In this study, the CAT observation region was located at the DT station ( Figure 1 ). The locations of the observation area and the two CAT systems are shown in Figure 1B . the horizontal distance between the two CAT stations is 3,015 m and the angle between the NS line and the north riverbank is ~31°

The DT station is the first hydrometric station along the main channel of the YR, situated ~1,100 km downstream of the TGD and ~630 km upstream from the estuary (Cai et al., 2019; Mei et al., 2021). Additionally, the DT station is the most widely acknowledged location of the topmost boundary of the tide, and the discharge is not altered by the tide (Shi et al., 2018). In the middle–lower reaches of the YR, the water levels frequently exceeded the warning levels owing to the continuous heavy rainfall during the rainy season. Thus, monitoring water discharge using CAT at the DT station is crucial for flood management in the middle–lower reaches of the YR.

The YR is ~6,300 km long and the area of YRB is 1.8 million km². The total annual water flow through the YR is 961.6 billion m³, accounting for 36% of the total runoff in Chinese rivers (Yu et al., 2020). The world’s largest hydroelectric project, the TGD, is situated in the middle reaches of the YR, it measures 2,309.5 meters in length and 185 m in height. There is an artificial lake (Three Gorges Reservoir) formed upon the accomplishment of the TGD, covering 1,084 km² with a total reservoir capacity of 39.3 billion m³ (Wang et al., 2020).

Precipitation in the YRB showed distinct seasonal patterns from 2018 to 2021 ( Figure 2 ). Precipitation data were obtained from the fifth generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5) hourly data (https://cds.climate.copernicus.eu) for global climate and weather. Precipitation in the YRB is typically high from March to May, followed by the plum-rain season over the middle–lower river areas from June to early July (Dai, 2021) ( Figure 2B ). During summer, the entire river catchment may be covered by the rain belt from June to August ( Figure 2C ). The runoff of the YRB exhibits a high consistency with rainfall and progressively declines from southeast to northwest (Gao et al., 2021), with low rainfall from November to February ( Figure 2A ) and high rainfall from June to August (Dai, 2021) ( Figure 2C ).

Discharge measurements were conducted using CAT for ~2.5 years (July 2018–January 2021) at the DT hydrometric station (near station S). As shown in Figure 1B , two CAT systems were set on both north (N) and south (S) riverbanks, with a distance of 3,015 m between the two stations. The monitoring systems were placed on a floating barge, and the CAT transducers were suspended 2 m under water. The CAT systems were supplied with a clock from GPS receivers to maintain and guarantee simultaneous operations of the systems. During the observation period, the acoustic pulse was modulated by an 11-order M sequence, and acoustic pulses were simultaneously transmitted from both transducers every 5 min with a central frequency of 9 kHz.

The travel-time method was used in CAT, assuming the same reciprocal travel path between two stations; therefore, the travel time of the acoustic signals from site N to site S (t_NS ) and site S to site N (t_SN ) can be represented as

where L represents the oblique distance between the two stations, c_CAT and u_CAT represent the section-averaged sound speed and velocity, respectively.

The discharge obtained by CAT (Q_CAT ) can be written as:

where θ is the flow angle, and A is the cross-sectional area. A was estimated using the mean water depth and mean distance, since two stations were fixed, and the error of A was mostly related to the water depth error. As Zhu et al. (2021) showed that an error of 0.19 m in mean water depth would induce an ~1% (~329 m²) error in the estimation of mean area.

During the CAT observation period, many moving-boat ADCP (600 kHz Rio Grande Workhorse, California, USA) observations were conducted to collect reference discharge data at the DT station. For each campaign, the ADCP was arranged under water (0.5 m), a differential GPS receiver was fixed above the ADCP to record the real-time position. During each campaign, ADCP sampling was conducted each 2 s using the ADCP bottom tracking mode. The bin number was set at 70 and each bin size was 0.5 m and the unmeasurable surface depth was 0.25 m. The accuracy of velocity was ± 0.25% of the measured velocity with a resolution of 0.1 cm/s.

Owing to the limitations of the moving-boat ADCP method, there are a blank area and the underwater depth of the ADCP in the surface layer and the near-bed flow velocity could not be measured by ADCP. Hence, water discharge in the surface and bottom layers and areas adjoining riverbanks were not measured. Generally, the discharge in these unmeasured areas can be ignored in small river systems; however, in large river systems such as the YR, estimation of the water discharge in these unmeasured areas is necessary. Hence, in this study, the velocities in the surface and near-bed layers were estimated using linear extrapolation of data of the nearest bin, that is, the surface velocity was estimated from data of the first bin and the bottom velocity was estimated from data of the deepest bin. The boat is difficult to start from the river bank, there will be a certain distance from the bank. The velocity in areas close to river banks was derived through extrapolation, assuming that the near-bank water column progressively became shallow with a steady water slope until it extended to the river bank (Gordon, 1989). Finally, the discharge of each ADCP transect was estimated via integration.

Missing ADCP data in the surface layer accounted for the largest fraction, with a range of 543 to 3,863 m³/s. Missing data in the bottom layer varied from 650 to 3,389 m³/s, whereas missing data in the left and right areas were negligible with their averages accounting for 0.2 and 0.3% of the total discharge, respectively. In total, 140 discharge estimates (Q_ADCP ) were collected through the moving-boat ADCP during the CAT observation period. The Q_ADCP ranged from 11,969 to 83,055 m³/s.

A HOBO water level logger with a pressure sensor (U20L-01) was attached at station S near the riverbed to measure the water depth (H) every 10 min with a precision of ± 0.1 cm and a typical error of ± 0.1% of the measured range of 1.0 cm. The collected water depth was further utilized to estimate the cross-sectional area and build an RC.

An RC relationship (Kawanisi et al., 2016) was established between the moving-boat ADCP discharges and water depths at station S as follows:

where c₁ and c₂ are the calibration constants and they are determined using the least-squares method.

Understanding the response of runoff to precipitation events and anthropogenic activities is essential for hydrological applications and water resource management (Wang et al., 2022). Baseflow is an essential component of runoff in hydrological basins (Dai et al., 2010), whereas stormflow is usually at a higher volume over a short period following major rainfall events. Estimating baseflow and stormflow can provide important references for the sustainability of water resources in the YRB. Hence, the HydRun toolbox (Tang and Carey, 2017), which can automatically distinguish baseflow and stormflow based on the recursive digital filter technique, was utilized in this work. HydRun can also match stormflow with their accompanying rainfall events using a flexible time step. Further details are available in Tang and Carey (2017).

The grouped frequency distribution is usually recommended when a large number of continuous variables must be evaluated (Mei et al., 2015), and it first groups parameters into different intervals based on their values, and then, gives each class a frequency. Thus, the relative frequency (RF) is determined by

where N_i represents the number that falls in a specific class and N is the amount of data.

Grouped frequency analysis was applied at the DT station (Q_CAT ) to determine the occurrence probabilities of water discharge and TGD outflow at different intervals.

Figure 3A shows the relationship between water depth (H) at station S and moving-boat ADCP discharge (Q_ADCP ). The power function in Eq. 4 is fitted to the relation to establish the RC, the RC (red line) and the 95% confidence intervals (gray lines) are presented in Figure 3A . In addition, a linear relationship (R² = 0.997) was established between the moving-boat ADCP-determined cross-sectional area and the water depth (H) at station S ( Figure 3B ). This empirical relationship was used to estimate the time series of the cross-sectional area.

Kawanisi et al. (2013) stated that the incorrect resolve of angle (θ) between the transmission line and the main flow direction might cause a considerable discharge estimation error and revealed that variations of ±1° could induce relative discharge errors of −5.4 and 5.5%. Hence, this study utilized an index velocity for u_CAT to avoid estimating flow direction. The index velocity ratings are shown in Figure 4 . The index velocity curve for CAT was resolved using linear regression, the measured section-averaged velocity u_ADCP = Q_ADCP /A_ADCP , with Q_ADCP representing the moving-boat ADCP discharge and A_ADCP representing the sectional area along the ADCP transect. Finally, the streamflow of CAT can be computed by:

CAT- and RC-derived discharges are shown in Figure 5A . Discharges of the YR ranged from 11,059 to 82,206 m³/s from July 2018 to January 2021 and displayed an evident seasonal variation. The discharge exhibits high consistency with the rainfall pattern, with fluctuations of high discharge and precipitation in summer and low discharge and precipitation in winter ( Figure 5A ). CAT shows a good consistency with the moving-boat ADCP results. The comparison between Q_ADCP and Q_CAT showed a good correlation with R² = 0.999 and RMSE = 891.9 m³/s ( Figure 6 ). Compared with previous studies (Zhu et al., 2021), the results of this study are higher by approximately 1%, which is mainly due to the index method and the consideration of the flow angle.

Figure 5B shows the outflow, water storage, and water level in the TGD. TGD data were collected from the National Rain and Water Discharge website (http://xxfb.mwr.cn/index.html); however, only data with 6-h intervals during the wet season (June to September) were collected. As shown in Figure 5B , during the observation period, the TGD outflow varied from 7,900 to 49,400 m³/s. Since 2010, the water level of the Three Gorges Reservoir has been planned to control downstream floods and minimize downstream sedimentation. Generally, the release of water from the TGD is scheduled to maintain a flood-restricted level of 145 m during the flood season ( Figure 5B ).

Significantly, a detail example of Q_ADCP , Q_CAT , and Q_RC presents in Appendix, during the period of water release from the TGD (July–September) and during the period of higher precipitation, the discrepancy between Q_RC and Q_ADCP were obvious, whereas Q_CAT continued to match well with the results of Q_ADCP ( Figure 5 ). Specifically, during the period of the TGD outflow, the uncertainty of Q_RC compared to Q_ADCP was within ± 20%, whereas the uncertainty was within ± 7% of Q_CAT compared to Q_ADCP . This revealed that the dam outflow or huge rainfall events induced dramatic fluctuations in the water level at the DT station, indicating that the uncertainties and errors obtained by RC were too large to be ignored, especially under unsteady flow conditions, and demonstrated the advantages of using CAT in large river channels.

Baseflow and stormflow were estimated from Q_RC and Q_CAT , respectively. Although both revealed similar fluctuations, the stormflow from the Q_RC was smoother, and it was difficult to capture the short- and high-frequency variations induced by rainfall events. Baseflow and stormflow obtained from Q_CAT at the DT station during the observation period are shown in Figure 7 . The baseflow varied from 11,059 to 62,231 m³/s with a mean of 25,485 m³/s. The stormflow, which mostly resulted from precipitation, varied from 0 to 34,822 m³/s with a mean of 5,918.1 m³/s. The mean proportions of baseflow and stormflow were 81.1 and 18.8%, respectively. The ratios of baseflow and stormflow in the flood and dry seasons were 80.9 and 81.7% and 19.1 and 18.3%, respectively. These values are similar to previous studies; for example, Dai et al. (2010) investigated the proportion of baseflow at several stations along the YR and revealed that its mean proportion at the DT station was ~82% and in the flood and dry seasons, it was ~81 and ~83%, respectively.

Grouped frequency analysis was applied to the TGD outflow, and the class interval for discharge was set to 10,000 m³/s in this study. The contribution of each month during the TGD outflow period is shown in Figure 8 . At the DT station, during the TGD dam outflow period, the water discharge is in the range of 30,000 to 60,000 m³/s, accounting for 70% of total intervals ( Figure 8A ). The occurrence probabilities of large flood events exhibited declining trends. The proportion of extreme discharge (> 60,000 m³/s) reduced from 6.9 to 0.7% ( Figure 8A ). In addition, the grouped distribution of the TGD outflow and the contributions of the TGD outflow to the grouped discharge at the DT station (Q_DT ) are also presented in Figures 8B, C . The TGD outflow occurred mainly in the range of 20,000 to 30,000 m³/s with a proportion of 43.5–77.6% over the 2.5-year period of observation ( Figure 8B ). For the class Q_DT > 30,000 m³/s, Q_DT increased from 30,000 to 80,000 m³/s and the proportion of TGD outflow gradually decreased from 54.2 to 43.5% in June, from 77.6 to 24.7% in July, and from 73.6 to 51.5% in August ( Figures 8B, C ). Taken together, the TGD organizes downstream runoff by boosting the proportion of normal streamflow and lowering the proportion of exceptional streamflow. Consequently, the management of the TGD forces the distribution of downstream runoff to become more centralized.

The TGD has been in operation since 2003. Previous studies have stated that the TGD has significantly flattened river discharge hydrographs, such as by increasing the discharge of 500–2,000 m³/s in the dry season and decreasing the annual flood peak flow by up to 20,000 m³/s (Guo et al., 2015). Especially, the regulation and management of the TGD have considerably eased river flow processes in the middle–lower reaches of the YR (Cai et al., 2019). Additionally, Mei et al. (2015) reported that from low- to high-runoff situations, obvious declining trends have led to low- and normal-runoff situations from 2003. Instead, the high-runoff situation presented uniform states without noticeable gradient patterns. Consequently, the role of the TGD on downstream hydrological processes is substantially more significant in the dry season than those in the flood season (Chen et al., 2016).

Seasonal areal precipitation characteristics during the observation period are shown in Figure 2 . Along the YR, during June–July–August (JJA), two maximum precipitation areas occurred upstream of the TGD and near the DT, respectively; therefore, the strong flood processes at the DT station during summer can be partially clarified by areal precipitation, but additional factors might affect changes in discharge downstream of the YR (such as the TGD effect). As shown in Figure 7 , compared with the baseflow, the stormflow, which mainly results from precipitation, accounted for 0 to 47.7% with a mean of 18.8%. Mei et al. (2015) argued that the hydrological processes of the YR were largely structured by the TGD and that rainfall events had little force on the discharge.

To enrich the cognition of the role of rainfall on the Q_DT of the YR, we followed Liang, 2014; Liang, 2015) to evaluate the cause–effect relationship between precipitation and discharge at the DT station (Q_DT ). The information flow (IF) in the natural unit of information (nat) per unit time (nat/h) during the CAT observation period was estimated. Causality was computed as the time rate of IF from one time series to another. When only two time series, that is, X₁ (Q_DT ) and X₂ (T_rain ) are considered, a model to fulfill the IF evaluation was given by Liang (2014), and the rate of IF from T_rain to Q_DT can be written as

where C_ij (i, j = 1 (i.e., Q), 2 (i.e., rain)) denotes the covariance between T_rain and Q_DT , C_i,dj represents the covariance between X_i and X j ' , and X j ' is the difference approximation of dX_j /dt using the Euler forward scheme.

IF_rain→Q represents the rate of IF from T_rain to Q_DT , which can be zero or nonzero. If IF_rain→Q is zero, T_rain does not cause Q_DT ; if the value is nonzero, it is causative. When there is a causal relationship, two cases can be discerned as stated by the sign of the IF: the positive value suggests that T_rain works to cause Q_DT more uncertain, whereas the negative value denotes that T_rain would stabilize Q_DT . Additionally, IF_rain→Q can be normalized to assess the importance of the influence of T_rain on Q_DT relative to other processes (Liang, 2015).

One-way causality analysis was used to assess the sensitivity of discharge at the DT station to the regions and changes of precipitation in the YRB. Positive IF ranging from 0 to 0.05 nat/h ( Figure 9A ) occurred in the upper and lower areas of the YRB, with the highest values around the DT station. The computed relative IF rates were up to ~40% near the DT station ( Figure 9B ). These demonstrate that during summer the flood processes at the DT station are partially caused by areal precipitation in the downstream reaches of the YR. A positive IF in the upstream can be interpreted as runoff caused by precipitation gradually entering the baseflow and eventually affecting the streamflow at the DT station. On the contrary, the non-positive IF exhibited in the middle areas of the YRB revealed the role of the TGD, which means that the runoff induced by the rainfall events in the middle areas would be controlled by the TGD, and the TGD would stabilize the downstream discharge. Mei et al. (2015) investigated and compared the characteristics of monthly areal precipitation during the pre-TGD and post-TGD periods and found that precipitation showed a minor decreasing trend since 2003 and stated that this decreasing trend was not adequately strong to support the vast changes in runoff along the YR, proving that TGD regulation significantly disturbed the hydrology of the YR.

In summary, we investigated the contributions of the TGD (human activities) and rainfall (natural factor) on the discharge and revealed the relationships between the river flow, rainfall, and dam outflow ( Figures 8 , 9 ). The YR is the China’s largest river and covers a vast river basin, natural factors (e.g., Typhoon, rainfall) are easy to induce flood events and enhance flood risk to human activities. Generally, variations of discharge are consistent with those of precipitation in natural hydrological conditions; nevertheless, the low and high flows are strongly altered by the TGD. Therefore, in this study, a quantitative understanding of the contributions of rainfall and the TGD are helpful for the development of effective flood control strategies.

The DT station is a widely recognized site for the tidal limit position; however, the geographical and temporal distributions of runoff in the YRB has changed significantly over the past decades owning to many large-scale water conservation projects along its course. Some studies suggested that the location of the recent tidal limit in the YR fluctuates from Jiujiang (~220 km upstream from the DT station) to DT. During the dry season, the upper limit of the tide is near Jiujiang, whereas during the flood season, the lowest bound of the tidal zone is near DT (Shi et al., 2018).

The continuous wavelet transform (CWT) method was used to investigate the characteristics of tidal species and the temporal evolution of tidal frequency spectra at the DT station (Sassi and Hoitink, 2013). CWT analysis can determine different tidal species, for example, the semi-diurnal (D₂ ) tidal species, but specific tidal components (e.g., M₂ ) cannot be resolved (Guo et al., 2015). More information on the CWT method and settings used to determine the specific tidal species are described in Guo et al. (2015). Here, the CWT method was applied to data on water depth at station S, velocity obtained by CAT (u_CAT), and discharge at the DT station (Q_CAT ) to decompose the time series data into the D2 tidal species because the semi-diurnal tide is evident along the YR.

At the DT station, the tidal signal was very weak, but the seasonal signals, which were driven by fluctuating river discharges, remained noteworthy ( Figure 10 ). The temporal fluctuations in the D₂ amplitudes are shown in Figure 10A . Evidently, D₂ showed a clear seasonal fluctuation of high amplitudes in winter and low amplitudes in summer. A high river discharge improves tidal amplitudes by boosting the nonlinear effect and promoting the transfer of astronomical tidal energy to shallow-water tides, which is the primary cause of lower amplitudes during the wet season (Godin, 1985). In addition, the attenuation of tidal amplitudes is related to frequency; generally, lower-frequency tidal components damp more slowly than higher-frequency tidal components (Godin, 1985). The amplitudes of water level in the D₂ bands present an evident significant seasonal signal, with values fluctuating from 0 to 0.08 m, respectively. In the flood and dry seasons, D₂ contributed 0.30% and 1.16%, respectively, to the water level at the DT station ( Figure 10A ). The tidal velocity in the D₂ band also presented a significant seasonal signal with a maximum value of 0.086 m/s, and the mean proportions of the velocity during the flood and dry seasons were 2.90% and 6.27%, respectively ( Figure 10B ). Both were directly driven by fluctuating river discharges.

Significant fortnightly tidal signals were detected at the DT station simultaneously ( Figure 10 ). A similar phenomenon was exhibited by Guo et al. (2015), who stated that this clear fortnightly signal was mostly generated inside the estuary owing to tidal interactions rather than river flow or oceanic tides. As oceanic tides and river flow have limited energy at the fortnightly frequency, tidal interactions are central sources of tidal semi-monthly or monthly changes. For example, the interaction between M₂ and S₂ causes fortnightly (spring and neap) variations. In such a long river tidal system, this result strongly suggests the spatial evolution of tidal dynamics caused by mixed tidal and fluvial processes.

The CWT analysis of the discharge showed fluctuations in the D₂ bands ( Figures 10C, D ) that were different from the amplitude and velocity ( Figures 10A, B ), which mostly resulted from the tidal damping processes. The high (low) discharges in summer (winter) lead to a stronger (weaker) tidal damping process and generate a low (high) tidal discharge in summer (winter). The discharge in D₂ bands varied from 19.4 to 502.9 m³/s, respectively, accounting for 0.11–1.11% of the total discharge. The velocity resolution (u_r ) of CAT is as follows:

where f means the frequency and L and C are the distances between two stations and sound speed, respectively. The velocity resolution considered in this study is 0.02 m/s, the precision of the water level is 0.5 cm, assuming the distance (~3,015 m) between two stations caused by the tidal wave was negligible, the theoretical minimum discharge estimated using the velocity-area method is ~0.3 m³/s, and thus, the CWT results are within the observation resolution and are reliable.

Results of CWT demonstrate that the effects of tidal waves on river transport were insignificant at the DT station, probably because the tidal wave propagated to the DT station; however, owing to the river discharge–controlled systems, the direction and velocity of flow did not change significantly, and the changes in water level and cross-sectional area caused by the tidal wave were negligible. In fact, tides assert a barrier impact on the discharge of the YR, which can be attributed mainly to the Stokes flux. Nevertheless, in the middle–lower reaches of the YR (i.e., at the DT station), river flow significantly controls river and tidal dynamics (Guo et al., 2015).

Taken together, the discharge regulated by the TGD takes a significant influence on the tidal propagation process along the YR; that is, a decrease in discharge can cause the tidal wave to move upstream and lead to an increase in tidal amplitude, even if the TGD is situated ~1,800 km upstream from the mouth of the YR. Hence, more attention should be paid to this man-made effect on tidal processes and the river–tide interactions since it would be easily overlooked as the TGD is sited far away from the river mouth. Additionally, understanding tidal wave effects in the middle–lower reaches of the YR is of significant social value for tidal prediction and water management in channels.

One objective of this study was to highlight the performance of CAT in continuously monitoring large river discharges in YR. The main drawback of traditional instruments (e.g., ADCP) is the insufficient number of velocity sample points in the cross-section for estimating cross-sectional average velocity. Unlike the traditional hydroacoustic systems, the CAT enables continuous and real-time observations of the depth- and range-averaged velocity with a transect, without disturbing shipping traffic in YR. The method of CAT in real-time could help in the increased ability to monitor the flood events and provide reference data to flood risk management.

Although some of our findings are preliminary, our results are encouraging. The CAT is capable of capturing discharge in large river basin; therefore, future studies should consider longer periods to determine the variations of floods in the YR and the role of the TGD. In addition, a preliminary result of discharge induced by tidal wave was revealed here, however, the YR has a vast area affected by tides, monitoring the tidal discharge in different sections of the YR is useful to study the river-tidal interactions in the YR.