Decomposing turbulence from waves remains challenging due to frequency overlap and wave-turbulence interactions. Existing decomposition methods, e.g., moving average, energy spectrum analysis, and synchrosqueezed wavelet transform (SWT), produce inconsistent turbulence estimates. Here, we introduce a rotating-coordinate-based method (RoCoM), founded on two assumptions: (1) the energy spectrum in the cross-wave direction remains unaffected by wave orbital velocities, and (2) wave-wise and vertical turbulence spectra are linearly proportional to the cross-wave spectrum, with proportional constants derived from frequencies higher than the wave-dominated frequency range. Both assumptions were validated with observational data collected from the Changjiang Estuary. Comparative analyses using both in-situ observations and controlled laboratory experiments show RoCoM avoids the energy trough problem inherent in the moving average and SWT methods, yielding the most accurate power spectra and turbulent kinetic energy (TKE) estimates. In-situ data reveal that the relative errors of RoCoM are approximately 16 % for total TKE and about 6 % for TKE within the wave-dominated frequency range. Laboratory experiments further confirm its superior accuracy, demonstrating relative errors of approximately 14 % for total TKE and about 7 % for wave-band TKE. RoCoM holds significant implications for marine material transport and coastal energy development by providing robust and precise turbulence and wave energy estimates. Nonetheless, its application is currently best suited for scenarios with predominant wave propagation from a single direction, while SWT remains advantageous in environments characterized by broader directional wave spreading.

Channel deepening and narrowing are common anthropogenic modifications in estuaries, but their combined effects on estuarine circulation, stratification, and sediment transport remain insufficiently understood. This study investigates these combined impacts in the North Passage of the Changjiang Estuary, where large-scale deepening and narrowing have significantly altered hydrodynamic and sediment processes. Our analysis demonstrates that channel deepening intensifies estuarine circulation by strengthening the landward near-bed flow, thereby enhancing sediment import. Contrary to initial expectations that narrowing would promote sediment flushing, our results indicate that narrowing increases stratification, steepens along-estuary salinity gradients, and suppresses vertical mixing. Intensified stratification further reinforces estuarine circulation, promoting sediment trapping at the saltwater intrusion limit. Additionally, enhanced tidal pumping driven by increased velocity and suspended sediment concentration gradients extends the estuarine turbidity maximum both upstream and downstream, a process often overlooked in engineered estuaries. These findings challenge conventional assumptions regarding the sedimentary impacts of narrowing, emphasizing instead its critical role in amplifying estuarine circulation and sediment trapping. Our results provide new insights into sediment dynamics in river-dominated estuaries, with significant implications for estuarine management, dredging operations, water quality control, and long-term morphological stability.

Human interventions influence sediment dynamics, and understanding these mechanisms is essential for predicting short-term and long-term estuarine development. The Deep Channel Navigation Project (DCNP) in the Yangtze Estuary is such a large infrastructural intervention that substantially alters sediment exchanges between channels and shoals and may thereby influence this estuarine development. However, the effect of these constructions on channel-shoal sediment exchange is up to now poorly known. In this study, we use an extensive dataset collected both in channels and on shoals and a numerical model to clarify the exchange mechanisms driving sediment transport patterns in a strongly anthropogenically modified environment. The results indicate that the stepwise construction of hydraulic structures leads to gradual changes in sediment exchange. The first phase was characterized by partially blocked sediment exchange with northward sediment transport towards the main channel and to the northern flats (2002–2010). Next, a transition period was characterized by weaker horizontal sediment exchange and reduced sediment supply (2010–2016). Since 2016, more efficient structures blocking sediment exchange further hinder northward transport and promote deposition on the southern flats. These processes point to the important role of engineering works in strengthening the southward growth of the delta. Moreover, data analyses suggest that northward over-jetty flow during high water induces a net sediment flux towards the channel due to water level gradients. The residual flow controls the net sediment transport both in the longitudinal and lateral direction over the tidal flats. Therefore, a clockwise residual circulation cell forms in the channel-shoal system, contributing to the channel siltation. These findings shed important insights into the role of sediment exchange in channel siltation and large-scale hydrodynamic and delta development. Such knowledge is crucial for sustainable future management of delta distributaries.

De-reclamation is a common strategy used for the restoration of tidal flats. In this study, we investigate the morphodynamic response of tidal channel networks and tidal flats after de-reclamation initiatives using the Delft3D numerical model. We find that tidal channel networks that have undergone reclamation and retreat projects have a lower drainage density (8.95 km⁻¹) than that of channel networks that formed naturally (11.33 km⁻¹), and the drainage efficiency of natural formed channel networks is almost three times greater than restored channel networks. These findings indicate that de-reclamation alone cannot fully erase the imprinting of the previous reclamation. We also find that the ultimate effectiveness of de-reclamation is affected by the geographical layout and unchanneled path length of the inchoate main creek system. In addition, following the implementation of de-reclamation, the immediate opening of previously enclosed areas amplifies the tidal prism, thereby intensifying tidal scouring and resulting in significant erosion, with erosion rate reaching hundreds of millimeters per day. Such losses can be remediated under sufficient sediment supply and prevented through the construction of artificial channels. However, this severe erosion may escalate under an insufficient sediment supply or a heightened tidal prism, potentially leading to permanent loss. These findings constitute an important reference for future engineering practices that support the safety and sustainability of coastal resources.

A decline of the fluvial sediment supply leads to coastal erosion and land loss. However, the fluvial sediment load may influence not only coastal morphodynamics but also estuarine hydrodynamics and associated saltwater intrusion. Previous studies revealed that suspended sediments influence estuarine hydrodynamics through various flow–sediment interactions. In this contribution, we systematically investigate how changes in fluvial sediment load and other climate-change-induced environmental change influence estuarine hydrodynamics and sediment dynamics. For this purpose, we utilize a well-calibrated fully coupled model in which hydrodynamics, saltwater intrusion, and sediment transport interact with each other, to explore saltwater intrusion in the Yangtze Estuary in response to a decline in the sediment load, modified discharge, and sea-level rise. Model results suggest that a 70% decline in the suspended sediment load weakens the impact of sediments on salinity-induced stratification and thereby reducing saltwater intrusion. Sea-level rise or discharge peak reduction increases saltwater intrusion. However, a fully coupled model accounting for sediment effects predicts a much larger increase in saltwater intrusion compared to noncoupled models. Whether this effect is important depends on estuarine sediment concentrations and therefore the potential role of sediments should be carefully investigated before applying a noncoupled model. This work highlights not only the relevance of a suspended sediment decline but also the use of fully coupled models for predicting saltwater intrusion in turbid estuaries and has broad implications for freshwater resource management in turbid estuarine systems influenced by human interventions and climate change.

Following publication of the original article (Zhu et al. 2023), the authors reported that Fig. 1 needed to be updated. The correct Fig. 1 has been provided in this Correction. The original article (Zhu et al. 2023) has been corrected.

Coastal tidal flats provide valuable ecosystems, but are highly sensitive to tidal dynamics, sea-level rise, and human activities. Tidal inundation depth and frequency are known to affect tidal flat morphodynamics. However, the causes, processes and extent remain uncertain, particularly given the associated changes in sediment availability. In this study, we monitored the hydrodynamics, sediment transport, and morphological changes on two tidal flats in the northern and southern parts of the Yellow River Delta, with contrasting tidal regimes. The data showed that longer inundation periods under diurnal tides gained additional sediment and deposition than under semi-diurnal tides, because of the associated increase in water depth and sediment availability. The wave impact increased at the site with a semi-diurnal tidal regime owing to the lower water depth, where a larger bed shear stress led to tidal flat erosion. These results indicated that the combination of tidal regime and the occurrence of powerful waves played a joint role in controlling bed erosion, sediment availability, and short-term tidal flat evolution. This has implications for coping with delta erosion by enhancing local sediment availability in diurnal tidal regions and restoring vegetation to attenuate waves in semi-diurnal regions of the Yellow River Delta.

The sediment load in the Yangtze River downstream of the Three Gorges Dam (TGD) has substantially declined in recent decades. The decrease is more profound below the TGD, e.g., a 97% decrease at Yichang, compared with that at the delta apex, 1200 km downstream, e.g., a 75% decrease, implying along-river sediment recovery. Two large river-connected lakes, i.e., Dongting and Poyang Lakes, may play a role in the re-establishment of the river’s morphodynamic equilibrium, but a quantitative data-based understanding of this interaction is not yet available. In this work, we collected a series of field data to quantify the sediment gain and loss in the river-lake system in the middle-lower Yangtze River, and evaluate the lake’s response to the reduction in riverine sediment supply. We find that Dongting Lake and Poyang Lake shifted from net sedimentation to erosion in 2006 and 2000, and back to a sedimentation regime again after 2017 and 2018, respectively. Natural morphodynamic adaptation and sand mining play an important role in the regime changes in the Dongting Lake whereas sand mining dominates the abrupt changes in the Poyang Lake. The Dongting and Poyang Lake contributed maximum by 38% (2015) and 17% (2006) (respectively) to the sediment recovery in the erosion regime, whereas the riverbed erosion dominates the main sediment source. These changes in the relative contribution of sediment sources also indicates a response time of ~ 20 years in the lakes towards a new equilibrium state. It is noteworthy that the lakes’ buffer effects may be overestimated as the supplied sediment from the lakes is rather small compared to the significant dam trapping in the upstream basin and sediment source from downstream degradation. The results imply that river management and restoration should take into account of the river-lake interactions and feedback impact at decadal time scales.

River discharge is known to enhance tidal damping and tidal wave deformation in estuaries. While the damping effect on astronomical tides has been well documented, river impact on tidal wave deformation and associated overtide generation (shallow water harmonics of one or more astronomical constituents, such as M₄) remains insufficiently understood. Overtides affect tidal asymmetry, extreme water levels, and subsequent sediment transport and flooding management, thus meriting in-depth examination. Being inspired by unusual overtide changes in the landward and seaward parts of the Changjiang Estuary under low and high river discharges, in this work, we use a schematized tidal estuary model to systematically explore overtide variations under different river discharges. Model results show enhanced overtide generation in the case with river discharge compared with that without river impact. The M₄ amplitude decreases in the landward parts of the estuary, but increases in the seaward parts under increasing river discharges. The potential energy of M₄ integrated throughout the estuary shows nonlinear variations and reaches a transitional maximum when the river discharge to tidal mean discharge (R2T) ratio at the mouth is close to unity. Similar nonlinear behaviors are observed for compound tides like MS₄ when more astronomical constituents are prescribed and triad tidal interactions are enabled. The space-dependent overtide variability is more profound in large estuaries with high river discharges like the Amazon and Changjiang estuaries. It is ascribed to the inherently nonlinear river-tide interactions, specifically the twofold effects of river discharge in enhancing bottom stress, which simultaneously enhances dissipation of astronomical constituents and reinforces the energy transfer to overtides. These findings highlight the profound nonlinear impact of river discharge on overtides, and inform the study of tidal asymmetry and compound flood risk in large estuaries and deltas.

The mechanisms controlling the formation of an estuarine turbidity maximum (ETM) in estuaries have been extensively investigated, but one aspect that has received much less scientific attention is the role of high suspended sediment concentrations in combination with tidal asymmetry in ETM formation. Particularly in highly turbid estuaries, sediment suspensions influence ETM development through a combination of horizontal sediment-induced density currents, a reduction in turbulent mixing, and water-bed exchange processes. In this study, we developed a schematic model resembling the Yangtze Estuary where the ETM is controlled by tidal pumping, estuarine circulation, and advection operating simultaneously. Model results suggest that high water slack tide asymmetry with Sediment-induced density effects (SedDE) favors landward migration of the ETM. In addition, without SedDE, stronger flood tidal dominance leads to more pronounced sediment trapping through tidal pumping. Depending on the type of tidal asymmetry, SedDE strengthen ETM growth by increasing estuarine circulation but may also lead to increased or reduced sediment concentration in the ETM due to enhanced or weakened landward tidal pumping, respectively. Higher near-bed sediment concentrations as a result of water-bed exchange processes, in turn, strengthen the effect of estuarine circulation but simultaneously strengthen the divergence of sediment by tidal pumping. Overall, the SedDE and higher near-bed sediment concentration, in combination with tidal asymmetry, play an important role in ETM formation and should be properly accounted for in studies on ETM dynamics in turbid estuaries.

Reclamation of low-lying tidal flats and floodplains adjacent to present shorelines has been implemented worldwide for both coastal defense and development. While it is technically feasible to monitor the short-term impact of tidal flat embankments, it is challenging to identify long-term and cumulative morphodynamic impact, particularly considering centennial sea-level rise (SLR). In this study, we construct a process-based hydro-morphodynamic model for a schematized tidal basin and examine its morphodynamic evolution under the combined influence of SLR and tidal flat embankments. We see that rising sea levels lead to inundation of low-lying floodplains just above high water, creating new intertidal flats that mitigate the drowning impact of SLR. This mitigation effect is lost if the low-lying floodplains and tidal flats are reclaimed, preventing any shoreline migration under SLR. Removing a large portion of intertidal flats within the tidal basin induces significant changes in basin hypsometry and potentially, a reversal of flood/ebb dominance. The resulting hydro-morphodynamic impact of large-scale tidal flat embankment is more significant than SLR at a centennial time scale. This suggests a need for much greater management awareness regarding the cumulative impact of human activities. These findings imply that allowing lateral shoreline migration under SLR sustains tidal basin's inherent morphodynamic buffering capacity, whereas reclaiming tidal flats significantly alters hydro-morphodynamic adaptation at the decadal to centennial time scales. It highlights the importance of conserving low-lying floodplains and tidal flats in tide-dominated systems to counteract the drowning impact of SLR.

Channel deepening often triggers positive feedback between tidal deformation, sediment import and drag reduction, which leads to the regime shift in estuaries from low-turbid to hyper-turbid state. In this study, a transition in profiles of suspended sediment concentration (SSC) is hypothesised by including a positive feedback loop of vertical mixing and settling. Such a hypothesis is validated by the historical observations in the North Passage of Changjiang (Yangtze River) Estuary, with decreasing SSC in mid-lower layers and increasing SSC near the bed after the deepening. A mobile pool of concentrated benthic suspensions (CBS) develops in the North Passage, with a tidally averaged length of ~20 km and a mean thickness of ~4 m. The width of the CBS pool is limited (<1 km) as the CBS is concentrated in the Deepwater Navigational Channel. The movements of the CBS pool, combined with tidal asymmetry (e.g., slack-water asymmetry and lateral flow asymmetry), results in sediment trapping in the middle reaches and on the south flank of the channel. Observations by a bottom tripod system show the response of friction/drag coefficient to sediment concentration: (1) nearly linear decrease within low SSC (<10 kg/m³); (2) constant and minimum coefficient (with drag reduction up to 60–80%) in the presence of CBS (10–80 kg/m³). An empirical relationship was derived, which can be used to predict the friction coefficient and the magnitude of drag reduction for sediment transport studies, particularly for modelling regime shifts in estuaries.

Estuarine tidal dynamics are influenced by changes in morphology and friction. In this work, we quantified changes in tidal damping in the Yangtze Estuary and explored the impact of morphology and friction using a numerical model. In-depth analyses of tidal data reveal a strong reduction in tidal damping from 1990 to 2010, followed by a slightly enhanced damping from 2010 to 2020 in the South Branch. The reduced tidal damping in the South Branch from 1990 to 2010 is controlled by sediment decline which induces an increase in water depth (erosion), thereby strongly amplifying tides. However, the effective bottom roughness (Manning coefficient) is increased by 60%, which is probably related to the (Formula presented.) 80% decrease in the suspended sediment concentration (SSC). Such an effect may enhance tidal damping, which counteracts the contribution of water depth increase on amplifying tides by (Formula presented.) 75%. From 2010 to 2020, the tides in the South Branch became more damped, suggesting a dominance of the decrease in SSC over the morphological changes. In the mouth zone, tidal dissipation is enhanced from 1997 to 2010, which is mainly caused by an overall increase in effective bottom roughness. Local structures dominate the increase in effective bottom roughness; however, fluid mud formation may contribute to a decrease after 2010. Overall, we argue that estuarine morphological and sedimentary changes in response to riverine sediment decline and local engineering works control the tidal evolution in the Yangtze Estuary, which is important for evaluation of human activities and estuarine management.

Global climate changes have accelerated sea-level rise (SLR), which exacerbates the risks of coastal flooding and erosion. It is of practical interest to understand the long-term hydro-morphodynamic adaptation of coastal systems to SLR at a century time scale. In this work we use a numerical model to explore morphodynamic evolution of a schematized tidal basin in response to SLR of 0.25–2.0 m over 100 years with special emphasis on the impact of lateral basin expansion. Starting from a sloped initial bed, morphodynamic development of the system leads to the formation of alternating bars and meandering channels inside the tidal basin and an ebb-tidal delta extending seaward from the basin. Imposing rising sea level causes progressive inundation of the low-lying floodplains, found along the basin margins, inducing an increase in basin plain area and tidal prism, as well as intertidal area and storage volume. Although the overall channel-shoal structure persists under SLR, lateral shoreline expansion alters the basin hypsometry, leading to enhanced sediment export. The newly-submerged floodplains partly erode, supplying sediment to the system for spatial redistribution, hence buffering the impact of SLR. The vertical accretion rate of the tidal flats inside the tidal basin lags behind the rate of SLR. However, lateral shoreline migration under SLR creates new intertidal flats, compensating intertidal flat loss in the original basin. In contrast, a constrained tidal basin without low-lying floodplains is subject to profound drowning and tidal flat losses under SLR. Overall, the model results suggest that an unconstrained tidal system allowing lateral shoreline migration has buffering capacity for alleviating the drowning impact of SLR by evolving new intertidal areas, sediment redistribution and morphodynamic adjustment. These findings suggest that preserving tidal flats located along the margins of tidal basins (instead of reclaiming them) sustains the system's resilience to SLR.

The Changjiang Delta (CD) is one of well-studied large deltas of critical socio-economical and ecological importance regionally and global representativeness. Cumulated field data and numerical modeling has facilitated scientific understanding of its hydro-morphodynamics at multiple spatial and time scales, but the changing boundary forcing conditions and increasing anthropogenic influences pose management challenges requiring integrated knowledge. Here we provide a comprehensive synthesis of the multi-scale deltaic hydro-morphodynamics, discuss their relevance and management perspectives in a global context, and identify knowledge gaps for future study. The CD is classified as a river-tide mixed-energy, muddy and highly turbid, fluvio-deltaic composite system involving large-scale land-ocean interacted processes. Its hydro-morphodynamic evolution exhibits profound temporal variations at the fortnightly, seasonal, and inter-annual time scales, and strong spatial variability between tidal river and tidal estuary, and between different distributary channels. As the river-borne sediment has declined >70%, the deltaic morphodynamic adaptation lags behind sediment decline because sediment redistribution within the delta emerges to play a role in sustaining tidal flat accretion. However, the deltaic channels have become narrower, deepened and growingly constrained under cumulated human activities, e.g., extensive embankment and construction of jetties and groins, possibly initiating a decrease in morphodynamic activities and sediment trapping efficiency. Overall, the CD undergoes transitions from net sedimentation and naturally slow morphodynamic adaptation to erosion and human-driven radical adjustment. A shift in management priority from delta development to ecosystem conservation provides an opportunity for restoring the resilience to flooding and erosion hazards. The lessons and identified knowledge gaps inform study and management of worldwide estuaries and deltas undergoing intensified human interferences.

An estuarine turbidity maximum (ETM) is a region of elevated suspended sediment concentration (SSC) resulting from residual transport mechanisms driven by river flow, tides, and salinity-induced density gradients (SalDG). However, in energetic and highly turbid environments such as the Yangtze Estuary, SedDG may also substantially contribute to the formation and maintenance of the ETM. Since this mechanism is relatively poorly understood, we develop a three-dimensional model to explore the effect of SedDG on tidal dynamics and sediment transport. By running sensitivity simulations considering SalDG and/or SedDG, we conclude that the longitudinal SedDG leads to degeneration and landward movement of the ETM. Moreover, two effects of the vertical SedDG are identified to be responsible for sediment trapping: One by enhancing the vertical sediment concentration gradients, and another by additionally affecting hydrodynamics including the water levels, velocities and salinities. The longitudinal and vertical SedDG leads to seasonal and spring-neap variations of upstream migration of the salt wedge: Vertical SedDG is more pronounced at neap tides in the wet season due to stronger stratification effects, whereas longitudinal SedDG is more pronounced at intermediate tides in the dry season due to weaker mixing and limited deposition. These findings imply that the SedDG contributes substantially to channel siltation and salt intrusion in highly turbid systems, and need to be accounted for when numerically modeling such phenomena.

Net sediment transport is predominantly seaward in fluvial-dominated estuaries worldwide. However, a distributary branch in the Changjiang Estuary, the North Branch, undergoes net landward sediment transport, which leads to severe channel aggradation. Its controlling mechanism and the role of human activities remain insufficiently understood, although such knowledge is necessary for better management and restoration opportunities. In this study we revisit the centennial hydro-morphodynamic evolution of the North Branch based on historical maps, field data, and satellite images and provide a synthesis of the regime change from ebb to flood dominance. The North Branch was once a major river and ebb-dominant distributary channel. Within which alternative meandering channels and sand bars developed. Deposition of river-borne sediment leads to infilling of the branch, while tidal flat embankment reduces the bankfull width and modifies the channel configuration, resulting in a profound decline in the sub-tidal flow partition rate. The North Branch then becomes tide-dominant with an occurrence of tidal bores and elongated sand ridges. Once tidal dominance is established, extensive tidal flat reclamation enhances the funnel-shaped planform, amplifying the incoming tides and initiating a positive feedback process that links tidal flat loss, sediment import, and channel aggradation. Overall, the shift in branch dominance is a combined result of a natural southeastward realignment of the deltaic distributary channels and extensive reclamation. One management option to mitigate channel aggradation is to stop the aggressive reclamation and allow tidal flats to build up, which might reduce the sediment import and eventually lead to a morphodynamic equilibrium in the longer term. Understanding the impact of tidal flat reclamation is informative for the management of similar tidal systems under strong human interference.

Accurate measurement of suspended sediment concentration (SSC) in highly turbid environments has been a problem due to optical or acoustic signal saturation and attenuation. The saturation returns a limited measurement range, and the attenuation raises an ambiguity problem that a low optical or acoustic output could mean a low or a high SSC. In this study, an integrated optic and acoustic (IOA) approach is proposed to (i) overcome the ambiguity problem; (ii) increase the measurement range to high SSC values; and (iii) obtain high-resolution SSC profiles. The IOA approach is a combination of Argus Suspension Meter (ASM), Optical Backscatter Sensor (OBS) and Acoustic Doppler Velocimeter (ADV). In this approach, the ASM-derived SSC is preferred because of its lowest relative error, followed by OBS and ADV. The ASM can produce high-resolution (1 cm interval) SSC profiles when it is not saturated (usually SSC < 9 g/L). When ASM is saturated, the SSC is recovered by OBS. Since the ambiguity problem is solved, the measurement range of OBS and ADV can be extended up to 300 g/L. The best way to use an ADV, however, is to have a rough estimation first and assist in the OBS conversion, because its estimates contain large uncertainty. To further mitigate the impact of sediment particle size on SSC retrieval, we suggest the usage of in-situ sediment samples for sensor calibration. The IOA approach was verified in the Yangtze Estuary which is a highly turbid system. Comparison of the IOA approach outputs against water sampling results demonstrates the reliability of the IOA approach with a relative error of 17–34%. The observed high SSCs were up to 63 g/L. The field data show that high SSCs were confined in the benthic layer (within 2 m above the bed) in the wet season under a high river discharge, whereas the suspension was better mixed throughout the water column in the dry season.

Tidal waves traveling into estuaries are modified by channel geometry and river flow. The damping effect of river flow on incident astronomical tides is well documented, whereas its impact on low‐frequency tides like MSf and Mm is poorly understood. In this contribution, we employ a numerical model to explore low‐frequency tidal behavior under varying river flow. MSf and Mm are locally generated by frictional mechanisms inside an estuary, and they are larger in amplitude far upstream in tidal rivers and persist landward of the point of tidal extinction. Increasing river flow nonlinearly modulates the longitudinal variations of MSf and Mm amplitudes. This is dynamically explained by flow‐enhanced asymmetry in subtidal friction over the spring‐neap (MSf) and perigee‐apogee (Mm) cycles, respectively. Estuaries act as frequency filters, where low‐frequency waves decay at a smaller rate and propagate more inland than high‐frequency waves. Strong inland penetration of low‐frequency tides informs compound flood management.

Tidal wave deformation and tidal asymmetry widely occur in tidal estuaries and lagoons. Tidal asymmetry has been intensively studied because of its controlling role on residual sediment transport and large‐scale morphological evolution. There are several methods available to characterize tidal asymmetry prompting the need for an overview of their applicability and shortcomings. In this work we provide a brief review and evaluation of two methods, namely, the harmonic method and the statistical method. The latter comprises several statistical measures that estimate the probability density function and various forms of skewness. We find that both the harmonic and statistical methods are effective and have complementary advantages. The harmonic method is applicable to predominantly semidiurnal or diurnal regimes, while the statistical methods can be used in mixed tidal regimes. Assisted by harmonic data, a modified skewness measure can isolate the contribution of different tidal interactions on net tidal asymmetry and also reveal its subtidal variations. The application of the skewness measure to nonstationary river tides reveals stronger tidal asymmetry during spring tides than neap tides, and the nonlinear effects of river discharges on tidal asymmetry in the upper and lower regions of long estuaries.