 8.98 | 0.05 | −0.35 |

CT (m) | 106.61 | 29.62 | 160 | 670 | 661 | 169.07 | 159.84 | 186.28 | 4.51 | 0.03 | 0.02 |

Reservoir inflow (m^{3}/s) | – | – | – | – | – | 12,700 | 3,600 | 68,200 | 8,700 | 0.69 | 1.61 |

Storage outflow (m^{3}/s) | – | – | – | – | – | 12,600 | 5,400 | 45,700 | 7,500 | 0.6 | 1.38 |

Variable . | Longitude (°) . | Latitude (°) . | River bed elevation . | River width . | The distance from the TGD (km) . | Mean . | Minimum . | Maximum . | Standard deviation . | Coefficient of variation . | Skewness . |
---|---|---|---|---|---|---|---|---|---|---|---|

TGD (m) | 111.00 | 30.83 | 66 | 2,310 | 0 | 162.46 | 145.07 | 175.04 | 10.18 | 0.06 | −0.39 |

FJ (m) | 109.46 | 31.01 | 75 | 912 | 187 | 162.78 | 145.32 | 175.40 | 9.93 | 0.06 | −0.39 |

WX (m) | 108.39 | 30.81 | 96 | 1,389 | 315 | 163.03 | 145.51 | 175.70 | 9.82 | 0.06 | −0.39 |

ZX (m) | 108.05 | 30.29 | 120 | 349 | 409 | 163.06 | 140.96 | 175.77 | 9.69 | 0.06 | −0.37 |

QXC (m) | 107.46 | 29.80 | 142 | 476 | 523 | 163.58 | 146.55 | 175.85 | 8.98 | 0.05 | −0.35 |

CT (m) | 106.61 | 29.62 | 160 | 670 | 661 | 169.07 | 159.84 | 186.28 | 4.51 | 0.03 | 0.02 |

Reservoir inflow (m^{3}/s) | – | – | – | – | – | 12,700 | 3,600 | 68,200 | 8,700 | 0.69 | 1.61 |

Storage outflow (m^{3}/s) | – | – | – | – | – | 12,600 | 5,400 | 45,700 | 7,500 | 0.6 | 1.38 |

## MATERIALS AND METHODS

### Continuous wavelet transform

*a*is the dilation (scale or frequency) parameter,

*b*is the translation (position or time) parameter; is a wavelet transform coefficient; the complex conjugate functions of ; and is the time interval of data series. The data are bounded in time, so the wavelet transform is affected by edge effects, called the cone of influence (COI) (Torrence & Compo 1998).

### Cross-wavelet transform and wavelet transform coherence

*et al.*2020). The XWT of two signals and with finite energy is defined as , where * denotes complex conjugation. The cross-wavelet power spectrum is defined as . The theoretical distribution of the cross-wavelet power of two signals with a background power spectrum and is given by Torrence & Compo (1998) as follows:where and are the standard deviations of sequences

*X*and

*Y*and is the degree of freedom. is the confidence level associated with the probability

*p*for a probability density function (pdf) defined by the square root of the product of two Chi-square distributions. In this study, 0.05 significance level was selected and (Grinsted

*et al.*2004).

*S*is a smoothing operator. For the Morlet wavelet, a suitable smoothing operator is given by:where denotes smoothing along the wavelet scale axis, denotes smoothing in time, and are normalization constants, and is the rectangle function. The statistical significance level of WTC is estimated using Monte Carlo methods (Grinsted

*et al.*2004). To determine the reliability of the water level data, 95% confidence intervals for the water level were calculated:where and are the mean and variance of data series, represents the 95% confidence intervals, and

*n*is the total number of data series. In this study, total samples obey normal distribution, 0.05 significance level was selected, and (95%) = 1.96.

In all results, the angles are measured counterclockwise. Arrows in common power regions indicate the local relative phase between the two time series (Grinsted *et al.* 2004; Fattouh 2016; Fatolazadeh *et al.* 2020). The areas with different colors have different interrelations between the two time series (Firouzi & Wang 2019). The thick black contours represent the 95% significance confidence level against red noise, as estimated through Monte Carlo simulations, which represent reliable time lags, and the thin black line indicates the COI where edge effects might distort, and is drawn as a thin black line. The color bar on the right denotes the wavelet energy (Schmidbauer & Roesch 2018).

## RESULTS AND DISCUSSION

### The impoundment process of the TGR

To understand the historical change process of the water level is the precondition for analyzing the WLTL in the TGR. The impoundment process of the TGR is divided into four stages according to the water level in front of the TGD: the cofferdam supported power generation stage, the preliminary operation stage, the experimental impoundment stage, and the normal operation stage. The perennial change process of the water level at the dam site is shown in Figure 3. In June 2003, the water level of the TGD was impounded to 135 m, two hydro-generators began to generate electricity, the TGR entered the cofferdam supported power generation stage, and the water level varied from 135 to 139 m. In October 2006, the TGD was built to 185 m and the water level reached 156 m, the TGR entered the preliminary operation stage, and the water level varied from 145 to 156 m. Subsequently, in November 2008, the TGD water level began to impound to 172.89 m for the first time, the TGR entered the experimental impoundment stage, and the water level varied from 145 to 172 m. In October 2010, the TGD water level reached 175 m for the first time, since then, the TGR entered the normal operation stage eventually, and the water level varied from 145 to 175 m. The main objective of this study is to investigate the time lag of water level under the regulation process after the TGR entered the normal operation period; however, there is no regular regulation process before the TGR enters the normal operation period (Figure 3). Hence, the water level data from 2011 to 2017 are chosen to analyze the WLTL.

### The annual operation process of the TGR

After the TGR entered the normal operation period, because the TGR had the comprehensive utilization functions such as flood control and power generation, according to the multi-year average daily water level change process of the water level in front of the dam from 2011 to 2017, the annual operation process could be divided into four sub-periods: water level decline period (DP), low water level operation period (LP), water level rise period (RP), and high water level operation period (HP), as shown in (Figure 4(a)). Meanwhile, the 95% confidence interval of water level is calculated to judge the reliability of the water level data and as a necessary step in wavelet analysis (Figure 4(a)). The 95% confidence intervals for four sub-periods are shown in Figure 4(e)–4(h).

First, the period from January 1 to June 21 is the DP, and the reservoir is emptied to store the inflow during the flooding seasons. From the perspective of the water decline rate, this period could be divided into two phases. The water level of the TGD was decreased from 173.40 m to 163.51 m in the first phase from January 1 to April 1, with a decrease rate of 0.12 m/day; the second phase is from April 13 to June 21; the water level of the TGD decreases from 163.77 to 145.54 m, with a decrease rate of 0.31 m/day, about 2.6 times of that in the first phase. The additional decrease rate of water level is likely due to the reservoir that has other water recharge between April 1 and April 13, which results in a slower rate of water level drop.

From June 22 to August 18 is the LP, with the water level fluctuating between 145.54 and 151.94 m. In order to protect the downstream human life and property from flood damage during the flood season, the reservoir is operated at a lower water level and the peak discharge of the Yangtze River is regulated.

From August 19 to October 31 is the RP; the water level is rising to meet the needs of comprehensive use of water supply, power generation, and transportation during the drying seasons. It continues to rise sharply from 147.75 to 174.53 m, with an increased rate of 0.42 m/day.

At last, from November 1 to December 31 is the HP of the TGR. The water level decreases slowly from 174.53 to 173.32 m, with a greatly slowing decrease rate of about 0.02 m/day. The discharge water is more than inflow to meet the needs of downstream agricultural irrigation and waterway maintenance.

### Response of water level to the TGR area impoundment and drainage

Figure 4(b) shows that there is no anomaly in the water level data of each hydrologic station, which strongly proves that the data are reliable. Moreover, from the statistical characteristics of the data, the higher elevation of the local river channel at the CT hydrologic station causes the water level of the CT hydrologic station to be higher than that at other stations as a whole (Table 1), which may have adverse effects on the analysis of the time lag.

Figure 4(c) shows the change process of the average water level in front of the dam from 2011 to 2017, FJ, WX, ZX, QXC, and CT in the TGR. FJ, WX, ZX, QXC's water level change process is consistent with the location of the TGD, which can be divided into four different operating periods as mentioned earlier. However, the variation of the water level in CT is quite different from that of the TGD. On the one hand, the mean square error of water level before the dam is 10.18, but at CT it is 4.51, which indicates that the change range of water level at the TGD is larger than that at CT. On the other hand, the change process of CT's water level is not consistent with the TGD, and there are no obvious water level stages.

Figure 4(d) shows the water level difference between FJ, WX, ZX, QXC, CT, and TGD. The trend of water level difference in the figure shows two different patterns. For one thing, from May 2 to October 14, there was a significant difference in water levels between FJ, WX, ZX, QXC, and TGD under the regulation processes, and this difference was mainly reflected through the water level difference, which mainly reveals two aspects: time and space. From the spatial point of view, the difference in water level increases gradually along with the dam site to the end of the reservoir. In terms of time, the water level difference tends to increase and then decrease over time, and the water level difference between each station and the dam site is the biggest in July. The maximum water level difference in FJ was 1.33 m on July 24, in QXC it was 5.79 m on July 2, 2.02 m in WX and 2.65 m in ZX, respectively, on July 7.

For another thing, from February 25 to November 3, compared with the other four stations, the water level of CT is much higher. Also, it has the greatest water level difference compared with the front of the dam, which even reached 23.67 m on July 2. In general, more randomness features of CT and other sites at such scale are indicated by the value of multi-year mean water level (Figure 4(c)). And the reservoir inflow and storage outflow of TGR is approximately the same during this period (Figure 2). The reason for the anomaly at CT is mainly because CT is too far from the TGD, and the geographical factors of the river channel, such as the channel depth altitude and the width of the river (Table 1), may exert a huge impact on the change of water level.

There is an obvious water level difference along the TGR in the research periods (Figure 4(d)). The difference may be caused by the gradual decrease of the river bottom elevation and the gradual increase of the water depth from CT to the TGD (Table 1), or it may also be due to the lag effect of water level between upstream and downstream in the reservoir area caused by the annual operation of the TGR. Analyzing the time lag between these water level signals has a great significance for understanding the influence of reservoir operation on the water level fluctuation in the reservoir area.

### Analysis of the time lag between TGD and different locations in the TGR area

The results of the XWT's analyses between FJ and TGD are similar to those of WX, ZX, and QXC, which show that there are small high energy areas (red) that passed the significance test, and large low energy (blue) areas that show lower coherence from 2011 to 2017 (Figure 5). In the LP and RP, XWT shows high cross-wavelet power bands and in phase (0°) in the 60–80 day band, this is simply because of the recurrence of water level fluctuations due to the flood regulation process of the TGD in summer, and this is not real WLTL. The time lags of the other two periods are not obvious. Also, in 2011 and 2015, the high energy zone that passes the significance test is narrow. In general, the XWT results of the four hydrological stations are very similar because they are consistent with the annual regulation process of the TGR, which can also be divided into four sub-periods.

CT is located at the end of TGR, and its wavelet spectrum sheds light on the factors of their corresponding time lag components and the epoch of the year each of them contributes to time lag. CT has been completely different from other stations since 2012, and it is very clear that all the phase relationships between CT and TGD tend to be very close to perfectly 90°. In the LP and RP (Figure 6), first, there are 4–32 day high energy signal bands, and there are also 64–200 day energy signal bands that passed significance tests, but the phase angles in these areas are messy. Second, the phase angles change from 60 to 90° in the regions of the 256–365 day band which pass the significance test, but the confidence interval range for these regions is beyond the COI range, and this indicates a negative or approximately negative correlation between TGD and CT. Meanwhile, there are no reliable time lag signals in DP and HP compared with other hydrological stations. It is confirmed that the distance exerts a huge impact on the time lags, and the river channel is another important factor because the geomorphology of the river channel is also highly correlated with the water level (Niu & Chen 2016).

The WTC method is used to comprehensively reflect the intensity of the covariance of the two station water level signals from a different time scale. It has an obvious advantage in displaying signal details, especially on a short length scale compared with XWT. Therefore, the relevant phase angle of WTC was adopted to reflect the sequence and length of WLTL. As for the phase angle in the WTC analysis, this is a demonstration of the advance or lag of the two time series, and the angle size represented by the arrow indicates the degree of advance or lag between two time series (Firouzi & Wang 2019; Perez Ciria & Chiogna 2020). Furthermore, we compute the WTC for each water level time series for the two considered intervals of scales (1–512 day scale and 1–8 day scale). It can help us to better evaluate differences in phase and amplitude at different temporal scales, which are characteristic for the different annual operation process. There are significant energy bands in the 2–8 days in the DP and RP between TGD and FJ, WX, but the wavelet coherent powers are low and the phase angles are more randomly distributed (Figures 7(a) and 8(a)). About 8 days appear in FJ and WX from 2013 to 2015 at 1–8 day scale (Figures 7(b) and 8(b)), but the energy was low (coherence smaller than 0.5). This indicates that the water level correlation is not significant during this period, and the time lag is not significant. However, there is a rather high coherency band and a strong correlation in the 0–1 days. The mean phase angle, which is over the regions with significant wavelet coherence and outside the COI, is 60 ± 15° and 45 ± 15°, implying a more reliable time lag in the LP and HP. Since the impoundment and discharge process of the TGD has led to the faster flow rate in the DP and RP (Figure 2), time lag is not the obvious reason for hydrological stations close to the TGD. Nevertheless, in LP and HP, the water level regulation in front of the TGD makes the water level slow, resulting a more obvious time lag in the reservoir area. Hadi & Tombul (2018) have indicated a high localized correlation between the streamflow and other variables (e.g. rainfall, temperature, and potential evapotranspiration), especially the upstream flow, and the upstream water flow in the TGR is artificially regulated in different periods. It indicates that the time lag analysis in different regulation periods is reasonable.

The time lag is mainly shown in the LP and HP, the power spectrum energy in the 8–12, 16–30, and 30–32 day bands which pass the 95% significant test between TGD and ZX (Figure 9(a) and 9(b)). However, all these regions show a chaotic phase angle and low energy (blue), which indicates a poor correlation and unreliable time lag. While in the DP and RP, there is a significant positive correlation in 1–2 days. According to the calculation results of the cross-wavelet power spectrum and wavelet coherence spectrum, we can infer that the water level of TGD is less than 2 days ahead of the ZX's water level. The previous research result shows that the phase angles in the higher frequency domain can change significantly over time and depend on different hydrological signals in different periods (Yu & Lin 2015). In the Yangtze River basin, the long and short periods are found in different phase relations. In the longer periods, the annual maximum streamflow is influenced by climatic variabilities, while in the shorter periods, it is influenced by other factors, for example, human activities (Zhang *et al.* 2007). Therefore, runoff changes under the TGD regulation have affected the time lag among the hydrological parameters of the Yangtze River basin, and this is mainly on short periodic scales such as the month or day.

It can be observed that the time lags between QXC and TGD increase at both short and long periods, compared with FJ, WX, and ZX (Figure 10(a) and 10(b)). Especially in the LP, there is a wider energy band that has passed the significance test compared with other stations, and the energy band is distributed over a range of 1–40 days. During the HP, the energy bands which passed the significance test also increase, and distribute within the range of 2–8 days. The scales of cycle correlation coefficient square are not high, most of them being below 0.5. And the chaos phase angles also demonstrate the poor correlation between the level of TGD and QXC. In the DP and RP, effective time lags can be found, which increases to 2–3 days compared with ZX, and the phase difference angles are 0 ± 15°, which indicates that there is a positive correlation between QXC and TGD. Even though the water flow is moving fast enough due to the fact that the reservoir is draining (Figure 2), the time lag caused by the flow's speed is not enough to offset the time lag caused by distance during this period.

The relationship between CT and TGD is also significantly different from that of other hydrological stations on the temporal scale from 1 day to 512 days. (Figure 11(a)). The area of a time–frequency plot above the 5% significance level is not a reliable indication of causality. Even if the scales were appropriately weighted for the averaging, two series can be perfectly correlated at one specific scale while the area of significant correlation is much less than 5% (Grinsted *et al.* 2004). It displays significant broadband coherence patterns between TGD and CT in the series of period bands, in particular from the 8–40 day scale in the LP and RP and 2–8 day scale in DP and HP. When we focus on the 1–8 day scale of the water level WTC, we observe a higher degree of complexity in comparison with the analysis at the 1–512 day scale. As shown in Figure 11(b), no consistent phase difference can be seen for TGD and CT in the corresponding period and time, and this may be the reason that CT could have few associations with TGD depending upon the local characteristics. CT is far farther from the TGD than other stations, and the river bottom is much higher than the other station (Table 1). Therefore, the time lag cannot be accurately reflected when the water flows from the end of the reservoir to the TGD. In general, the results in this research manifest that the distance can affect the periodical length of time lag, and also affect the period in which the time lag occurs. The reason for the great change in the lag time may be due to the geographical environment and runoff factors of the channel (Hadi & Tombul 2018).

## CONCLUSIONS

In this study, based on the TGR's dispatching processes, the different staging periods were carried out to quantitatively reveal the impacts of TGR's normal operation period on the water level's time lag. Multiple statistical approaches including CWT, XWT, and WTC were proposed to clarify the coherence and detail the features of time lag property between river dynamics at hydrological stations along the Yangtze River.

The TGR contains an annual cycle of impounding and draining water under human activities considering the need for flood control, hydropower, water supply, etc. Overall, the annual operating period can be divided into four sub-periods: the DP, the LP, the RP, and the HP, which is fully demonstrated by the variation of water level in front of the dam and upstream sites such as FJ, WX, ZX, and QXC, while the similar features are not reflected in CT hydrological station since it has complex geographic conditions. In general, upstream water levels are higher than that of the TGD, and the maximum difference occurred in July according to the average water level changes from 2011 to 2017. Besides, the average daily increases and decreases of water level during the RP and DP are 0.12 and 0.42 m/day. In the LP and HP, the water level presents regular oscillatory movement, which is directly related to the regular water storage and drainage dynamics of the TGD on river stage dynamics.

A wavelet transforms coherence analysis can provide a clear view of the co-movement between two time series to improve the characterizing ability for the lag property. From 2011 to 2017, XWT confirms that the water level signals of the two stations in the upper and lower reaches of the TGD generally have a high energy frequency band of about 60–80 days (June to September), which is a significant resonant periodic component between upstream and downstream. This exactly confirms the about three month cycle time for the TGR's impounding and draining water process, but it is not a reliable time lag. Second, in the time scale of annual water level regulation, the phase angle obtained by WTC analysis indicates that the change of the downstream lags behind the change of the upstream. On the one hand, the mean phase angles of river dynamics between TGD and FJ station, WX and QXC stations were 60 ± 15°, 45 ± 15°, and 0 ± 15°, respectively. Nevertheless, the chaotic mean phase angles of ZX and CT generally pointed out poor correlations that were ascribable to time scales of water level and the river channel landform under the regulatory processes. During the LP and HP, there is a 1–2 time lag between TGD and FJ, and between TGD and WX. Moreover, there is about 1–2 time lag between TGD and ZX, and about 2–3 time lag are demonstrated between TGD and QXC during the DP and RP. The reason is the artificial regulation of the water level by controlling the amount of discharge, which changed the velocity of the flow, and therefore, the time lag is changed. Furthermore, due to the abnormal time lag caused by the special geographical location of the CT station, it is not reliable to analyze the time lag by CT. These results further verify that the longer the distance from the TGD, the longer the time lag, which indicates that the temporal lags can vary concerning the temporal scales of water change level processes and the different local water level regions, such as river width and river bottom elevation. To establish assessment scenarios under the construction of large-scale water conservancy facilities in TGR's area, the approach in this study may be useful to help decompose hydrological time series, extracting frequencies in which natural and anthropic components are mainly localized, before their use in modeling approaches. It should be noted that the river dynamics in hydrologic stations are not only controlled by river dynamics in upstream stations, but also influenced by stochastic factors such as multiple tributary inflows, climate changes, and human activities in the basin between each two studied hydrologic stations. Further research could be carried out comparing the results of the integrated data analysis with the results coming from the models of the main physical processes under different stochastic factors.

## AUTHOR CONTRIBUTIONS

K. H.: Writing – original draft and formal analysis. Y. C. and J. L.: writing – original draft, conceptualization, and methodology. H. S. and C. C.: investigation and formal analysis.

## FUNDING

The study was financially supported by the National Natural Science Foundation of China (U1802241 51509066, 11371117, and 51909053), Innovative Research Group of Heibei Natural Science Foundation (E2020402074), the University Science and Technology Research Project of Hebei, China (ZD2019005), and the Innovation Fund of Postgraduate, Xihua University (YCJJ2020109).

## CONFLICTS OF INTEREST

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.