Estimation of Tidal Current Asymmetry in an Archipelagic Region: The Zhoushan Islands

Abstract

Tidal current asymmetry (TCA) often occurs in coastal regions. It can significantly influence bedload sediment transport. Recently, the statistical skewness of the tidal current velocity was calculated to represent the TCA. In archipelagic region, the tidal current directions vary temporally and spatially from channel to channel. This creates complexity in finding the flood–ebb axis about which to discuss the axial dissymmetry of tidal currents. In the present work, a method that involves taking the main flood direction (MFD) as the axis to split the tidal current was suggested. The MFD is the most probable direction of the strongest flood flow during each tidal cycle. The method was applied in an archipelagic region: The Zhoushan Islands. The results show that the calculated skewness well represented the TCA in waters around islands, and the degree of the TCA was mainly determined by the residual current. When the direction of the residual current was the same as the MFD, the skewness was positive, which indicated flood dominance. On the contrary, when the direction of the residual current was opposite to the MFD, the skewness was negative, which indicated ebb dominance. The stronger a residual current is, the more significant the TCA will be. Islands play an important role in forming residual circulations. Large ones force flows to move offshore around headlands or along curved channels, because of centrifugal forcing, while small ones often cause segregated flood/ebb conduits and form residual circulations. In the waterways between the Zhoushan Islands, the ebb current generally carries more sediment than the flood current. Therefore, ebb dominance always means sediment is more likely to be deposited, and vice versa. Further research into sediment transport modeling is suggested.

1. Introduction

Tidal current asymmetry (TCA) is quite common in coastal regions. It means there is a difference between the flood and ebb tidal currents. Instances of the current during the flood stage being stronger than the current during the ebb stage are is referred to as flood dominance (FD), while the opposite case is called ebb dominance (ED). Researchers have shown that TCA may significantly influence bedload sediment transport [1,2,3]. Estimating the TCA can help improve predictions of siltation in waterways between islands, which are often used as cargo channels. The spatially varying flood/ebb flow directions from channel to channel create difficulties in estimate the TCA. Yet the TCA in waters around islands has rarely been mentioned. Major factors that may cause TCA, and the roles of islands, are unsolved questions worthy of discussion.

Researchers have evaluated TCA based on harmonic analysis [4,5,6]. The degree of TCA is evaluated based on the phases and amplitudes of the tidal constituents, which interact and produce tidal wave deformation. Blanton et al. [7] studied the degree and direction of tidal wave deformation in a semidiurnal tidal estuary by analyzing the amplitude and the phase relationships between the M2 tide and its overtides, M4 and M6. Byun et al. [8] applied harmonic analysis to a shallow and semidiurnal tidal bay to evaluate the influence of shallow-water tidal constituents on the TCA. Manoj et al. [9] applied the harmonic method to two semidiurnal tidal estuaries to compare which tide was subjected to the most asymmetry. However, concerning TCA, harmonic analysis can only be applied in semidiurnal regimes because multiple tidal interactions may either augment or cancel each other out in mixed tidal regimes [10].

Recently, the statistical skewness of the tidal current velocity was calculated to represent TCA. Nidzieko et al. [11] defined the velocity skew as the asymmetrical distribution of ebb and flood tidal currents over a tidal cycle. Maren et al. [12] studied the relative influence of hydrodynamics and sediment properties on sedimentation based on Nidzieko’s method. Song et al. [13] modified this method to considerably simplify the attribution of specific constituents to the TCA. They found that only a few combinations of tidal constituents that meet the frequency conditions of 2${\mathsf{\omega }}_1$ = ${\mathsf{\omega }}_2$ or ${\mathsf{\omega }}_1$ + ${\mathsf{\omega }}_2$ = ${\mathsf{\omega }}_3$ can give rise to long-term mean asymmetry, regardless of the significance of the constituents [14]. Researchers [15,16,17,18,19] have applied the modified method to different mixed tidal estuaries and bays, and identified the particular tidal constituents that contribute the most to tidal asymmetry. Gong et al. [20] proposed that tidal current duration asymmetry can be calculated by replacing the water level acceleration term with the velocity acceleration term in the formula of Song et al.

Most of the previous studies on TCA cared about estuaries where the river discharge often causes the falling flow to overwhelm the rising flow, which means ED [21,22,23]. The situations in archipelagic regions, however, have rarely been mentioned. The Zhoushan Islands are located outside the mouth of Qiantang River, where the biggest tidal range and the strongest tidal current along the China’s east coast often occur [24]. As a preliminary study to estimate the TCA in this major tidal archipelagic region, we firstly focused on the barotropic tide processes. That is, only the depth averaged results are discussed. The modeling period covered mid-summer (July) to early autumn (September) when the Yangtze River Plume spreads offshore and leaves the Zhoushan Islands [25].

In archipelagic regions, the characteristic that flood/ebb directions are different from channel to channel create a great challenge in estimating TCA. Directions at each position must be chosen to represent the flood/ebb directions when the axial dissymmetry is discussed. A grid-based method that involves taking the main flood direction (MFD) as the axis to split the tidal current is suggested in the present work. The method used to determine the MFD is described in Section 2.1, along with a brief introduction to the skewness method. The numerical model used in this study is described in Section 2.2. The model results and verifications are shown in Section 3. Section 4 contains a detailed discussion, and a brief conclusion is drawn in Section 5.

2. Methods and Data

2.1. Methods

In an archipelagic region, the tidal current directions vary temporally and spatially from channel to channel. Therefore, to apply the statistical method, the directions in which to estimate the TCA must first be determined. The method should be grid-based. The MFD, which means the greatest possible direction of the strongest flood flow during each tidal cycle, was used to split the tidal current. The grid-based process for determining the MFD is shown below:

(1)

Determine the flood periods via tidal level changes in each grid.

(2)

Identify the directions of the strongest flow during each flood period.

(3)

Choose the most probable direction as the MFD.

When the MFD in each grid has been determined, the statistical skewness of the tidal velocity along the MFD can then be calculated, following Nidzieko [11], to estimate the TCA. The equation reads:

$${\gamma }_v=\frac{{\mu }_3}{{\mu }_2^{3/2}}$$

(1)

$${\mu }_m=\mathrm{E}\left[{\left(v\right)}^m\right]$$

(2)

where ${\gamma }_v$ is the statistical skewness, ${\mu }_3$ is the third moment about zero, and ${\mu }_2$ is the second moment about zero of the tidal velocity (v) along the MFD. The tidal current is FD when ${\gamma }_v$ > 0 and is ED when ${\gamma }_v$ < 0.

2.2. Model Description

In this study, a numerical model based on Delft-3D was established to cover the research area shown in Figure 1. Delft-3D is open-source software which can be downloaded from https://oss.deltares.nl/web/delft3d/ (accessed on 28 April 2022) and compiled. It uses the primitive hydrodynamic equations to solve motions, under Boussinnesq and quasi-hydrostatic approximations. A Cartesian coordinate system is used in the horizontal direction, while a sigma coordinate system is used in the vertical direction. It has been widely used in coastal dynamics [26,27,28]. One can visit the website for more details.

All forcings (tidal forcing, wind fields, river runoffs, open boundary temperature, and salinity) were included to validate the model results via comparison with observations. Most of the channels between the Zhoushan Islands are heavily used for cargo and fishery work, which makes it risky to carry out field observations. However, we deployed two moorings to carry out ADCP (acoustic doppler current profile) and CTD (conductivity, temperature, and depth) measurements. The positions (S1, S2) of these two moorings are shown in Figure 1. In addition, tidal level observations from 4 tidal gauges were also used to validate the simulated tidal levels. They were taken from National Marine Data Information Center (https://www.cnss.com.cn/tide/, accessed on 28 April 2022). Positions (T1–T4) are also shown in Figure 1.

The model had 149,019 grids in total. The minimum grid size near islands was 400 m while grids in the open sea area were slightly larger and reached 3000 m. The topography was interpolated from ETOPO_1. The open boundary tidal harmonics were taken from OTPS (https://www.tpxo.net/otps, accessed on 29 April 2022), and 11 tidal constituents (K1, O1, M2, S2, M4, M6, P1, Q1, N2, K2, and MS4) were considered. The Yangtze River run-off data were taken from the Datong station. The wind field data were taken from ASCAT (https://manati.star.nesdis.noaa.gov/datasets/ASCATData.php, accessed on 28 April 2022). The open boundary temperature and salinity data were taken from HYCOM + NCODA Global 1/12° Analysis (https://www.hycom.org/dataserver/gofs-3pt0/analysis, accessed on 30 April 2022).

3. Results

3.1. Validation of the Model Results

Synchronous observational data from four tidal gauges (T1–T4) and two mooring systems (S1–S2) were used to validate the simulated tidal levels and tidal currents. The positions of these gauges and systems are shown in Figure 1. Tidal levels were measured at all six sites, but tidal current observations were only conducted at S1 and S2. Comparisons of the model results with the observational data are shown in Figure 2 and Figure 3.

The correlation coefficients (CC) and root mean square (RMS) are shown in

Table 1. CC and RMS between observational data and model results.

Site	Tidal Level		Flow Velocity		Flow Direction
	CC	RMS	CC	RMS	CC	RMS
T1	0.9705	0.0696	/	/	/	/
T2	0.9638	0.0593	/	/	/	/
T3	0.9740	0.0632	/	/	/	/
T4	0.9607	0.0743	/	/	/	/
S1	0.8075	0.0954	0.8224	0.1307	0.8992	0.0020
S2	0.9684	0.0528	0.9411	0.0431	0.8010	0.0025

. The CC at all sites are greater than 0.8. The RMS at all sites is less than 0.01, which suggests that the model results are in good agreement with the observations.

3.2. The MFD

The MFDs in the Zhoushan Islands, as calculated using the steps described in Section 2.1, are shown in Figure 4. In this verification, the following regions were focused on: (1) the Luotou Channel, (2) the Guanmen Channel, and (3) the Dongji Islands. The locations of these regions are marked by the black boxes.

To validate that the calculated MFD represented the major direction during flood tides, the maximum tidal currents during each flood period over 16 days (8–23 September) at selected points and the MFDs are shown in Figure 5. The MFD at each point is consistent with the most likely direction of the tidal current at the maximum flood level.

Figure 6 shows the MFD for each of the study areas. In the Luotou Channel, the tidal currents run roughly E–W. The tidal current enters the channel from the eastern entrance, and its direction greatly varies at the cape from SW–NE to NE–SW. In the Guanmen Channel, the tide flows into the channel from the eastern entrance and out of the channel from the northwestern exit, and the MFD(W-E) is relatively consistent with the direction of the channel. A sharp turning of the tidal current appears near Daxie Island. In the Dongji Islands, the MFD is SE–NW. However, the tide turns near the islands.

Furthermore, the tidal currents at maximum flood and maximum ebb in the study areas are shown in Figure 7. The tidal currents in the Luotou Channel are stronger than those outside the channel, and the currents in the middle of the channel are stronger than those on either side. In Area I, the tidal currents are stronger on the west than on the east at the maximum flood. On the contrary, they are stronger on the east at the maximum ebb. Similarly, in Area II, the tidal currents are stronger on the west than on the east at the maximum flood and stronger on the east side than the west side at maximum ebb. In the Guanmen Channel, the flow velocity on the north is higher than that on the south at the maximum flood in Area III, whereas the south’s flow velocity is higher at the maximum ebb. In the Dongji Islands, the tidal currents are weaker on the north side of the islands than on the south side of the islands at the maximum flood, and they are weaker on the south side at the maximum ebb.

3.3. The TCA

The skewness in the Zhoushan Islands, as calculated using the steps described in Section 2.1, are shown in Figure 8. The regions we discuss are those listed in Section 3.2. Verification of the MFD was divided into two steps: (1) a comparison of the calculated skewness and the relative deviation between flood and ebb tides, and (2) a comparison of the skewness of the simulation and the observation.

To prove that the calculated skewness can represent the TCA, the relative deviations between flood and ebb tides at the six selected points were calculated. The equation reads:

$$\delta =\frac{v_f-v_e}{0.5\times \left(v_f+v_e\right)}$$

(3)

where $\delta$ is the relative deviation, $v_f$ is the average velocity during the flood, and $v_e$ is the averaged velocity during the ebb. Therefore, the relative deviation is the ratio of the difference in velocity between the flood and ebb to the average velocity of the flood and ebb. We compared the relative deviation with the calculated skewness. These deviations are shown in

Table 2. Calculated skewness and relative deviation.

Point	Skewness	Relative Deviation
1	0.92	0.47
2	−1.42	−0.90
3	−0.26	−0.16
4	−0.30	−0.17
5	1.09	0.44
6	−0.58	−0.21

. Based on this comparison, the relative deviation has the same sign as the skewness. Moreover, the relative deviation was roughly proportional to the skewness at each point. This shows that the calculated skewness well represents the strength of the flood and ebb tide. The skewness is positive when the flood flow’s velocity is stronger than the ebb flow’s velocity and negative when the ebb flow’s velocity is stronger than the flood flow’s velocity. Furthermore, the greater the difference in tidal current velocity between the flood and ebb stages, the greater the absolute value of skewness; conversely, the smaller the difference in tidal current velocity between the flood and ebb stages, the smaller the absolute skewness value.

In addition, the skewness calculated on the basis of the model results at S1 and S2 was compared with those based on observations. The skewness of the simulations were −0.2624 and −0.0915, while the calculated skewness of the observations were −0.2765 and −0.1066. The error is minor, and the simulated result is satisfactory. Therefore, the calculated skewness is correct.

4. Discussion

4.1. Role of Residual Currents

In estuaries, the main causes of TCA are often river discharges [21,22,23], while around islands, residual currents might be the major factor. Here, the residual current means the Euler mean flow averaged during a tidal period. It can be calculated via harmonic analysis. The residual currents and velocity skewness in three selected regions are shown in Figure 9. In the Luotou Channel, both the residual currents (Figure 9a) and the MFDs (Figure 6a) are northwestward on the west side of Areas I and II. The directions of the residual currents are the same as the MFDs. Therefore, the skewness there is positive, which indicates FD. On the contrary, the residual currents flow in the opposite directions to the MFDs on the eastern sides of Areas I and II, and negative skewness appears, which indicates ED. In the Guanmen Channel (Figure 9b), there is an ED area south of Area III because the residual currents run opposite to the MFDs, while the residual currents on the north side run along the MFDs, resulting in FD. In the Dongji Islands, the residual currents on the south sides of the islands flow northward, which is the same as the MFD. As such, the tidal currents show FD. The residual currents on the north side of the islands flow southward, which is against the MFD. In turn, the tidal currents show ED. Therefore, the signs of TCA are determined by the relationship between the directions of the residual currents and the MFDs. When the directions of residual currents are the same as the MFDs, the TCA will be positive, which indicates FD. When the directions of the residual currents are opposite to the MFDs, the TCA will be negative, which indicates ED.

4.2. Role of Islands

In archipelagic regions, the presence of islands will tremendously influence the residual current patterns. At the eastern entrance of the Loutou Channel, as shown in Figure 10, flood flows around the Beilun Headland head offshore into the channel and ebb flows also run offshore outside the channel because of centrifugal forcing [29]. They form two residual rings: one clockwise outside the headland and one anticlockwise inside the channel. A similar pattern can also be found at the western part of the channel around Jintang Island. These flow patterns with curvature are in good agreement with Nidzieko et al. [30]. On the other hand, the islands often cause segregated flood/ebb conduits and form residual circulations [31,32]. As shown in Figure 9b, at the eastern entrance of the Guanmen Channel, several small islands force the flood flows to mainly run into the channel from the north and the ebb flows to run out from the south, which leads to an anticlockwise residual circulation outside the channel. A similar situation can also be found around the Dongji Islands (Figure 9c), where the flood flows are blocked by islands from moving further northward, causing ED in the northern shadow of the islands and FD to the south.

5. Conclusions

To estimate the TCA in an archipelagic region, the major challenge is determining the direction about which to discuss the axial dissymmetry. In the present work, a grid-based method that involved taking the MFD, which means the most probable direction of the strongest flood flow during each tidal cycle, to split the tidal current was suggested. A numerical model was established to apply this method to the Zhoushan Islands. The model results were found to be in good agreement with the observations, and the calculated skewness well represented the TCA in the archipelagic region.

Around the Zhoushan Islands, the degree of TCA was mainly determined by the residual current. When the residual current flows in the same direction as the MFD, the skewness is positive, which indicates FD. On the contrary, when the direction of the residual current is opposite to that of the MFD, the skewness is negative, which indicates ED. The stronger the residual current, the more significant the TCA. Islands play an important role in forming residual circulations. Large ones force flows to move offshore around headlands or along curved channels because of centrifugal forcing, while small ones often cause segregated flood/ebb conduit and form residual circulations.

Further research may include the baroclinic structures of the TCA in this archipelagic region and the influence of TCA on sediment transport during seasons when the Yangtze River plume covers this coastal area. As an example, the Guanmen Channel’s ED nature means that it is easily silted because the ebb flow carries more turbid water from the Yangtze estuary.