Seasonal and Interannual Variations in M₂ Tidal Current in Offshore Guangdong

Abstract

Understanding tidal changes and their potential forcing mechanisms enables a better assessment of non-stationary tidal effects for projecting extreme sea levels and nuisance flooding. In this study, we investigate the seasonal and interannual changes in the M₂ tidal current off the Guangdong coast using currents observed via two different types of high-frequency radar from 2019 to 2022. The results indicate significant seasonal changes in the M₂ tidal current in the coastal areas of the Pearl River Estuary and Cape Maqijiao, with the largest relative deviations occurring in summer, reaching 10–20%. Observations of thermohaline profiles from 2006 to 2007 and 1978 to 1988 show that runoff in summer can reach these two areas and change the stratification of seawater, in turn affecting tidal currents. A comparative analysis of the two areas suggests that the greater the runoff, the wider the area where the M₂ tidal current experiences significant seasonal variation. No significant interannual changes in the M₂ tidal current were detected offshore of Guangdong during the observation period. However, an abrupt change occurred in the coastal area of Shantou in 2021, primarily caused by the distortion of the antenna patterns.

1. Introduction

Coastal tide-gauge records and satellite radar altimetry data collected over the past century have revealed that ocean tides exhibit unexpected seasonal, interannual, and decadal changes [1,2,3]. The effects of variations in astronomical forcing are small and can be ruled out [4,5]. Previous studies have found that the evolution of ocean tides is related to changes in geometry [6,7], stratification [4,8], mean sea-level rise [2,9], and internal tides [10,11]. River runoff significantly influences stratification and circulation in coastal regions, making these areas prone to large temporal changes in tides [4,12,13].

Owing to their low spatial resolution, it is difficult for traditional observation methods to capture the fine spatial structures of tidal temporal variability caused by ocean processes, such as stratification and mixing, especially in estuarine and bay areas where offshore ocean dynamic processes are extremely complex [12,13]. High-frequency ground wave radar (HFR) provides real-time, continuous, all-weather monitoring of ocean surface currents with high spatial resolution across expansive areas, making it a valuable tool for addressing this problem. Thus, HFR observations have been widely used in research on the main characteristics of coastal tides [14,15,16].

Previous studies based on observational data and numerical models have mainly discussed the mean characteristics of tides, tidal wave movement, and tidal wave energy balance in the South China Sea (SCS) [17,18,19,20,21,22,23,24]; there has been limited research on the temporal variations in tides in the region. Using 17 tide gauge data from 1954 to 2012, Feng et al. (2015) [25] analyzed the long-term variations in the main tidal constituents along the coasts of China and adjacent seas, and concluded that the M₂ amplitude of the Chinese coasts has been increasing, with higher rates in the Bohai and Yellow Seas and lower rates in the SCS. Pan et al. (2021) [26] extracted the long-term trends in the amplitudes of four major constituents using tide gauge observations and satellite altimeter data. The results show that the tidal amplitudes are stable in most areas of the SCS but show significant trends in a few areas. Using the mooring current profile observations from September 2011 to May 2013 in the northern SCS, Zhao et al. (2019) [27] found that the baroclinic diurnal tide exhibits significant seasonal characteristics and becomes the strongest in summer. However, little is known about the seasonal and interannual changes in tidal currents along the Guangdong coast, owing to the lack of high-resolution observations. In recent years, the development of HFRs along the Guangdong coastal region has provided continuous high-resolution surface current observations that facilitate further investigation of the spatial and temporal changes in tides.

The Pearl and Hanjiang Rivers are the two largest rivers along the Guangdong coast, discharging 3.138 × 10¹¹ m³ and 0.246 × 10¹¹ m³ of fresh water per year into the northern SCS, respectively (China River Sediment Bulletin). Influenced by the SCS monsoon, the runoff from the Pearl and Hanjiang Rivers exhibits significant seasonal variability. During the flood season, the runoff accounts for approximately 80% of the total annual runoff, with the majority occurring in summer [28]. The spread of the Pearl River Plume (PRP) presents distinct seasonal and interannual variability because of the seasonal and interannual variations in the SCS monsoon and river runoff [29,30,31]. PRP significantly influences water properties and changes the distribution of stratification [31,32], which might affect the temporal variations in tidal currents in the coastal region of Guangdong.

Therefore, this study focuses on the seasonal and interannual changes in the M₂ tidal current off the Guangdong coast using HFR observations in the coastal areas of the Pearl River Estuary and Shantou. The remainder of this paper unfolds as follows. Section 2 presents the materials and methods. Seasonal and interannual changes of M₂ tidal currents are discussed in Section 3. A discussion and summary are presented in Section 4 and Section 5, respectively.

2. Materials and Methods

2.1. Materials

The HFR detects ocean surface currents based on the Bragg scattering and Doppler shift [15]. In recent years, four HFRs have been deployed to observe the surface currents at Nanao (NAND), Huilai (HULA), Wanshan (WASH), and Shangchuan (SHCH) in Guangdong Province, China (Figure 1). The radar type deployed at Nanao and Huilai was OSMAR-S (Beijing Highlander Digital Technology Co., Ltd., Beijing, China), with temporal and spatial resolutions of 20 min and 3.3 km, respectively. The radar type for Wanshan and Shangchuan was OSMAR-071G (Hubei Zhongnan Pengli Marine Exploration System Engineering Co., Ltd., Yichang, China), with a temporal resolution of 10 min and a spatial resolution of 5 km. The accuracy and reliability of the current products extracted using these two radar systems were determined through a series of experiments [16,33,34,35,36]. The HFR observations for 2019–2022 were analyzed in the study.

During the period of 23 October to 25 October 2019, an intercomparison of the currents observed by OSMAR-S and the moored acoustic Doppler current profiler (ADCP, Teledyne RD Instruments, San Diego, the United States) was performed; an intercomparison between OSMAR-071G and ADCP was conducted from 12 November to 14 November 2019.

The hourly currents observed by buoy MF14005 (Figure 1) in 2018 were obtained from the South China Sea Area and Island Center, Ministry of Natural Resources.

Four conductivity–temperature–depth (CTD) profiler cruises were conducted in the coastal area of Shantou: the 2006 summer cruise (14 July–24 August 2006), the 2006 winter cruise (20 December 2006–24 January 2007), the 2007 spring cruise (1 April–25 April 2007), and the 2007 autumn cruise (19 October–5 December 2007). Continuous hydrological surveys were conducted during 1978–1988 in the coastal areas of the Pearl River Estuary. One of the CTD stations was located within the core area of the HFR Wanshan-Shangchuan (113.5°E, 21.5°N). Surveys were conducted once a month during 1978–1981, and once every two months during 1982–1988.

In July 2022, the antenna patterns of the Nanao and Huilai radars were measured using a portable antenna pattern-measuring device based on an unmanned aerial vehicle platform.

2.2. Methods

Harmonic analysis of the ocean current data was conducted using the MATLAB program package T_Tide (v1.4) [37]. A series of observations $y\left(t\right)$ with a temporal interval ${∆}_t$ and several optional parameters were passed to T_Tide. The tidal response model is constructed as follows:

$$x\left(t\right)=b_0+b_{1}t+{\sum }_{k=1}^N{\alpha }_k{e}^{i{\sigma }_{k}t}+{\alpha }_{-k}{e}^{-i{\sigma }_{k}t}$$

(1)

where $N$ is the number of tidal constituents, ${\sigma }_k$ is the known frequency, and ${\alpha }_k$ is the unknown complex amplitude. T_Tide automatically identified 35 tidal constituents. The first two terms describe the possible offset and linear drift. The liner drift was not considered in this study.

The analysis result is a pair of complex values $\left\{{\alpha }_k,{\alpha }_{-k}\right\}$ for each tidal component, which were converted into four parameters:

$$L_k=\left|{\alpha }_k\right|+\left|{\alpha }_{-k}\right|$$

(2)

$$l_k=\left|{\alpha }_k\right|-\left|{\alpha }_{-k}\right|$$

(3)

$${\theta }_k={\displaystyle \frac{ang\left({\alpha }_k\right)+ang\left({\alpha }_{-k}\right)}{2}}mod 180$$

(4)

$$g_k=v_k-ang\left({\alpha }_k\right)+{\theta }_k$$

(5)

For horizontal current, $L_k$, $l_k$, ${\theta }_k$, and $g_k$ are the semi-major axis, semi-minor axis, the inclination of the northern semi-major axis, and the Greenwich phase, respectively. $l_k$ >(<) 0 represents the counterclockwise (clockwise) rotation of tidal current.

To describe the differences in the tidal currents from different periods in the same location, the relative deviation of the tidal currents is defined as follows:

$$D={\displaystyle \frac{\sqrt{{\sum }_{N=1}^{360}{\left({Mag1}_N-{Mag2}_N\right)}^2/360}}{{Major}_1}}\mathrm{ }\times 100$$

(6)

where ${Mag1}_N$ and ${Mag2}_N$ are the amplitudes of the two tidal ellipses in direction $N$, and ${Major}_1$ is the semi-major axis. The unit is %.

3. Results

3.1. Comparison of Tidal Current

Observations from the ADCP, buoy MF14005, and HFR Nanao-Huilai were used to analyze the M₂ tidal current characteristics in the coastal areas of Shantou (

Table 1. Tidal ellipses for M₂ tidal currents observed by ADCP, buoy MF14005, and HFR Nanao-Huilai.

Observation Instrument	Period	M2
		Semi-Major (m/s)	Semi-Minor (m/s)	Phase (°)
ADCP 1	23 October 2019–25 October 2019	0.334	0.036	278.0
OSMAR-S 2	1 January 2019–31 December 2019	0.395	0.019	277.7
OSMAR-S 2	1 January 2020–31 December 2020	0.379	0.028	279.0
Buoy	1 January 2018–31 December 2018	0.286	0.045	273.4

¹ ADCP: acoustic Doppler current profiler; ² OSMAR-S: high-frequency ground wave radar.

). Harmonic analysis of the observations showed that the coastal areas of Shantou belong to regular semi-diurnal tidal current, and the M₂ tidal current dominates the overall tidal current. The maximum velocity observed by the ADCP was 0.872 m/s, and the M₂ tidal current accounted for approximately 40% of the total amplitude. Based on the harmonic analysis of the ADCP current, the M₂ tidal current had a semi-major axis of 0.334 m/s, a semi-minor axis of 0.036 m/s, and a phase of 278.0°. For buoy MF14005, the M₂ tidal current had a semi-major axis of 0.286 m/s, a semi-minor axis of 0.045 m/s, and a phase of 273.4°. Based on the harmonic analysis of the HFR current during 2019–2020, the M₂ tidal current had a semi-major axis of 0.379–0.395 m/s, a semi-minor axis of 0.019–0.028 m/s, and a phase of 277.7–279.0°. The M₂ tidal current observed by the HFR is consistent with that obtained from the ADCP and buoy and is consistent with a previous study [38].

The characteristics of the M₂ tidal current in the coastal areas of the Pearl River Estuary were analyzed using ADCP and HFR Wanshan-Shangchuan observations (

Table 2. Tidal ellipses of M₂ tidal currents observed by ADCP and HFR Wanshan-Shangchuan.

Observation Instrument	Period	M2
		Semi-Major (m/s)	Semi-Minor (m/s)	Phase (°)
ADCP 1	12 November 2019–14 November 2019	0.169	0.012	139.2
OSMAR-071G 2	1 January 2019–31 December 2019	0.107	0.012	104.7
OSMAR-071G 2	1 January 2020–31 December 2020	0.111	0.012	142.2
OSMAR-071G 2	1 January 2021–31 December 2021	0.105	0.009	141.7
OSMAR-071G 2	1 January 2022–31 December 2022	0.110	0.010	139.7

¹ ADCP: acoustic Doppler current profiler; ² OSMAR-071G: high-frequency ground wave radar.

). The harmonic analysis of the observations showed that the coastal areas of the Pearl River Estuary belong to regular semi-diurnal tidal current, with the M₂ tidal current being the dominant component. The semi-major axis of the M₂ tidal current observed by the ADCP was slightly larger than that obtained by the HFR, while the semi-minor axis and phase calculated from both ADCP and HFR were similar.

A comparison between HFR, ADCP, and the buoy showed that the tidal current observed by HFR was accurate and reliable and that the HFR data were suitable for further applications. The seasonal and interannual variations in tidal currents offshore of Guangdong were analyzed using the M₂ tidal current because it was the most important tidal component in this area.

3.2. Seasonal Variations in M₂ Tidal Current

The M₂ tidal currents in the coastal areas of the Pearl River Estuary were obtained by conducting a harmonic analysis of the ocean current data for all four seasons of 2021, and the seasonal variations in the M₂ tidal current were analyzed (Figure 2). Clear differences were observed in M₂ tidal currents at the edges of the radar observation region, which may be due to the poor radar echo signal in these areas. To reduce the influence of currents in the edge area, only the data from the core area observed by HFR were used in subsequent analyses for the coastal areas of the Pearl River Estuary. In 2021, the M₂ tidal current in the coastal area of the Pearl River Estuary showed a northwest–southeast direction (Figure 2a), which is consistent with previous research results [16,38]. Although the major and minor axis of M₂ tidal currents in summer and autumn were almost identical to those of the full year of 2021, the inclination was significantly deflected in summer, followed by autumn. The tidal ellipses for M₂ tidal currents in spring and winter were almost identical to those of the full year of 2021. This indicates that the M₂ tidal current off the Pearl River Estuary shows significant seasonal change, with the largest differences of M₂ tidal currents in summer, followed by autumn. The comparison results for the other years showed similar patterns to those obtained for 2021.

Here, we assessed whether the relative deviation of the M₂ tidal currents was suitable for analyzing the differences in the tidal currents. The regional average relative deviations for spring, summer, autumn, and winter in 2021 were 5.2%, 14.3%, 11.2%, and 7.0%, respectively, while the maximum relative deviations were 8.7%, 20.3%, 13.6%, and 8.5%, respectively. The relative deviation of the M₂ tidal current in the coastal areas of the Pearl River Estuary was the highest in summer, followed by autumn. The relative deviations in spring and winter were minimal. These changes in the relative deviation corresponded to the differences in the tidal ellipses of the M₂ tidal currents. This implies that the relative deviation of the M₂ tidal current can quantitatively describe significant changes in tidal currents. Thus, this approach was used in the present study.

Salinity data from the upper seawater layer showed that freshwater from the Pearl River can spread to the coastal areas of the Pearl River Estuary during summer and autumn, significantly reducing seawater salinity (Figure 3a). The impact of Pearl River freshwater on seawater was the greatest during summer, and salinity levels below 32 PSU (the outer boundary of the PRP [30,31]) were observed from 1978 to 1988. The average salinity in summer during this period was 31.95 PSU. During autumn, the impact was relatively lower, with an average salinity of 33.62 PSU, which was significantly lower than that observed during spring (34.12 PSU) and winter (34.07 PSU). The vertical standard deviation of salinity can effectively represent the strength of stratification: the larger the standard deviation, the stronger the stratification. The standard deviations of salinity during summer and autumn were 1.24 and 0.14 PSU, respectively. The standard deviation of salinity during summer was significantly greater than that during autumn, indicating stronger stratification during summer than during autumn (Figure 3b). The seasonal variation of the stratification in the continental shelf affects the vertical pro-file of the viscosity coefficient, which affects the velocity profile, ultimately leading to the seasonal variation of the M2 tidal current [4]. In summer, the Pearl River experiences its highest runoff, and freshwater spreads into the coastal areas of the Pearl River Estuary, strengthening the stratification of seawater. Consequently, the relative deviation of the M₂ tidal current in this area reaches 20.3% during summer. In autumn, it is still affected by freshwater; however, the stratification weakens because of the reduced Pearl River runoff, and the relative deviation reaches only 13.6%.

Next, the M₂ tidal currents in the coastal areas of Shantou were analyzed for the four seasons of 2019 (Figure 4). The major axis of the M₂ tidal current in 2019 showed a northeast–southwest direction, parallel to the coastline. Near Cape Maqijiao, there were some subtle changes in the inclination of the M₂ tidal currents across the four seasons. At individual points near Cape Maqijiao, the M₂ current rotated counterclockwise in autumn and winter, while the M₂ currents in other areas rotated clockwise. The corresponding relative deviations in all four seasons were significantly larger near Cape Maqijiao, reaching 15–20%. The area with significant relative deviation was larger in summer, and the maximum relative deviation in summer was the largest, reaching 22.1%. The maximum relative deviations in spring, autumn, and winter were 20.5%, 20.7%, and 20.7%, respectively. Except for the area near Cape Maqijiao, the tidal ellipses for M₂ tidal currents in four seasons were basically consistent with those in the whole year of 2019. The corresponding relative deviations were also small, with average values of 4.3%, 7.8%, 5.9%, and 7.8% for spring, summer, autumn, and winter, respectively. Compared with the overall tidal current data from 2019, the relative deviation near Cape Maqijiao was the highest in summer. This might be due to poor radar echo signals in the edge areas. However, such deviations were negligible in other edge areas; therefore, this explanation was ruled out. The comparison results for the four seasons in other years were similar to those in 2019.

The region near Cape Maqijiao is located at the outlet of the Hanjiang River. In spring, autumn, and winter, the freshwater from the Hanjiang River is confined to the northeastern side of Cape Maqijiao, and in summer, it spreads outward significantly, resulting in the presence of freshwater on the southwestern side of Cape Maqijiao (Figure 5). Owing to runoff, the stratification in the waters near Cape Maqijiao is the strongest in summer, followed by spring (Figure 6). The runoff of the Hanjiang River is the highest in summer, and freshwater spreads into the coastal areas around Cape Maqijiao, strengthening the stratification and ultimately resulting in the maximum relative deviation of the M₂ tidal current. Although freshwater runoff is small and limited to the northeastern side of Cape Maqijiao in spring, autumn, and winter, the relative deviation in the waters near Cape Maqijiao still reaches 15–20%. This may be due to the sharp topography of Cape Maqijiao, which affects the propagation of tides; however, further verification is required.

The relative deviation of the M₂ tidal current was the highest in summer in both the coastal areas of both the Pearl River Estuary and Cape Maqijao, while the area with significant seasonal changes in the M₂ tidal current was larger in the coastal areas of the Pearl River Estuary. According to the China River Sediment Bulletin, the annual runoff from the Pearl River is approximately 13 times that of the Hanjiang River. This indicates that greater runoff results in a wider area with obvious seasonal variations in the M₂ tidal current.

The above analysis, based on observations from different radar systems in different regions, shows that the M₂ tidal current exhibits significant seasonal variation in areas affected by runoff. The extent of these seasonal variations in the M₂ tidal current and the corresponding relative deviations are influenced by seasonal variations in runoff. In the nearshore areas of Guangdong, the relative deviation of the M₂ tidal current can reach 10–20%. Guangdong coastal current has significant seasonal changes, and influences the spread of the river plume, which could affect the extent of significant seasonal variations in the M2 tidal current.

3.3. Interannual Variations in M₂ Tidal Current

The interannual variations in M₂ tidal currents in the coastal areas of the Pearl River Estuary were analyzed using the observations from HFR Wanshan-Shangchuan for the period 2019–2022. Compared with the M₂ tidal current in 2019, the relative deviations in the core area were minimal from 2020 to 2022, with average relative deviations of 4.2%, 6.0%, and 4.4% and maximum relative deviations of 8.3%, 9.1%, and 8.5%, respectively (Figure 7). These results indicate that there was no significant interannual change in the M₂ tidal current in the coastal areas of the Pearl River Estuary from 2019 to 2022.

Using the observations from HFR Nanao-Huilai during 2019–2022, the interannual variations in the M₂ tidal current in the coastal areas of Shantou were analyzed (Figure 8). The spatial distribution of the M₂ tidal current in 2020 was nearly identical to that in 2019, with an average relative deviation of 4.9%. However, in 2021, the M₂ tidal currents showed significant changes in most of the observation areas when compared to 2019; for example, the major axis became shorter, the minor axis became longer, and the inclination was significantly deflected (Figure 8b). The relative deviation of the M₂ tidal current between 2019 and 2021 was significantly larger, with an average relative deviation of 17.9% and a maximum relative deviation of 33.4%. The spatial distribution of the M₂ tidal current in 2022 was nearly identical to that in 2021, with an average relative deviation of 9.3% (Figure 8c). The consistency between the M₂ tidal currents in 2020 and 2019, as well as between 2022 and 2021, indicates that no significant interannual change occurred in the M₂ tidal current in the coastal areas of Shantou, and the M₂ tidal current likely exhibited an abrupt change in 2021.

The above analysis, based on observations from different radar systems in different regions, shows that there is no significant interannual change in the M₂ tidal current in the coastal areas of Guangdong. This finding is consistent with traditional cognition, as tidal currents are mainly affected by the movement of celestial bodies and are thus very stable.

The M₂ tidal currents were highly stable before and after the sudden change observed in 2021 (Figure 8). The abrupt change in the M₂ tidal current in 2021 may have been caused by the changes in the hydrological environment in the coastal area [4] or changes in the surrounding environment of the radar antennas [39,40]. However, while the M₂ tidal current showed significant seasonal variations only near Cape Maqijiao, the abrupt change in 2021 occurred in the entire radar observation area. This suggests that the abrupt change in the M₂ tidal current in 2021 was not caused by changes in the nearshore hydrological environment.

The antenna patterns of the Nanao and Huilai radars were measured in July 2022 (Figure 9). The results indicated that these patterns significantly deviated from the ideal situation and were distorted. The Nanao and Huilai radars were established in January 2018 and December 2017, respectively. Over time, objects within the near-field range of the radar antenna (such as metal railings, houses, fences, woods, rocks, and water bodies) have changed. Owing to the mutual electromagnetic coupling between the objects and the antenna, the antenna patterns deviate from the ideal situation, which leads to changes in the ocean current data [39,40]. Therefore, the sudden change in the M₂ tidal current in 2021 was most likely caused by distortions in the antenna patterns owing to environmental changes around the Nanao and Huilai radar stations since their establishment.

4. Discussion

In this study, seasonal and interannual changes in the M₂ tidal current off the Guangdong coast are analyzed and the effects of stratification caused by rivers are discussed. Although seasonal changes have been observed in the other constituents, amplitudes of these constituents are not significantly larger than the root-mean-square errors of HFR. Therefore, seasonal changes in the other constituents were not discussed in this study. Offshore tidal changes are complex and susceptible to changes in geometry, sea-level rise, stratification, and internal tides [2,3]. Although anthropogenic activities, such as offshore wind farms, are present in the HFR observation areas, they do not change the topography as significantly as in ports and estuaries. Therefore, the seasonal variations in the M₂ tidal current off the Guangdong coast are likely independent of the alterations in geometry. According to the China Sea Level Bulletin, the rate of sea-level rise in the SCS was 3.6 mm/year from 1980 to 2022. In addition, the complex topography and strong oceanic stratification of the SCS make it one of the most active tidal waters in the world [41,42]. Studies on other areas suggest that rising sea levels and changes in internal tides can cause tidal changes [9,11]. A more comprehensive study discussing the influence of these factors on tidal changes is a direction for future research.

5. Conclusions

In this study, the M₂ tidal current in the coastal areas of Guangdong was analyzed using observations from ADCP, buoy, and HFR. The M₂ tidal current characteristics obtained from HFR were consistent with the results of ADCP and the buoy. Observation results show that the coastal areas of Guangdong exhibit a regular semi-diurnal tidal current, with the M₂ tidal current as the dominant component. Seasonal and interannual variations in the M₂ tidal currents in the coastal areas of Guangdong were analyzed using observational data from different radar systems in different regions. The M₂ tidal current exhibited significant seasonal variations in areas affected by river runoff. Analysis of temperature–salinity profiles for the periods 2006–2007 and 1978–1988 indicated that the river plume enhanced the stratification of seawater. Seasonal variation in stratification affects vertical eddy viscosity and, in turn, the vertical profile of currents, thereby causing variations in the M2 tidal current. The runoff is the highest in summer, resulting in the largest relative deviation of the M₂ tidal current, reaching 10–20%. The larger the runoff, the wider the area in which the M₂ tidal current exhibits significant seasonal variation. No significant interannual variation in the M₂ tidal current was observed during the observation period; however, a sudden change occurred in the coastal areas of Shantou in 2021. Further analysis indicated that this sudden change was mainly caused by the distortion of antenna patterns.