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 applied to the upper Yangtze River estuary (YRE) to examine 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 can accurately reproduce the water level dynamics in the upper YRE, with a root mean squared error (RMSE) of 0.061–0.150 m seen at five gauging stations for both the pre- and post-TGD periods. This confirms the hypothesis that the response of water level dynamics to hydrodynamics at both ends is mostly linear in the upper YRE. The regression model calibrated during the pre-TGD period was used to reconstruct the water level dynamics that would have occurred in the absence of the TGD's freshwater regulation. Results show that the spatial–temporal alterations in water levels during the post-TGD period are mainly driven by the variation in freshwater discharge due to the regulation of the TGD, which results in increased discharge during the dry season (from December to March) and a dramatic reduction in discharge during the wet-to-dry transitional period. The presented method to quantify the separate contributions made by changes in boundary conditions and geometry to spatial–temporal water level dynamics is particularly useful for determining scientific strategies for sustainable water resources management in dam-controlled or climate-driven estuaries worldwide.

Water level is an important factor affecting estuarine environments as they influence hydrological, ecological, and biogeochemical processes in many ways (such as flood control, water quality, and carbon and nutrient cycles). It has previously been demonstrated that water level dynamics are mainly controlled by river flow alteration in the catchment and tidal variation near the estuary mouth, resulting in a positive surface water level gradient along the estuary axis in the landward direction

Water level dynamics in estuaries are nonstationary since they are subject to nonlinear interactions with the barotropic tide that can be modified by channel geometry, bottom friction, and river discharge. This nonlinear relationship can be approximated by the balance between tidally averaged residual water level slope and bottom friction. As a consequence, the water level dynamics can be expressed by semi-analytical solutions of the one-dimensional St. Venant equations, provided that adequate information (tidal forcing at the estuary mouth, river discharge at the upstream end, and simplified channel geometry) is available

Numerous studies have been conducted to understand the potential environmental impacts of the Three Gorges Dam (TGD), the largest dam in the world, since its operation beginning in 2003 has dramatically changed the downstream hydrology and sediment delivery in the Yangtze River. Key factors influenced by the operation of TGD include hydrodynamics

The Yangtze River, which flows from west to east in central China, is one of the world's most important rivers due to its great economic and social relevance. It has a length of about 6300 km and a basin area of about 190 000 km

Map of the Yangtze River basin

Apart from river flows, upstream-propagating tides are also a major source of hydrodynamic energy in the upper YRE, which is characterized by a meso-tide with a mean tidal range of

Hydrological data for both the pre-TGD (1978–1984) and post-TGD (2003–2014) periods of water level from six tidal gauging stations mentioned above along the estuary were collected, together with the corresponding river discharges observed at the DT hydrological station. Here, it is worth noting that the observed river discharges at the DT hydrological station were generally derived from a well-calibrated stage–discharge relationship, which is established by concurrent measurements of stage and discharge (through approximately 50–70 filed measurements of flow depth and velocity in each year to account for the cross-sectional changes) over a wide range of river discharge conditions. 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. 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 were 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.

In this study, we hypothesize that the water level dynamics on a daily timescale show a regular and predictable pattern. Thus, we propose that the daily mean water level variation

Here,

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 study period is divided into two periods: pre-TGD and post-TGD. The data during the pre-TGD period are 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 was 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 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

the contribution made by changes in the boundary conditions (

and the contribution made by changes in the geometry (

It is worth noting that the quantity

Alterations in difference between predicted and observed daily averaged water levels as a function of observed daily averaged water levels for both the pre-TGD and post-TGD periods at different gauging stations along the upper YRE:

The proposed triple linear regression model was applied to reproduce the water level dynamics observed during both the pre-TGD and post-TGD periods for the given upstream river discharges as well as water levels observed at the DT hydrological station and the water levels observed at the TSG gauging station (see Fig.

Calibrated linear regression coefficients for both the pre-TGD and post-TGD periods along the upper YRE.

Spatial interpolation of the triple linear regression coefficients was performed by means of piecewise cubic Hermite interpolants

Interpolated linear regression coefficients

Using the calibrated regression models and interpolated linear regression coefficients (see Fig.

Reconstructed spatial–temporal water levels,

Figure

Longitudinal variability of reconstructed water level

Using Eqs. (

Table

Alterations in water levels induced by the combined impacts of natural and anthropogenic changes

Monthly averaged alteration in water level (m) attributed to changes in boundary conditions (

Figure

Alterations in river discharge and water level observed at DT and TSG, respectively, during the post-TGD period relative to the pre-TGD period over the climatological year. The daily averaged river discharge and water level were smoothed using a moving average filter with a span of 30 d.

Relative contributions made by riverine

We now quantify the alterations in variance contributions made by riverine (denoted by

Alterations in variance contributions of riverine

In this study, we have explored the alterations in spatial–temporal water level dynamics along the main course of the YRE, with a special focus on quantifying the effects caused by the changes in boundary conditions and geometry. Through the use of a triple linear regression model, we reconstructed the spatial–temporal water level dynamics solely induced by changes in boundary conditions in the post-TGD period. When compared to the observed and simulated values in the pre-TGD period, it is possible to quantify the alterations attributed to the boundary conditions and geometry via Eqs. (

It is notable that the alterations in water levels induced by the geometric changes

Illustration of the effect of riverbed deepening on the water level dynamics along the channel.

Although the proposed triple linear regression model can satisfactorily reproduce the daily water level hydrodynamics along the upper YRE, the adopted boundary conditions at both ends of an estuary are not fully independent since the water level dynamics at TSG gauging station are influenced by the upstream river discharge observed at DT hydrological station, especially during the wet season, which brings substantial freshwater discharge. Such a drawback can be improved by using water level dynamics, either observed or predicted using harmonic analysis, from an outer gauging station that has a negligible impact from freshwater discharge. Our results here suggest that the construction of the TGD may have impacted the morphological evolution and hence the geometry in the estuarine area since the sediment loads observed at DT have decreased from 470.4 million tons annually in 1951–1985 to 138.7 million tons in 2003–2015, a substantial reduction of approximately 70 %

There is 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

The MATLAB codes and data used in this paper can be obtained open-access from a publicly accessible and version-controlled GitHub repository (

The supplement related to this article is available online at:

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, HP, ZH, and TZ reviewed the paper.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research has been supported by the National Natural Science Foundation of China (grant no. 51979296), the Guangdong Provincial Department of Science and Technology (grant no. 2019ZT08G090), and the Guangzhou Science and Technology Program of China (grant no. 202002030452).

This paper was edited by John M. Huthnance and reviewed by Xi Feng and one anonymous referee.