IntroductionPorts are crucial connections between sea and land transport and are important to economic development support. Most of the ports worldwide are located in estuarine areas influenced by complex interactions among waves, tidal currents, river flows, and heterogeneous bathymetry. Siltation in navigation channels is a classic problem in port management, and the amount of siltation is directly associated with environmental conditions, morphological configurations, and human behaviors. Dredging is one type of maintenance to reduce siltation; however, port dredging has resulted in high operating costs and potentially negative environmental impacts. A more sustainable method is necessary to reduce sediment transport in ports and to make channel maintenance more efficient.Previous studies have focused on hydrodynamics and sediment transport in ports and navigation channels. In the Botlek Harbor, within the Port of Rotterdam, salinity-induced density gradients trapped suspended particulate matter (SPM) near the head of the saline water intrusion, determined the availability of SPM exchange between the tidal river and harbor, and caused high siltation rates in the harbor (Nijs et al. 2009). In the Port of Götenborg in Sweden, extensive anthropogenic activities, such as ship traffic and dredging, changed the natural harbor depth and disturbed salinity stratification and patterns of sediment transport (Johannesson et al. 2000). The study based on an experiment of a physical model between the Meuse River and a yacht harbor in Roermond City, the Netherlands, showed that siltation could be substantially reduced through designing a sill in the entrance and a permeable pile-groyne upstream of the entrance (Schijndel and Kranenburg 1998). More recently, studies using numerical models have become more popular because they overcome scaling difficulties in large-scale physical modeling systems as in the case of SPM and sediment transport in the sea near Daishan Island, Zhejiang Province, China (Li et al. 2019). Prumm and Iglesias (2016) investigated the morphodynamic response of the estuary to the expansion of the Port of Ribadeo, Spain, by simulating the impact of port expansion under representative conditions. Results highlighted the significant morphodynamic changes on the eastern bank of the estuary including migration of the tidal delta and infilling of the southeastern and eastern channels. A fully calibrated three-dimensional hydrodynamic model of the Sydney Harbor was used to determine the dominant force of regulating estuarine circulations in the channel under conditions of low river discharge. Modeling studies of the Sydney Harbor revealed that the highly variable cross-channel bathymetry may cause intratidal asymmetries in along estuarine circulations (Xiao et al. 2019). In the present research, a diagnostic study combining field and numerical methods improves understanding of observed downdrift port siltation adjacent to the river mouth. Model results calibrated with observed surface elevations and current velocities provide insights into residual circulations for a range of spring-neap tidal forces and wave conditions over the complex bathymetry.The study site is located in the central-southern portion of the Taiwan Strait, a transitional zone between the East China Sea and the South China Sea. The mean width of the strait is approximately 180 km. Tidal waves surge into the strait and cause high velocities (Jan et al. 2002; Yu et al. 2017). Exposed riverine sediment from the Zhuoshui River, north of Mailiao Port in Taiwan, is one of the major sources of sediment supply in this region (Milliman et al. 2007). The annual mean discharge of the Zhuoshui River is approximately 164.8 m3/s but is up to 24,000 m3/s during tropical cyclones. Bottle samples collected from bridge stations in the Zhuoshui River during the passage of tropical cyclones suggested that the sediment concentration could exceed 40 g/L for the major duration of the storm (Milliman et al. 2007). Field observations shortly after the passage of a typhoon suggested fine-grained sediments settled rapidly near the river mouth. After Typhoon Morakot in 2009, fine-grained sediment was found in the coastal zone near the river mouth. When this area was resurveyed in 2010, all the fine-grained sediment had been dispersed. It was conjectured that tidal currents and strong wind-driven waves during winter were the mechanisms that transported sediment away from the river mouth (Chien et al. 2011).A diagnostic study combining field and numerical methods is conducted to improve the understanding of observed morphological evolution in the navigational channel of Mailiao Port. The total area of Mailiao Port is 1,597.7 ha, the interior harbor is 515 ha, the width of harbor opening is 380 m, and the lengths of the navigation channel is approximately 15,000 m (south-wing) and 7,500 m (north-wing). The navigation channel depth is 24 m at the mean-tide level and can accommodate a 300,000-t vessel. Based on the final report of the MHAC (2020), the average daily siltation volume calculated during 2014–2018 was 18,797 m3/day. Data analysis based on the rate of topographical changes using the empirical orthogonal function (EOF) is discussed in the “Data Analysis using EOF” section. The “Numerical Model” section describes the numerical model for the Yunlin Coast consisting of model description, setup, calibration, and model performance. Results of model simulation are discussed in the “Results and Discussion” section. Finally, “Summary and Conclusions” section concludes the paper.Numerical ModelModel DescriptionNumerical models are widely used by engineers to simulate various aspects of waves, currents, sediment transport, and bathymetric changes in the nearshore ocean and to describe the coastal processes and effects of coastal structures (Bertin et al. 2009; Elias et al. 2006; Keshtpoor et al. 2015; Larson 2005; Malhadas et al. 2009; Pao et al. 2021). NearCoM-TVD 10.0 (Chen et al. 2014; Shi et al. 2011a), a coastal modeling system, integrates the wave model SWAN and a modified version of the circulation model SHORECIRC with sediment transport formulas (Kobayashi et al. 2008; Soulsby 1997; Van Rijn 2011). The numerical model SHORECIRC is a quasi-three–dimensional model that incorporates the mixing effects of vertical structure to a 2D horizontal model for simulating nearshore circulation (Svendsen et al. 2004). Conventional finite-difference schemes often produce unphysical oscillations while modeling coastal processes with abrupt changes or discontinuities, such as tidal bore formation, breaker zones, and moving shorelines. In contrast, a total-variation-diminishing (TVD)-type finite volume, a property of certain discretization schemes used to solve hyperbolic partial differential equations, allows for the robust treatment of discontinuities through the shock-capturing mechanism (Harten 1983). The wave model Simulating Waves Nearshore (SWAN) has been developed (Booij et al. 1999) to estimate wave conditions in small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents (Ris et al. 1999). This comprehensive model describes a number of nearshore phenomena, such as surf-beat, edge waves, and longshore currents, while allowing for alongshore variations in the hydrodynamic conditions (Dongeren et al. 2016).Based on the depth integration, the formulations of the SHORECIRC model (Svendsen et al. 2004) in Cartesian coordinates are given as follows:(1) ∂η∂t+∂Huα∂xα=0(2) ∂Huα∂t+Huαuβ∂xβ+fα+gH∂η∂xα+1ρ∂Tαβ∂xβ+1ρ∂Sαβ∂xβ+ταbρ−ταsρ+ROT=0where H = η + h, η = wave-averaged surface elevation; h = still water level; ρ = density; uα = component of the short-wave-averaged velocity; and fα = Coriolis force caused by a deflection of the moving object path within a rotating coordinate system. The parameters Tαβ, Sαβ,ταb,ταs, and ROT are, respectively, the depth-integrated Reynold’s stress, the wave-induced radiation stress (Higgins and Stewart 1962, 1964), the bottom shear stress, the wind-induced surface stress (Church and Thornton 1993), and the rest of terms associated with 3D dispersion.Waves and currents create bottom shear stress, a force at the seabed that influences sediment texture distribution, microtopography, habitat, and anthropogenic use (Dalyander et al. 2013). The wave-averaged bottom stress equation in the SHORECIRC model (Svendsen and Putrevu 1991) is given as follows:(3) ταb=12fρu0(β1ubα+β2Uwα)where ubα = current velocity at the bottom; and u0 = magnitude of current velocity ubα or the magnitude of wave velocity Uwα when Uwα > ubα. The current velocity, ubα, with the weighting factor β1 and the magnitude of wave velocity, Uwα, with the weighting factor β2 are the other contributors to the shear stress ταb. The weighting factors (β1 and β2) are the function of Uwα/ubα and the angle between wave and current vectors taken from the laboratory experimental data under the monochromatic wave conditions (Svendsen and Putrevu 1991). The values β1 = 1.0 and β2 = 0.5 (Chen et al. 2014, 2015; Shi et al. 2011a) are used in the present model. The friction factor, f, can be calculated by using the Manning formula, which integrates the effect of water depth, H, into a given Manning coefficient, M (Gauckler 1867; Manning 1891).(4) Sediment transport and the evolution of seabed in the coastal zone are driven by waves and wave-induced currents. The total sediment transport rate combining the effect of currents and waves on the bed shear stress (Soulsby 1997) is given as follows:(5) qa=Asua[|u|2+0.018Cdurms2−ucr]2.4(1−1.6tanβ)where As = sediment load; |u| = magnitude of the current velocity; ucr = critical velocity for erosion determined by the water depth and the mean grain size of the sediment (D50); urms = root mean square of the wave orbital velocity; and β = bed slope. The drag coefficient (Cd) plays an important role in calculating the total sediment transport rate, which is inversely parameterized to the wave stirring and can be defined as follows:(6) The magnitude of wave stirring is also influenced by the bed roughness (zo = 0.001 m). The total load sediment transport model is closely connected to current-dominated conditions in which tidal currents and wave-induced currents determine the direction of net transport, but waves can enhance the magnitude of transport through urms (Soulsby 1997).The seabed evolution can be described by using the sediment transport flux in generalized curvilinear coordinates(7) (1−p)∂h1∂t+∂fmorqa∂xa=0where h1, p, and fmor = bed evolution, bed porosity, and morphological factor, respectively. Eq. (7) is solved by using an upwinding first-order finite-difference scheme. The dissipation is minimal due to the small-time step used in the circulation model.Model Setup and CalibrationThe domain of numerical simulations indicated by the red line box (the length and width of 72 and 19 km, respectively) was rotated 60° clockwise, so the simulated nearshore circulations and sediment fluxes are presented as flowing in the alongshore and cross-shore directions [Figs. 5(a and b)]. The model resolution is 20 m near the Mailiao Port and 200 m in the rest of the domain [Fig. 5(c)]. The tidal boundary condition is provided by the global tidal-level forecast of Oregon State University with eight tidal constituents (K1, O1, P1, Q1, K2, M2, N2, and S2) (Martin et al. 2009). The wave boundary condition is based on the measurements of the offshore wave buoy at the Hsinchu station (25-m water depth). The navigation channel of Mailiao Port consists of two routes to enable the passage of vessels to the port, namely the north wing (W1) and the south wing (W2), and the measurements used for model calibration were taken in several positions as shown in Fig. 4(a). The Mailiao Tides Level Station (MTLS) was applied to monitor the tidal level at the entrance of Mailiao Port. In 2010, a tide gauge and acoustic Doppler current profiler (ADCP) were deployed between the entrance of Mailiao Port and the navigation channel (T1 and T2). ADCPs were deployed at the edge of the ebb tidal delta (T3, 10-m depth) and on the delta of the Zhuoshui River (T4, 6-m depth). Two ADCPs in time period 2018–2019 were deployed to measure the impact of waves and currents near the navigation channel (ADCP1, 400 m from the edge of the navigation channel and ADCP2, 1,000 m from the edge of the navigation channel). These observed time series of surface elevations and current velocities were applied to the model calibration.The simulations were divided into five cases, as shown in Table 1; Case 1 (30 days), Case 2 (13 days), Case 3 (13 days), Case 4 (10 days), and Case 5 (10 days). In this research, Case 3 and Case 4 were chosen to represent different wave conditions during the winter and summer seasons, respectively. Figs. 6(a and d) show the tidal boundary conditions of Case 3 (October–November 2018) and Case 4 (April 2019). Both the figures show similar results with the high tide levels (1.0–2.0 m) and the low tide levels (−1.0 to −1.2). Figs. 6(b and e) indicate the wave boundary conditions of Case 3 and Case 4 taken from stations of ADCP2 (10-m depth) and ADCP1 (21-m depth) in the offshore area. The highest wave in both cases is around 3.0 m, whereas the lowest wave is around 0.2 m. Wind-driven waves in the period of October–November 2018 (Case 3) were dominantly directed from the north, as shown in the scattered data, whereas the wave direction recorded in April 2019 (Case 4) dominantly came from the south.Table 1. Measurement used for model calibrationTable 1. Measurement used for model calibrationCaseStationWater depth (m)TimeCase 1T19April 2010T29T313T46Case 2ADCP121April 27–May 6, 2018Case 3ADCP210October 25–November 16, 2018Case 4ADCP121April 1–11, 2019Case 5ADCP121May 17–27, 2019All casesMLTS23All time periodModel PerformanceCalibration involves the adjustment of model parameters to produce a more reliable simulation (Montanari and Toth 2007). Selecting the appropriate friction parameters [for example, the Manning coefficient in Eq. (4) and the bed roughness zo in Eq. (6)] in the numerical simulation will determine the success of the modeling calibration. This optimization process for model performance requires several iterative steps by comparing the simulated and observed data. Model calibration was conducted between simulation results and observation data at MTLS for surface elevation and offshore area for tide level, velocity in longshore, and cross-shore direction using ADCP. The coherence between the model and measurements was analyzed using the correlation coefficient (R), model skill (S), and the root-mean-square error (RMSE). Considering that Mn and Cn are the measured data and the computed data, respectively, at N discrete points, the formulas are given by(8) R=(1/N)∑n=1N(Mn−Mn¯)(Cn−Cn¯)σCσM(9) S=1−∑n=1N|Cn−Mn|2∑n=1N(|Cn−Mn¯|2+|Mn−Mn¯|2)(10) RMSE=[1N∑n=1N(Mn−Cn)2]1/2The correlation coefficient (R) is commonly used to describe the strength of linear association between two quantitative variables, as shown in Eq. (8). Willmott (1981) presented a qualitative calibration method called model skill (S), as shown in Eq. (9). The perfect agreement between the model and observation can be reached if the value of S = 1, while the lowest value, S = 0, indicates complete disagreement. RMSE can also be used to measure the spread of observed data about the predicted values as shown in Eq. (10), the standard deviation of the residuals. The residuals describe that the distance of data points is from the regression line. RMSE is always between 0 and 1, in which the smaller value presents higher accuracy of the numerical model. For instance, if the distribution of data points lies precisely on the regression line, the RMSE is 0. RMSE is frequently used by researchers due to the easier interpretation results by converting the error metric back into similar units (Chai and Draxler 2014; Neill and Hashemi 2018).The bottom friction coefficient, Manning’s number, of 0.02 is applied to the entire model domain, making bottom friction a function of water depth [Eq. (4)]. In general, the comparison between observed data and simulation results demonstrates that the validated numerical model can simulate the flow field of the study site (Tables 1 and 2). Table 2 demonstrates that the values of the correlation coefficient, model skill, and RMSE for the surface elevation of five cases vary between 0.965–0.983, 0.907–0.971, and 0.232–0.454, respectively. The correlation coefficient for surface elevation shows that model results are strongly correlated with the observations. The model skill for surface elevation also shows a strong model agreement with the observed values. For the comparison of the model and observed velocity, the correlation coefficient for cross-shore velocities (u) varies from 0.934 (Case 2) to 0.159 (Case 3). The correlation coefficient for the longshore current velocities (v) ranges from 0.789 to 0.951, except for T2 (Case 1) which shows R = −0.002. The model skill denotes that the velocities in the cross-shore direction vary from 0.177 to 0.921 and the velocities in the longshore direction vary from −0.002 to 0.951. Overall, the correlation coefficient is greater than 0.98 and the model skill is greater than 0.9 for the simulated surface elevation in most of the stations. The correlation coefficient is greater than 0.79, the model skill is greater than 0.71, and the RMSE is less than 0.3 m for the simulated longshore current in most of the stations.Table 2. Model performance of the five model simulationsTable 2. Model performance of the five model simulationsCaseStationηuvηuvηuvCase 1MLTS0.978——0.962——0.238——T10.965——0.948——0.278——T20.9830.379−0.0020.9600.177−0.0020.2460.4230.047T3—0.7870.789—0.8290.781—0.1020.322T4—0.8070.801—0.7510.710—0.1930.280Case 2MTLS0.966——0.907——0.454——ADCP10.9700.9340.9510.9620.9210.9510.2670.0770.119Case 3MTLS0.979——0.932——0.393——ADCP20.9730.1590.7960.9670.0910.7940.2450.0850.314Case 4MTLS0.975——0.965——0.249——ADCP10.9800.8100.9510.9630.3950.9280.2520.1390.161Case 5MTLS0.973——0.962——0.259——ADCP10.9780.7900.8310.9710.7230.7960.2320.1260.212Fig. 7 compares the modeled results and observed surface elevation and velocities from ADCP2 for Case 3 and ADCP1 for Case 4. The simulated surface elevation of Case 3 [Fig. 7(a), the RMSE is 0.245 and the NRMSE is 17.5%] indicates an underestimate from the observed data during flood tides. NRMSE is a normalized RMSE obtained by dividing the RMSE value with the mean of tidal amplitudes. During ebb tides, the model results almost coincide with the observed surface elevation. The comparison of the tidal surface elevation for Case 4 shows a similar trend as Case 3, in which the observed tidal range is larger than the simulated results (the RMSE is 0.252 and the NRMSE is 16.8%). The velocity in the longshore direction of Case 3 shows that the modeled results are in a similar trend as the observational data, except for greater values in longshore velocities from October 30 to November 1, 2018 [Fig. 7(c)], most likely due to the influence of Typhoon Yutu. The comparison between the model results and observations in Case 4 demonstrates that the modeled longshore currents fit the observation during flood tides, whereas modeled longshore currents are greater than the observations during ebb [Fig. 7(f)]. The modeled results of cross-shore currents are underestimated compared with the observation in ADCP1 (21-m depth, near the navigation channel) as shown in Fig. 7(e), possibly owing to the change in the main direction of tidal currents change near the navigation channel over the abrupt depth that was not captured by the model bathymetry with a resolution of 20 m.Results and DiscussionSeasonal Variations in Significant Wave Heights and DirectionsThe simulated wave and flow field during two representative conditions, the northeastern monsoon during the winter season (Case 3, November 2–3, 2018) and the southern wind condition during the summer season (Case 4, April 1–2, 2018), are discussed in this section. The simulated flow field in Case 1, Case 2, and Case 5 are mainly dominated by tides due to weaker wave energy during the spring and summer seasons (the significant wave heights observed by the offshore data buoy are generally less than 1 m). Fig. 8 shows the magnitude and the direction of simulated significant wave heights in the study area during the winter and summer season [see the wave heights and direction in Figs. 6(b, c, e, and f)]. During the winter season when the magnitude of offshore waves is approximately 2.5 m, the simulated significant wave heights near the port are approximately 1 m and predominantly from the northwest toward the east. The observed wave heights and directions in Figs. 6(e and f) show that the wave direction during the summer season is from the south to the north with relatively milder wave energy than that in the winter season. During the summer season when the magnitude of offshore waves is approximately 1.5 m, the magnitude of significant wave heights is approximately 0.5 m near the port and waves propagate directly toward the entrance of the port. The simulated flow field under the interaction of waves and tidal currents during two representative conditions, namely the northeastern monsoon during the winter season and the southern wind condition during the summer season, are further discussed in the subsequent section.Seasonal Variations in Residual CirculationsTidal currents produce variations in the flow fields at different tidal stages. Both the modeled and observed current velocities (Fig. 7) show that the velocity in the longshore direction is more dominant. The velocity in the cross-shore direction is small and random [see the example in Case 3, Fig. 7(b)]. The average discharge of Case 3 is 24.95 m3/s and the average discharge of Case 4 is 11.73 m3/s. The velocities of the riverine flow are negligible when compared with the annual mean discharge of the Zhuoshui River (∼164.8 m3/s) and the discharge during tropical cyclones as well. Therefore, the effect of the riverine flow on current velocities near the navigational channel and the port entrance is insignificant compared with tidal currents or wave-driven longshore currents. The model results show that the tidal currents move toward the south during ebb tides, and the tidal currents move toward the north during flood tides. A striking difference between the intensity of residual circulations in Case 3 and Case 4 is shown in Fig. 9 (the tidal amplitude is approximately 0.5 m which are similar in both cases). The residual circulations refer to the flow integrated over one tidal period defined by the dominant constituent [for example, the period of M2 is 12.74 h; see Eq. (11)].(11) uresidual=112.74∑i=112.74uiTherefore, residual circulations can be used to estimate the direction and the intensity of the net sediment transport which possibly causes siltation or erosion near the navigation channel of Mailiao Port. In Case 3, the residual flow moves from the north toward the south. The port basin and the navigational channel near the port entrance are relatively stable without disturbances induced by tides and waves. The location of 2 km from the port entrance is influenced by the residual circulations with a speed up to 0.3 m/s from the north [see the yellow arrow in Fig. 9(a)]. In Case 4, the magnitude of residual circulations decreases during the summer season. The location of 2 km from the port entrance is influenced by the residual circulation with the speed of approximately 0.15 m/s originally coming from the north toward the south. The northward transport is enhanced with the additional flow coming from the south with a speed of 0.2–0.3 m/s occurring near the port entrance in the navigational channel [see the red arrow from both the north and south in Fig. 9(b)]. The model results for residual circulations under different wave conditions demonstrate that the magnitude and the direction of the simulated residual circulations near the edge of the navigation channel are modulated by offshore wave conditions.Simulated Morphological Change and a Countermeasure to Reduce SiltationThe simulated residual sediment flux and the resulting morphological evolution during two representative conditions are further discussed based on the total load transport formula of Soulsby (1997). D50 is given as 0.1 mm according to the sample from the field experiment [see the location in Fig. 4(a)]. The critical shear stress for erosion defined by Van Rijn (1984) varies between 0.39 and 0.45 m/s at a water depth of 5–30 m based on the given D50. Therefore, the sediment transport near the navigation channel can be triggered by the relatively strong current velocities [ranging between 0.5 and 1.0 m/s, see the example of observed and modeled velocities in the longshore direction in Figs. 7(c and f)]. Similar to the pattern of the simulated residual circulations, the simulated residual sediment transport rate at the location of 2 km from the port entrance is influenced by tides and wave-induced currents from the north. The simulated sediment transport rates for Case 3 and Case 4 come from the south toward the navigation channel and the entrance of the port (indicated by red vectors in Fig. 10). Moreover, the black and red contours in Fig. 11 illustrate the model results of morphological change after 1 month of simulation with a morphological factor of 12 which implies a 12-month multiplier to the sediment continuity equation. The simulated morphological evolution displays changes in the depth along the navigation channel during both seasons. The seabed change location is consistent with the spot indicated by the red circle in Fig. 4(a).The model results indicate that tidal currents play an important role in net transport southward, and wave-driven longshore currents may further transport the sediments from the riverine deposition near the mouth. The model results also indicate that the magnitude of sediment transport rate is more persistent under the northeast monsoon condition during the winter season. The magnitude and direction of wave-induced longshore current along the Yunlin Coast during the typical winter season are illustrated in Fig. 12(a). The wave-induced longshore currents (∼0.3 m/s) may contribute to 30%–60% of the total flow intensity under the interaction of tides and waves [0.5–1.0 m/s; Fig. 7(c)].The Mailiao Port has three existing jetties which are the North, West, and South Jetty [shown in Fig. 4(b)]. The length of the existing North Jetty is 700 m. Model simulation demonstrates that the longshore current interacts with the South Jetty and forms a circulation pattern that may transport sediment material into the navigational channel and causing the morphological evolution [Figs. 11(c and d)]. It is suspected that the North Jetty is incapable of blocking the supply of sediment transport from the deposited riverine sediment near the river mouth because the simulated morphological change is also significant near the West Jetty [Figs. 11(a and b)]. A striking difference can be seen when the North Jetty is extended to a water depth of 22 m (similar to the West Jetty). 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