Quantifying the impacts of the Three Gorges Dam on the spatial-temporal water level dynamics in the upper Yangtze River estuary

. Understanding the alterations in spatial-temporal water level dynamics caused by natural and anthropogenic changes is essential for water resources management in estuaries, as this can directly impact the estuarine morphology, sediment transport, salinity intrusion, navigation conditions, and other factors. Here, we propose a simple triple linear regression model linking the water level variation on a daily timescale to the hydrodynamics at both ends of an estuary. The model was 5 applied to the upper Yangtze River estuary (YRE) for examining the inﬂuence of the world’s largest dam, the Three Gorges Dam (TGD), on the spatial-temporal water level dynamics within the estuary. It is shown that the regression model

factors influenced by the operation of TGD include hydrodynamics (Cai et al., 2019c), morphological evolution (e.g., Yang et al., 2011Yang et al., , 2014Lai et al., 2017;Yuan et al., 2020), sediment and flow 55 discharges (e.g., Chen et al., 2016;Guo et al., 2018), nutrient transport (e.g., Wang et al., 2020), river-lake interaction (e.g., Guo et al., 2012;Mei et al., 2015), and thermal dynamics (e.g., Cai et al., 2018a;Liu et al., 2018). However, due to the long distance from the TGD to the downstream estuary, quantification of the potential impacts of the TGD (mainly due to its seasonal freshwater regulation) on the spatial-temporal water level dynamics is a challenging task, as flow alterations are gener-60 ally concurrent with geometric changes induced by natural and anthropogenic factors. In addition, water level dynamics in the downstream estuary is highly sensitive to even small changes in the upstream basin. Here, we present a simple yet powerful triple linear regression model linking the water level variation at a daily timescale to hydrodynamics at both ends of the upper Yangtze River estuary (YRE). The advantage of this regression model is that it allows a separate quantification m near the estuary mouth at Zhongjun station. According to observations at the Zhongjun station, the average ebb tide duration (7.4 h) is longer than the averaged flood tide duration (5 h), indicating 90 an irregular semidiurnal character (Zhang et al., 2012). Unlike previous studies (e.g., Qiu and Zhu, 2013;Lu et al., 2015;Alebregtse and de Swart, 2016) which focused on tidal hydrodynamics near the estuary mouth, here, we mainly concentrate on the water level dynamics under the impacts of the TGD's seasonal regulation over the upper reach of the YRE.
These data were obtained from the Yangtze Hydrology Bureau of the People's Republic of China.
The daily averaged water levels were determined by averaging the hourly values, which were interpolated from daily high and low water levels using shape-preserving piecewise cubic interpolation.

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All the water levels at different gauging stations were corrected to the national mean sea level of Huanghai 1985. The data during the period 1985-2002 was not included since most of the water level data were not available. However, the collected data were sufficient to represent the hydrodynamic condition before and after the TGD's operation.

Triple linear regression model
In this study, we hypothesize that the water level dynamics on a daily time scale shows a regular and predictable pattern. Thus, we propose that the daily-mean water level variation Z (at an arbitrary location within the estuary) in response to hydrodynamics observed at both ends of the estuary can be described by the following triple linear regression model: Here, Z 0 is the intercept representing a base water level which is in equilibrium with climate and local conditions, so that the water level variation is linearly proportional to the river discharge Q imposed at the upstream boundary, and the water levels Z down and Z up are imposed at the seaward and upstream boundaries of the estuary, respectively. In Equation (1), 'std' denotes the 120 standard deviationfunction. Here. :::::: Here, : the seaward boundary should be in principle located far from the upstream boundary with negligible river discharge influence. :: In :::: this ::::: study, ::: the :::: DT :::::::::: hydrological :::::: station :::: was :::::: chosen :: as ::: the :::::::: upstream ::::: end, ::::: while ::: the :::: TSG ::::::: gauging :::::: station :::: was :::: used ::: as :: the ::::::::::: downstream :::: end. The source code of the proposed triple linear regression model is available at https://github.com/Huayangcai/Triple-Linear-Regression-Model-V1.0-Matlab-Toolbox. It is worth 125 noting that daily averaged water levels observed :::: there :: is ::: no :::::: unique ::::::::::::: stage-discharge ::::::::::: relationship at the DT hydrological station are not uniform for identical river discharge (see Figure S1 in the Supplementary Material) due to the ::::: owing :: to ::: the ::::::::::::: stage-discharge ::::::::: hysteresis ::::: effect :::::: caused ::: by :::: flow ::::::::::: unsteadiness, ::::::: together :::: with ::: the : influence of external forcing, either the potential influence induced by the tidal forcing (especially during the dry season) or the exerted residual water level slope up-130 stream of the DT hydrological station (owing to the relative importance of river discharge between the main stream and the tributaries, especially during the flood season). Thus, in order to explicitly account for the influence of extern ::::::: external forcing in both upstream and downstream reaches, here we have explicitly introduced the z up into the regression model, and hence the dynamics of residual water level slope along the upper YRE. Z 0 , α, β and γ are linear regression coefficients that are 135 determined from the observed data according to a least-squares fit technique. In this study, the DT hydrological station was chosen as the upstream end, while the TSG gauging station was used as the downstream end. It should be noted that the imposed downstream water level Z down also implicitly accounts for other nontidal factors, such as wind, ocean temperature and ocean salinity, which are assumed to be negligible in the regression model when compared with the tidally induced water level 140 fluctuations featured by a typical spring-neap cycle (see Figure S2 in the Supplementary Material).
In Equation (1), the relative importance of variance contributions made by riverine p r and tidal p t forcing can be estimated by the following formulas:

Quantifying the separate impacts due to boundary and geometry changes
In order to quantify the geometric change induced by the combined influences of both natural and anthropogenic modifications and separate these from boundary effects (induced by the changes in upstream and downstream conditions, primarily due to the TGD's freshwater regulation), the entire 150 study period is divided into two periods: pre-TGD and post-TGD. The data during the pre-TGD period is used for model calibration. Subsequently, the calibrated regression coefficients were then adopted for the same model over the post-TGD period to estimate the expected water levels if there existed no significant geometric change induced by the construction of the TGD. Here we use the true observed hydrodynamics at both ends of the estuary (i.e., the discharge and water level at the 155 upstream end and the open-ocean water level at the seaward end).
In this manner, the total alteration of water level (induced by both the boundary changes and the geometric alteration) in the post-TGD period relative to the pre-TGD period can be quantified as: which represents the difference in observed water level for the post-TGD (Z obs,post−TGD ) period 160 and the pre-TGD (Z obs,pre−TGD ) period. This total alteration is due to two distinct effects: 1) The contribution made by changes in the boundary conditions (∆ BOU ), defined as the difference between the water level values simulated for the post-TGD (Z sim,post−TGD ) and pre-TGD (Z sim,pre−TGD ) period: 165 2) The contribution made by changes in the geometry (∆ GEO ), defined as the difference between the observed (Z obs,post−TGD ) and simulated (Z sim,post−TGD ) values of water level for the post-TGD period: Equations (4)-(6) can be combined, yielding the following expression: where ε = Z sim,pre−TGD − Z obs,pre−TGD represents the model bias (i.e., mean error) between the simulated and observed water level during the calibration period (i.e., the pre-TGD period). To evaluate the model performance in estimating water level alterations, we require that the bias ε should be small when compared with ∆ BOU and ∆ GEO at different time scales (i.e., seasonal and 175 annual).
It is worth noting that the quantity ∆ BOU (including both the upstream and downstream boundary conditions) should be interpreted as the water level alteration owing to the overall influences driven by both human interventions and climate change. However, in this study the largest contribution to the alteration in upstream boundary condition (i.e., river discharge) can be primarily attributed to the TGD's operation, since the TGD alone accounts for more than 30% of the total storage capacity of the dams constructed between 1987 and 2014 along the Yangtze River (Li et al., 2016). In addition, we note that the only other dam (Gezhouba, abbreviated by GZB, see Figure 1a) along the main course of the Yangtze River was constructed in 1981 (before the TGD) ::: and :::::: should ::: not ::::::::::: considerably ::::::: influence ::: the ::::::::: discharge :::::: regime ::::: since :: it :: is : a ::::::::::::: run-of-the-river :::::::::::: hydroelectric :::::: system. With regard to 185 the downstream boundary condition, the adopted water levels observed at TSG station implicitly account for the potential impacts induced by both anthropogenic (such as channel dredging) and climate (such as global sea level rise) changes. Meanwhile, it is also worth noting that the quantity ∆ GEO should be interpreted as the water level alteration due to the overall impacts caused by both the bathymetric change and the storage area change.

Performance of the triple linear regression model
The proposed triple linear regression model was applied to reproduce the water level dynamics observed during both the pre-TGD and post-TGD periods (see Figure 2). For ::: for the given upstream river discharges and water levels observed at the DT hydrological station and the water levels ob-195 served at the TSG gauging station ::: (see ::::: Figure  (accounting for 4%-13% of the standard deviations of the observed water levels, see Table 1) at the five water level stations, which leads support to our hypothesis that the response of water level dynamics to hydrodynamics at both ends of the estuary is largely linear in the upper YRE owing to the explicit inclusion of Z up in the regression model. Table 1 presents the calibrated linear regression coefficients for both study periods, where we observe a general reduction in the Z 0 , α and β param-  (1). In this case, the model performance is more or less the same as the original triple linear regression model (see Figure S3 and Table S1 in the Sup- Spatial interpolation of the triple linear regression coefficients was performed by means of piecewise cubic Hermite interpolants (e.g., Matte et al., 2014) in order to correctly reproduce the water level dynamics at arbitrary locations along the estuary. Figure 3 shows the four spatially interpolated model coefficients together with vertical error bar (estimated using the Matlab 'regress.m' function with 95% confidence intervals) along the upper YRE for the pre-TGD and post-TGD periods. Generally, a longitudinal reduction in coefficients (e.g., Z 0 and β in Figure 3a, c) in the landward direction suggests a weakening effect of these parameters on the total variations in water levels, which corresponds to the external forcing from the seaward end of the estuary. On the contrary, if the coefficients 220 are increased :::::::: increasing : (e.g., α and γ in Figure 3b, d), this corresponds to an enhancement from the upstream end. However, we observed an exception from the MAS to WH stations, where the coefficient α was reduced (see Figure 3b), suggesting a switch of the effect of river discharge in the upstream part of the estuary. The standard error :::: error :::: bars : presented in Figure 3 represents ::::::: represent : the standard deviation of the estimated linear regression coefficients, which suggests that 225 the proposed triple linear regression model is robust with limited uncertainty ::::: fitting :::: well.

Reconstructions of spatial-temporal water level dynamics
Using the calibrated regression models and interpolated linear regression coefficients (see Figure 3), the spatial-temporal water level dynamics for the two study periods can be reconstructed along the upper YRE for the climatological reference year (Figure 4), which is defined by eval-230 uating for each day of the year the average value of all measurements available over the study period for the same day (though February 29 th during leap years was not considered). Subsequently, we used the Matlab 'gradient.m' function (returning the one-dimensional numerical gradientof imposed vector ::: i.e., ::::::::: 'gradient' ::::::::: calculates ::: the :::::: central ::::::::: difference ::: for :::::: interior ::::: data :::::: points, :::: while :: it ::::::::: calculates :::::: values ::::: along ::: the ::::: edges ::: of ::: the :::::: matrix :::: with :::::::::: single-sided :::::::::: differences, :::: see :::::: details 235 :: in ::::::::::::::::::::::::::::::::::::::::::::::: https://www.mathworks.com/help/matlab/ref/gradient.html) to estimate the residual water level slope based on the reconstructed water levels along the YRE. In Figure 4, we note that there is a local minimum water level slope which occurs in the central part (between JY and ZJ) of the YRE, which shifts by approximately 30 km landward after the TGD begins operation. Such a shift of local minimum water level slope is very likely to be linked to the abnormal tidal range reduction observed 240 at the ZJ gauging station after the TGD begins operation (Cai et al., 2019c) and this might be related to a minimum in energy flux divergence (Giese and Jay, 1989;Jay et al., 2015), with implications for sedimentary processes. occurs in autumn and winter seasons, which correspond to a dramatic reduction in river discharge during the wet-to-dry transition period (i.e. autumn) and slightly increased river discharge during the dry season (i.e. winter) due to the operation of the TGD since 2003. Conversely, changes during the spring and summer are relatively minor, which is mainly due to negligible change in the river discharge. It should be noted that the water levels in the downstream reaches (x < 200 km) were 250 slightly increased during the spring, while they are approximately constant in the upstream part.

Influence of the TGD on the spatial-temporal water level dynamics
Using Equations (4)- (7), the triple linear regression model can quantify the contributions induced by the changes in boundary conditions (i.e., upstream freshwater and water level alterations at DT and downstream water level alteration at TSG) and in geometry to the water level variability during the 255 post-TGD period. In this study, the regression model calibrated during the pre-TGD period was successively applied to the post-TGD period, keeping the same coefficients (i.e., Z 0 , α, β, γ) obtained before. The simulated water levels were compared with the actual measurements and their differences (i.e., ∆ GEO in Equation (4)) represent the alterations caused by geometric changes, which can be attributed to the combined influences of natural and anthropogenic changes. Compared to the 260 pre-TGD period, it is possible to isolate the influence on water level dynamics from the boundary conditions impacts (i.e., ∆ BOU in Equation (3)).  (4)-(7) based on the observed and simulated water levels for the pre-and post-TGD periods. It can be seen that the model bias ε is generally smaller than the cal-265 culated ∆ BOU and ∆ GEO (with ε/∆ BOU and ε/∆ GEO being 0.8% and 0.1% at the annual scale on average, respectively), which suggests that the impacts due to model errors on the analysis of water level dynamics is negligible. At the annual scale, we observe that the changes in the boundary conditions tends to increase the mean water level, while the geometric effect acts in the opposite direction, leading to an overall reduction in water level along the upper YRE.
270 Figure 6 shows the intra-annual variability (in a climatological year) of water level alterations at five gauging stations along the upper YRE. It is observed that the overall impacts of boundary conditions and geometry effects can be divided into three distinct periods. From January to March, the total alteration ∆ TOT increased by approximately 0.28 m on average, while it remained more or less constant during May to June (increasing slightly by 0.01 m), and it generally decreases during the 275 rest of the year by approximately 0.54 m (see Figure 6a). Noticeably, the increase of ∆ TOT from January to March is mainly caused by changes in the boundary conditions (see Figure 6b), which is primarily attributed to the freshwater regulation of the TGD, and leads to an increased discharge during the dry season. Additionally, a significant decrease of ∆ TOT in autumn (from September to November) is observed, due to the combined effects of boundary conditions and geometry. In 280 Figure 6b, we observe that the alterations caused by boundary condition variations ∆ BOU are positive throughout the year except for October and November, which can be primarily attributed to the operation of the TGD, corresponding to a substantial reduction in freshwater discharge during the wet-to-dry transitional period. Such a boundary effect is partially due to the rise of the seaward water level, especially during the period when freshwater discharge is reduced (see Figure 7). The 285 water level alteration caused by the geometric effect ∆ GEO is negative and tends to increase along the channel, which is due to the cumulative effect of mean water level in the landward direction.
We now quantify the alterations in variance contributions made by riverine (denoted by ∆p r ) and tidal (denoted by ∆p t ) forcing using Equations (2) and (3) to understand the impacts of freshwater regulation on the spatial-temporal water level dynamics. On average, it can be seen from Table   290 3 that the contributions made by the riverine forcing p r to the overall water level variance are increased during the post-TGD period. In particular, the p r values at the JY and ZJ gauging stations were substantially increased by 16.16% and 13.61%, respectively. Further upstream, less alteration (ranging from 0.16%-1.87%) by the riverine forcing contributed to the overall water level variance.
There exists a long tradition of statistical, analytical and numerical studies on tide-river interactions in estuaries worldwide, such as the Columbia River estuary in the USA (e.g., Kukulka and Jay, 2003;Jay et al., 1990;Pan et al., 2018b), the St. Lawrence River estuary in Canada (e.g., Godin, 1999;Matte et al., 2013Matte et al., , 2014, the Mahakam River estuary in Indonesia (e.g., Buschman et al.,355 2009; Sassi and Hoitink, 2013), the Yangtze River estuary in eastern China (e.g., Guo et al., 2015Guo et al., , 2020Yu et al., 2020) and the Pearl River estuary in southern China (e.g., Zhang et al., 2018;Cai et al., 2018bCai et al., , 2019b. These studies showed that as tides propagate along the estuary the tidal ampli-tude, phase and shape were influenced by the bottom friction, channel geometry and river discharge. In this study, with the proposed simple yet effective triple linear regression model, we are able to 360 isolate and to quantify the impacts of the boundary (such as freshwater regulation due to dam's operation) and geometric (such as channel dredging) effects on the tide-river dynamics. Such a novel approach should be particularly helpful for determining scientific guidelines for sustainable water resources management (e.g., dredging for navigation, flood control, salt intrusion prevention etc.) in estuaries worldwide, especially for dam-controlled estuaries. In addition, the proposed method can 365 also be used to quantify the potential impacts of changes in boundary conditions induced by climate change (such as intensifying precipitation, global sea level rise, etc.) in natural estuaries without considerable human interventions.

Data availability
The MATLAB codes and data used in this paper can be open-access from a publicly ac-

Author contributions
All authors contributed to the design and development of this work. The model was originally developed by HC. HY carried out the data analysis. GL built the model and wrote the paper. PM,

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HP, ZH and TZ reviewed the paper.

Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.

Financial support
This research has been supported by the National Natural Science Foundation of China (Grant