As a tide propagates into the estuary, river discharge affects tidal damping, primarily via a friction term, attenuating tidal motion by increasing the quadratic velocity in the numerator, while reducing the effective friction by increasing the water depth in the denominator. For the first time, we demonstrate a third effect of river discharge that may lead to the weakening of the channel convergence (i.e. landward reduction of channel width and/or depth). In this study, monthly averaged tidal water levels (2003–2014) at six gauging stations along the Yangtze River estuary are used to understand the seasonal behaviour of tidal damping and residual water level slope. Observations show that there is a critical value of river discharge, beyond which the tidal damping is reduced with increasing river discharge. This phenomenon is clearly observed in the upstream part of the Yangtze River estuary (between the Maanshan and Wuhu reaches), which suggests an important cumulative effect of residual water level on tide–river dynamics. To understand the underlying mechanism, an analytical model has been used to quantify the seasonal behaviour of tide–river dynamics and the corresponding residual water level slope under various external forcing conditions. It is shown that a critical position along the estuary is where there is maximum tidal damping (approximately corresponding to a maximum residual water level slope), upstream of which tidal damping is reduced in the landward direction. Moreover, contrary to the common assumption that larger river discharge leads to heavier damping, we demonstrate that beyond a critical value tidal damping is slightly reduced with increasing river discharge, owing to the cumulative effect of the residual water level on the effective friction and channel convergence. Our contribution describes the seasonal patterns of tide–river dynamics in detail, which will, hopefully, enhance our understanding of the nonlinear tide–river interplay and guide effective and sustainable water management in the Yangtze River estuary and other estuaries with substantial freshwater discharge.

Tide–river interactions and resulting residual water level profiles play a
crucial role in large-scale river deltas (e.g. the Mississippi River delta
in the US, the Rhine–Meuse delta in the Netherlands, the Pearl
River delta and the Yangtze River delta in China and the Ganges–Brahmaputra
delta in Bangladesh, among others) because tide–river dynamics exert a tremendous
impact on delta morphodynamics, salt intrusion and deltaic ecosystems

The impact of river discharge on tidal wave propagation, especially on tidal
damping, in estuaries has long been the subject of intensive scientific
interest

Although the important role played by the residual water level on estuarine
hydrodynamics has been recognised for some time

The tide–river dynamics in the Yangtze River estuary, located on the east
coast of China, have received increasing attention in recent years owning to
intensive climate change and human intervention (e.g. the Three Gorges Dam
construction or the Deep Waterway Project) on both riverine and marine processes

The remainder of this paper is constructed as follows. An overview of the study area and the datasets used to study the seasonal behaviour of tidal damping and residual water level slope is given in Sect. 2. Section 3 introduces the analytical hydrodynamic model for reproducing tide–river dynamics in estuaries. The main results illustrating the seasonal behaviour of tidal damping and the residual water level slope are presented in Sect. 4, after which a discussion is presented in Sect. 5. Finally, some conclusions are drawn in Sect. 6.

Sketch map of the Yangtze River basin

The Yangtze River estuary, located on the east coast of China, extends

Monthly averaged hydrological data (including tidal range and water level)
from the following six tidal gauging stations along the Yangtze
River estuary were collected from the Yangtze Hydrology Bureau of the
People's Republic of China for the period from 2003 to 2014: Tianshenggang (TSG); Jiangyin (JY), located
46 km upstream of TSG; Zhenjiang (ZJ), located 155 km upstream of TSG;
Nanjing (NJ), located 236 km upstream of TSG; Maanshan (MAS), located 284 km
upstream of TSG; and Wuhu (WH), located 330 km upstream of TSG. The tidal amplitude
was defined as half of the tidal range either during the flood or the ebb
period, and we determined the mean value by averaging the tidal amplitudes
during flood and ebb periods. To correctly calculate the residual water level
slope, measured water levels from the gauging stations were corrected to
the Yellow Sea 1985 vertical datum of local mean sea level. Figure

The dynamics of the residual water level can be derived from the one-dimensional
momentum equation

Temporal (monthly averaged) variations of the observed tidal range,

Assuming a negligible advective acceleration influence and density effect,
integration of Eq. (

To correctly reproduce the residual water level profile in estuaries, an
iterative procedure is required to properly calculate the friction term as
presented in Eq. (

Dimensionless parameters adopted in the analytical model for tide–river dynamics.

Concentrating on a predominantly tidal constituent (e.g.

The analytical solutions for the main tide–river dynamics can be obtained by
solving a set of four implicit equations:
the damping/amplification equation,

The main dependent dimensionless parameters in
Eqs. (

Scatterplot and liner regression line of tidal damping rate,

To understand the importance of seasonal changes in river discharge on
tide–river dynamics, we first explore the seasonal variation of the tidal
damping rate and the residual water level slope (Fig.

The study period covers tide–river dynamics under both low and high flow
conditions, where the monthly average river discharge observed at DT
ranges from approximately 9174 to 61 400 m

Longitudinal variation of the main geometric characteristics (cross-sectional area, width and depth) along the Yangtze River estuary. The thick black lines represent the best-fitting curves.

Characteristics of geometric parameters in the Yangtze River estuary.

The main geometric characteristics (including the tidally averaged
cross-sectional area, width and depth) used in this paper were extracted from
a digital elevation model (DEM) produced from Yangtze River estuary
navigation charts surveyed in 2007. The elevations have been corrected to the
local mean sea level of the Yellow Sea 1985 vertical datum. Figure

Comparison of analytically computed tidal amplitude,

The analytical model was calibrated and verified against the observed tidal
amplitude and residual water level along the Yangtze River estuary on the
basis of the monthly averaged hydrological data during the 2003–2014 period. The
adopted seaward tidal amplitude (at TSG) and upward river
discharge (at DT) in the analytical model are displayed in
Fig.

The calibrated analytical model is subsequently used to explore the response
of the main tide–river dynamics (represented by the damping/amplification
number

Contour plot of the damping number

For a typical tidal river, it is usually observed that the tidal range is
reduced when the residual water level rises in the landward direction owing
to the residual water level slope, which is mainly balanced by the residual
frictional effect

Contour plot of the residual water level slope

Figure

Longitudinal variation of the main tide–river dynamics

To understand the main processes that control the development of a maximum
tidal damping, we used the average values of the observed tidal amplitude at
TSG and the river discharge at DT as model inputs and
reproduced the main tide–river dynamics along the Yangtze River estuary.
Figure

Longitudinal variation of the estuary shape number

It is also worth examining the longitudinal and seasonal variations of the
two controlling parameters represented by the estuary shape number

Relationship between the tidal damping number

Based on the analytical results, in Fig.

Relationship between the estuary shape number

The underlying mechanism for achieving a critical river discharge for maximum
tidal damping can be primarily attributed to the cumulative effect of the
residual water level

Although the current analytical model can reproduce the first-order
tide–river dynamics well, it also has some limitations. The fundamental assumption
is that the tidal wave can be described by a combination of a steady residual
term (generated by the river discharge) and a time-dependent harmonic wave
(introduced by the tidal flow). Thus, the proposed model can only capture the
tidal asymmetry caused by tide–river interaction while it neglects the tidal
asymmetry introduced by astronomical tides (e.g. nonlinear interactions
among

It is assumed that both the tidally averaged cross-sectional area and channel
width can be approximated by exponential functions following
Eqs. (

Knowledge of the development and evolution of tide–river dynamics that
determine the behaviour of tidal damping and residual water level slope under
external forcing (e.g. tidal and riverine flow) and geometry changes (e.g.
deepening and land reclamation) are essential for improving the sustainable
water management in estuaries. Adopting the method proposed in this study,
one can evaluate the influence of human intervention on the
estuarine system (such as large-scale sand excavation, dredging for
navigational channels or freshwater withdrawal), on flood control structures
(e.g. storm surge barriers, flood gates) and on the aquatic environment (e.g. such
as salt intrusion and the related water quality). For instance,

As tide propagates into an estuary, it is distorted and becomes asymmetric
due to significant nonlinear interactions with geometry and river flow. Tidal
asymmetry is regarded as one of the most important mechanisms generating
residual sediment transport

Both observations and analytical model results show a critical value of river discharge that causes maximum tidal damping in the upstream part of the tidal river, challenging the concept of how river discharge dampens tidal waves. The residual water level slope, mainly balanced by the residual frictional effect, plays a key role in determining the evolution of tide–river dynamics under a wide range of tidal and riverine forcing conditions. A critical position along the estuary is where there is maximum tidal damping, upstream of which the residual water level slope is reduced. The location of this position moves seaward with an increase in river discharge. From that position landwards, the effect of river discharge on tidal damping becomes weaker instead of stronger, indicating a weakening of the backwater effect induced by the residual frictional effect. It is worth noting that the underlying mechanism of generating critical position along the estuary is similar to that of generating critical river discharge due to the fact that for a given (constant) river discharge, the effect caused by river discharge becomes stronger with distance upstream in a tidal river, which is analogous to a river discharge increase at a given (fixed) location.

Moreover, analytical model results show that more river discharge is required
to change the maximum tidal damping critical value from a negative to a
positive gradient for the seaward positions where the tide exerts stronger
impact. The underlying mechanism has to do with the fact that river discharge
affects tidal damping: on the one hand, attenuating tidal motion by
increasing the quadratic velocity in the numerator, and on the other hand,
reducing the effective friction by increasing the water depth in the
denominator. The occurrence of critical river discharge suggests the
cumulative effect of the residual water level (increasing the water depth and the
cross-sectional area) that exceeds the threshold of tide–river dynamics,
beyond which tidal damping weakens with river discharge. To the best of our
knowledge, this is one of the few studies that shows the gradient switch of
the cross-sectional area (i.e.

All of the data used in this study were obtained from the source mentioned in Sect. 2.

The supplement related to this article is available online at:

All authors contributed to the design and development of the work. The experiments were originally carried out by HC. XZ, LG and MZ carried out the data analysis. FL and HC prepared the paper with contributions from all co-authors. HHGS, EG and QY reviewed the paper.

The authors declare that they have no conflict of interest.

The authors thank the two anonymous referees for their constructive comments and suggestions, which have greatly improved the quality of this paper.

This research has been supported by the Open Research Fund of the State Key Laboratory of Estuarine and Coastal Research (grant no. SKLEC-KF201809), the National Natural Science Foundation of China (grant nos. 51709287, 41106015, 41476073, 41506105 and 41876091), the Basic Research Program of Sun Yat-Sen University (grant no. 17lgzd12) and the Guangdong Provincial Natural Science Foundation of China (grant no. 2017A030310321). The work of Erwan Garel was supported by a FCT research contract (IF/00661/2014/CP1234).

This paper was edited by Insa Neuweiler and reviewed by two anonymous referees.