The Response of Turbidity Maximum to Peak River Discharge in a Macrotidal Estuary

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Article The Response of Turbidity Maximum to Peak River Discharge in a Macrotidal Estuary

Yuhan Yan 1,2,3, Dehai Song 1,2,* , Xianwen Bao 1,2,3 and Nan Wang 3

1 Key Laboratory of Physical Oceanography, Ministry of Education, Ocean University of China, Qingdao 266100, China; [email protected] (Y.Y.); [email protected] (X.B.) 2 Pilot National Laboratory for Marine Science and Technology, Qingdao 266237, China 3 College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, China; [email protected] * Correspondence: [email protected]

Abstract: The Ou River, a medium-sized river in the southeastern China, is examined to study the estuarine turbidity maximum (ETM) response to rapidly varied river discharge, i.e., peak river discharge (PRD). This study analyzes the difference in ETM and sediment transport mechanisms between low-discharge and PRD during neap and spring tides by using the Finite-Volume Community Ocean Model. The three-dimensional model is validated by in-situ measurements from 23 April to 22 May 2007. In the Ou River Estuary (ORE), ETM is generally induced by the convergence between river runoff and density-driven ﬂow. The position of ETM for neap and spring tides is similar, but the suspended sediment concentration during spring tide is stronger than that during neap tide. The sediment source of ETM is mainly derived from the resuspension of the seabed. PRD, compared with low-discharge, can dilute the ETM, but cause more sediment to be resuspended from the seabed. The ETM is more seaward during PRD. After PRD, the larger the peak discharge, the longer the recovery time will be. Moreover, the river sediment supply helps shorten ETM recovery time. Mechanisms for this ETM during a PRD can contribute to studies of morphological evolution and pollutant ﬂushing.

Citation: Yan, Y.; Song, D.; Bao, X.; Keywords: estuary; turbidity maximum; peak river discharge; stratiﬁcation; spring-neap modulation; Wang, N. The Response of Turbidity recovery time; FVCOM Maximum to Peak River Discharge in a Macrotidal Estuary. Water 2021, 13, 106. https://doi.org/10.3390/ w13010106 1. Introduction Estuaries have been recognized as areas where buoyancy forcing from river discharge Received: 22 November 2020 alters the water density from that of the adjoining ocean [1]. The buoyancy forcing naturally Accepted: 29 December 2020 forms saltwater intrusion and generates the estuarine gravitational circulation, which fur- Published: 5 January 2021 ther affects sediment transport, sediment trapping, and the formation of estuarine turbidity

Publisher’s Note: MDPI stays neu- maximum (ETM) [2,3]. Unlike large rivers, the fluvial flow of small/medium-sized rivers is tral with regard to jurisdictional clai- likely to form a peak river discharge (PRD) due to a lack of connected lakes and tributaries ms in published maps and institutio- acting as sponges, i.e., a rapidly varied large-volume flux during a short period under nal affiliations. natural conditions (e.g., heavy rainfall) [4]. PRD events impart high buoyancy in a short time, which alters saltwater intrusion and estuarine circulation, and further sediment transport. Moreover, changes in salinity intrusion and ETM can also affect coastline/submarine topography evolution [5–7], pollutant flushing, and socioeconomic development [8,9]. In Copyright: © 2021 by the authors. Li- the context of increasing global-warming-induced inundation risks [10], studies on PRD censee MDPI, Basel, Switzerland. have become important. This article is an open access article ETM is characterized by a region with a maximum suspended sediment concentration distributed under the terms and con- (SSC) along an estuary, which is recognized as an efficient trap for fluvial and marine ditions of the Creative Commons At- suspended sediment [11,12]. Downstream suspended sediment carried by river runoff tribution (CC BY) license (https:// cooperates with three fundamental upstream suspended sediment transport mechanisms creativecommons.org/licenses/by/ 4.0/). to converge at ETMs. Tidal upstream current dominant asymmetry, which is correlative to

Water 2021, 13, 106. https://doi.org/10.3390/w13010106 https://www.mdpi.com/journal/water Water 2021, 13, 106 2 of 23

specific tidal compound constituents (e.g., M2 and M4) [13], can carry net upstream suspended sediment due to the stronger currents during floods compared to ebbs (called the tidal pumping effect) [14]. Density-driven compensation exchange estuarine flow, which drives the near-bed residual current landward, can also lift the greater lower-layer suspended sediment upstream [15]. Tidal straining, which mixes suspended sediment higher up during floods than during ebbs and drives an exchange flow downstream near the surface and upstream near the bottom, causes another process of ETM formation [16,17]. It is noteworthy that the significance of these mechanisms is related to estuarine stratification and the ETM’s location along the estuaries [3]. In addition, tidal lag effects (scour lag and settling lag) [18,19] and asymmetry in flocculation processes [20,21], similar to tidal straining, can also contribute to suspended sediment trapping, which induces SSC tidal asymmetry. ETMs caused by topographic trapping are not necessarily associated with the tidal distortion and salt-wedge, but they are always spatially fixed and probably have double convergence locations [22,23]. Lateral circulation, which has significant variation with wind and flooding, may modify ETMs [24,25]. Changing PRD and tidal amplitude with spring-neap modulation affect resuspension/deposition, stratification, and estuarine exchange flow. Larger tidal flow magnitude and restrained stratification during spring tides can suspend more seabed sediment into the water and help suspended sediment mix more highly than during neap tides in mesotidal and macrotidal estuaries [22,26,27]. Additionally, increasing spring tidal flow magnitude enhances upstream transport related to the tidal pumping effect, and reduces the estuarine exchange flow [28,29]. On the other hand, PRD inputs high SSC and alters the location of the salt-wedge; furthermore, it rebuilds stratification and the exchange flow, and limits the upstream tidal flow [30,31]. In the first part of this work [32], the impact of PRD on the lateral flow of the Ou River in China was explored. We continued to use the Ou River as a case study, which is a typical medium-sized river frequently suffering PRD during the plum-rainy/typhoon season. The remainder of this paper is structured as follows. In Section2, the study area as well as the numerical model and experimental setup are introduced. In Section3, the model results under different setups are described. The effects of PRD on the ETM are discussed in Section4, and the conclusions are summarized in Section5.

2. Study Area and Methodology 2.1. Study Area The Ou River ﬂows 388 km to the East China Sea, mainly through the Huang-Da-Ao Passage (Figure1b). The Ou River discharge varies quickly in a short time during the plum- rainy/typhoon season, and the annual discharge of the river is 13.9 km3 [33]. The Ou River basin drains an area of ~1.80 × 104 km2, and the headwater comes from a mountain with peak elevation of 1856.7 m in the southwest Zhejiang Province [34]. Most of the rainfall is concentrated in plum-rainy/typhoon season (April to September), and annual precipitation varies from 1100 to 2200 mm [35]. The river runoff in plum-rainy/typhoon season accounts for 78% of the annual total [36]. The Ou River Estuary (ORE) is tide-dominated, and the largest tidal range and the smallest tidal range are 7.21 m and 1.14 m at the Huang-Hua tidal station (HH in Figure1), respectively, indicating a macrotidal regime [37]. Water 2021, 13, 106 3 of 23 Water 2021, 13, x FOR PEER REVIEW 3 of 23

Figure 1. (a) The Ou River Basin with the Xuren hydrologic station. (b) Zoom-in of the blue box in (a); bathymetry of the Figure 1. (a) The Ou River Basin with the Xuren hydrologic station. (b) Zoom-in of the blue box in (a); bathymetry of the ORE (color, unit: m). The red line is the along-channel section used in this study. LKI: Ling-Kun Island; DMI: Da-Men ORE (color, unit: m). The red line is the along-channel section used in this study. LKI: Ling-Kun Island; DMI: Da-Men Island, Island, NYI: Ni-Yu Island; ZYAI: Zhuang-Yuan-Ao Island; NSD: North Submerged Dike; SCSD: South Channel Sub- mergedNYI: Ni-Yu Dike; Island; JXS: Jiang-Xin-Si; ZYAI: Zhuang-Yuan-Ao QSB: Qing-Shui-Bu; Island; NSD: ZY: NorthZhuang-Yuan; Submerged WN: Dike; Wu-Niu; SCSD: LW South: Long-Wan; Channel QLG: Submerged Qi-li-Gang; Dike; HH:JXS: Jiang-Xin-Si;Huang-Hua. QSB: Qing-Shui-Bu; ZY: Zhuang-Yuan; WN: Wu-Niu; LW: Long-Wan; QLG: Qi-li-Gang; HH: Huang-Hua.

TheThe ORE ORE is split split into into the the North North and and South South Channels Channels by Ling-Kun Island. To To meet the demanddemand of of land use by socioeconomic development,development, a submerged dike (South Channel Submerged Dike) was built in 1979 in the South Channel to silt the South Channel and Submerged Dike) was built in 1979 in the South Channel to silt the South Channel and naturally and gradually form land. The North Channel, as a main channel, is further naturally and gradually form land. The North Channel, as a main channel, is further di- divided into the northeastward Sha-Tou Passage and the Middle Passage; it stretches along vided into the northeastward Sha-Tou Passage and the Middle Passage; it stretches along the North Submerged Dike, Ling-Ni Dike, and several islands, including Da-Men Island, the North Submerged Dike, Ling-Ni Dike, and several islands, including Da-Men Island, Ni-Yu Island and Zhuang-Yuan-Ao Island (see Figure1b for details). Ni-Yu Island and Zhuang-Yuan-Ao Island (see Figure 1b for details). 2.2. Model Configuration 2.2. Model Configuration The hydrodynamic model and configuration used here is the same as that in the first partThe of this hydrodynamic study [32], which model is and based configuration on a three-dimensional used here is unstructured the same as that grid in primitive the first partequation of this Finite-Volume study [32], which Community is based Ocean on a three-dimensional Model (FVCOM) [unstructured38,39]. Considering grid primitive a three- equationdimensional Finite-Volume domain, the Community horizontal Ocean Reynolds-averaged Model (FVCOM) momentum [38,39]. Considering equation ignoring a three- dimensionalsurface forcing domain, after hydrostatic the horizontal approximation Reynolds-averaged [38] is given mo asmentum follows: equation ignoring surface forcing after hydrostatic approximation [38] is given as follows: ∂u ∂∂∂uuu∂u ∂u ∂u ∂ u∂Pt ∂∂∂ PtPc∂Pc ∂ ∂ u∂u + u ++++ v + w − f −=++ v = + + Km ++ Fu (1) ∂t ∂x uvw∂y ∂z fv∂x ∂x ∂z Kmu∂z F (1) ∂∂∂txy ∂ z ∂∂∂ xxzz ∂

Water 2021, 13, 106 4 of 23

∂v ∂v ∂v ∂v ∂Pt ∂Pc ∂ ∂v + u + v + w + f u = + + K + F (2) ∂t ∂x ∂y ∂z ∂y ∂y ∂z m ∂z v where t is the time, x, y, and z are the east, north, and vertical axes in Cartesian coordinate system, (u, v, w) is the three-dimensional Cartesian velocity vector, f is the Coriolis parameter; Pt is the barotropic pressure, and Pc is the baroclinic pressure; Km is the vertical eddy viscosity coefﬁcient; Fu and Fv represent the horizontal momentum diffusion terms. The bottom boundary conditions for u and v are:

∂u ∂v 1 K , = τ , τ (3) v ∂z ∂z ρ bx by √ 2 2 where τbx, τby = Cd u + v (u, v) are the x and y components of bottom stresses. The bottom friction coefﬁcient Cd affected by SSC is showed in Equation (5). To understand sediment trapping in estuaries, the SSC dynamics in the water column ignoring horizontal diffusion are described in [40,41]:

∂C ∂(uC) ∂(vC) ∂[(w − w )C] ∂ ∂C + + + s − K = 0 (4) ∂t ∂x ∂y ∂z ∂z v ∂z

where C(x, y, z, t) is the suspended sediment dry mass per water volume (grams per liter or kilograms per cubic meter), ws is the suspended sediment settling velocity, and Kv is the eddy diffusivity for SSC. The vertical coordinate z ranges from the surface elevation η(x, y, t) to bottom topography—H(x, y, t). In high-turbidity systems, sediment trapping can be enhanced by the suppression of turbulence due to turbidity-induced stratification in the bottom boundary layer [17,42]. As a result, Wang [43] applied the flux Richardson number Rf, which is an index of the vertical density stratification using the Mellor-Yamada Level 2.5 Turbulence Closure model, into the bottom friction coefficient to reproduce these effects into a numerical model:

" #2 κ Cd = (5) (1 + AR f ) ln(zb/z0b)

where κ is the von Kármán constant, zb is the near-bottom layer thickness, z0b is the bottom roughness, and A = 5.5 is an empirical constant. According to Mellor and Yamada [44], the ﬂux Richardson number Rf can be calculated as:

1/2 2 R f = 0.725 Ri + 0.186 − Ri − 0.316Ri + 0.0346 (6)

where the gradient Richardson number (Ri) can be calculated as:

g ∂ρ/∂z Ri = − (7) ρ (∂u/∂z)2 + (∂v/∂z)2

On the other hand, to quantitatively couple sediment transport with hydrodynamic, the equation of state using a bulk-density relation is represented as follows: ρw ρ = ρw + 1 − × C (8) ρs

where ρw is the seawater density, and ρs is the porosity sediment bulk density. Vanished sediment ﬂux at the free surface is required:

∂C K − Cw = 0 for z = η. (9) v ∂z s Water 2021, 13, 106 5 of 23

The net sediment ﬂux (Eb) normal to the bottom is the difference between the deposition and erosion, yielding

∂C K − Cw = E for z = −H (10) v ∂z s b assuming small surface and bottom slopes. The well-accepted Ariathurai and Krone formulation [45] for Eb is:

 | | E τb − 1 if |τ | ≥ τ Erosion  0 τce b ce Eb = (11) |τb|  C ws 1 − if |τ | < τ Deposition b τcd b cd

where E0 is the constant erosion rate parameter, Cb is the SSC close to the bottom, τb is the bottom shear stress, and τce and τcd are the critical shear stress for erosion and deposition, respectively. Sediment settling is an essential process in estuarine sediment trapping [3]. For ﬁne particles and high SSC, the cohesiveness of sediments becomes noteworthy; the settling velocity depends on the SSC and the turbulence intensity capturing processes. As a result, a general expression [46] for the settling velocity including physical processes such as free settling, ﬂocculated settling, and hindered settling is   ws0 C ≤ C0 w = m Cn1 (12) s 1 C > C  2 2 n2 0 (C + m2 )

where ws0 is the free settling velocity, C0 is the critical concentration for ﬂocculation, and m1, m2, n1, and n2 are empirical settling coefﬁcients. The validated parameters in the suspended sediment model are summarized in Table1.

Table 1. Parameters used in the suspended sediment transport model.

Parameter Value Reference −1 −2 τce 0.6 (kg·m ·s ) Tested −1 −2 τcd 0.6 (kg·m ·s ) Tested −5 −2 −1 E0 5 × 10 (kg·m ·s ) Tested −5 −1 ws0 −2.11 × 10 (m·s ) Tested m1 −0.05 Tested n1 1.2 Mehta and McAnally [46] m2 6.2 Mehta and McAnally [46] n2 1.6 Mehta and McAnally [46] −3 C0 0.2 (kg·m ) Mehta and McAnally [46] −3 ρs 1100 (kg·m ) Tested −4 z0b 2.5 × 10 (m) Tested

The model has a higher horizontal resolution (about 100 m) in the North Channel and Middle Passage (Figure2) with 18 sigma layers in the vertical. FVCOM is implemented using a mode-split approach for computation efficiency, in which the three-dimensional momentum, salinity and SSC are integrated with internal mode time step (2 s) and sea elevation, defined as external mode, is integrated with a shorter time step (1 s). Different from the first part [32], the model was run starting on 9 December 2006, as we do not have the measured SSC data in 2005 for validation. In this part, the model was initiated with zero water level and velocity and was first run for 120 days with a fixed river discharge, including both OR and NR (the daily average on 8 April 2007) as well as the open boundary salinity (the monthly average in April 2007), to reach a quasi-equilibrium state. Due to the lack of observed river input SSC, the multiyear average of the river SSC during the plum- rainy/typhoon season (0.2 kg·m−3) was set in the model [33]. The model was then run Water 2021, 13, 106 6 of 23

with the daily average river discharge for another 45 days, from 8 April to 22 May in 2007, and the results from the last 35 days were analyzed. The wind wave was nonsigniﬁcant Water 2021, 13, x FOR PEER REVIEWin the ORE due to the shelter effect of the island [47] and thus was not considered in6 thisof 23

study. This case was marked as the Control Run (Run 0).

FigureFigure 2.2. MeshMesh gridgrid ofof thethe OREORE modelmodel usedused inin thisthis study.study.Red Red curve curve indicates indicates open open boundary. boundary.

2.3.Table Validation 1. Parameters used in the suspended sediment transport model. FieldworkParameter was carried out in the OREValue from 23 April to 22 MayReference 2007 (day of the year 113~142). Tidal elevation at a short-term tidal gauge (shown as T1 in Figure1b) τce 0.6 (kg·m−1s−2) Tested was recorded hourly by Temperature-Depth (Compact-TD) over the entire observation. τcd 0.6 (kg·m−1s−2) Tested Meanwhile, electromagnetic-current-meters and Conductivity-Temperature-Depths (CTDs) E0 5 × 10−5 (kg·m−2s−1) Tested were used to record the current velocity and salinity during the neap tide from 11:00 −5 −1 24 April to 12:00ws0 25 April (UTC +0800,−2.11 day× 10 of (m·s the year) 114.46~115.50)Tested and the spring tide from 11:00m1 May to 12:00 2 May 2007−0.05 (UTC +0800, day of the yearTested 121.46~122.50), with one-hourn intervals1 at C1~C3 stations (shown1.2 in Figure1b). Mehta and McAnally [46] To validatem2the numerical model, the RSR,6.2 which is the ratio Mehta of the and root McAnally mean square [46] error (RMSE) normalizedn2 by the standard deviation1.6 of the observation Mehta [and48] isMcAnally used, which [46] is calculated as: 0 −3 C q 0.2 (kg·m ) Mehta and McAnally [46] −3 2 ρs ∑1100(Xobservation (kg·m −) Xmodel) Tested = 0b RSR q −4 . (13) z 2.5 × 10 (m) 2 Tested ∑ Xobservation − Xobservation 2.3. Validation Fieldwork was carried out in the ORE from 23 April to 22 May 2007 (day of the year 113~142). Tidal elevation at a short-term tidal gauge (shown as T1 in Figure 1b) was recorded hourly by Temperature-Depth (Compact-TD) over the entire observation. Mean- while, electromagnetic-current-meters and Conductivity-Temperature-Depths (CTDs) were used to record the current velocity and salinity during the neap tide from 11:00 24 April to 12:00 25 April (UTC +0800, day of the year 114.46~115.50) and the spring tide from

Water 2021, 13, x FOR PEER REVIEW 7 of 23

11:00 1 May to 12:00 2 May 2007 (UTC +0800, day of the year 121.46~122.50), with one- hour intervals at C1~C3 stations (shown in Figure 1b). To validate the numerical model, the RSR, which is the ratio of the root mean square error (RMSE) normalized by the standard deviation of the observation [48] is used, which is calculated as: ()− 2  XXobservation model RSR = . 2 (13) ()−  XXobservation observation The Nash-Sutcliffe efficiency (NSE) is also used to validate the model, which is given as: ()− 2  XXobservation model NSE =−1 . 2 (14) ()XX− Water 2021, 13, 106  observation observation 7 of 23 X is the variable being evaluated; and the overbar indicates the temporal average. Comparison between the observed and simulated tidal elevation at T1 is shown in Figure 3. Referring to the performance ratings (Table 2) in previous study [49], both RSR (0.24) The Nash-Sutcliffe efficiency (NSE) is also used to validate the model, which is and NSE (0.94) of tidal elevation showed very good values. Comparisons between the given as: observation and simulated current velocity/directionq at C1~C3 are shown in Figure 4. The 2 RSR and NSE for along-channel flow are∑(X givenobservation in Table− Xmodel 3. Most) RSRs are less 0.50, and NSE = 1 − q . (14) NSEs are greater than 0.75, indicating very good values. Comparisons2 between the simu- ∑ X − X lated and observed salinities are also shownobservation in Figureobservation 5, and their RSRs and NSEs are summarizedX is the variablein Table being3. Most evaluated; RSRs are andless 0.60, the overbar and most indicates NSEs are the over temporal 0.65, indicating average. Comparisonthat the model between could thereproduce observed the and salinity simulated variation tidal elevation(Table 3). atComparison T1 is shown between in Figure the3. Referringsimulated toand the observed performance SSC are ratings shown (Table in Figure2) in previous 6, which study focus [on49 ],the both bottom RSR SSC (0.24) as andETMs NSE are (0.94) most significant of tidal elevation near the showed bottom very[3]. Percent good values. bias (PBIAS) Comparisons is used to between validate the the observationSSC, given as and [49]: simulated current velocity/direction at C1~C3 are shown in Figure4. The RSR and NSE for along-channel flow() are given−× in Table3. Most RSRs are less 0.50,  XXobservation model 100 and NSEs are greater than 0.75,PBIAS indicating= very() good values. Comparisons. between the(15) simulated and observed salinities are also shown X inobservation Figure5, and their RSRs and NSEs are summarized in Table3. Most RSRs are less 0.60, and most NSEs are over 0.65, indicating The performance rating of the PBIAS for sediment is listed in Table 2. PBIASs of SSC that the model could reproduce the salinity variation (Table3). Comparison between the are concluded in Table 3, and all values reach a satisfactory level, indicating the model simulated and observed SSC are shown in Figure6, which focus on the bottom SSC as can reproduce suspended sediment dynamics. Note that the river SSC during flooding ETMs are most significant near the bottom [3]. Percent bias (PBIAS) is used to validate the SSC,can rise given an asorder [49]: compared to a low-discharge condition [33], so the lack of observed river SSC may be the reason that SSC simulations are comparatively inaccurate. Overall, this ∑ (Xobservation − Xmodel) × 100 numerical model is ablePBIAS to describe= the hydrodynamics and. suspended sediment (15) ∑(Xobservation) transport in the ORE.

Water 2021, 13, x FOR PEER REVIEW 8 of 23

FigureFigure 3.3. ObservedObserved (dot(dot redred line)line) andand simulatedsimulated (solid(solid blueblue line)line) tidaltidal elevationelevation at at the the T1 T1 station. station.

FigureFigure 4.4. ObservedObserved (dot(dot redred line)line) andand simulatedsimulated (solid(solid blueblue line)line) verticalvertical averagedaveraged currentcurrent velocityvelocity andand currentcurrent directiondirection −1 duringduring neapneap tidetide ((aa––cccurrent currentvelocity velocityin in m m·s·s−1;; d–f current direction in degree)degree) andand springspring tidetide ((gg––ii currentcurrent velocityvelocity inin m·s−1; j–l current direction in degree) at the C1~C3 stations. m·s−1; j–l current direction in degree) at the C1~C3 stations.

Figure 5. Observed (dot red line) and simulated (solid blue line) vertical averaged salinity (PSU) during (a–c) neap tide and (d–f) spring tide at the C1~C3 stations.

Table 2. General performance ratings [49].

Performance PBIAS (%) RSR NSE Rating for Sediment Very Good 0 ≤ RSR ≤ 0.50 0.75 ≤ NSE ≤ 1 PBIAS < ±15 Good 0.50 < RSR ≤ 0.60 0.65 ≤ NSE < 0.75 ±15 < PBIAS < ±30 Satisfactory 0.60 < RSR ≤ 0.70 0.50 ≤ NSE < 0.65 ±30 < PBIAS < ±55 Unsatisfactory RSR > 0.70 NSE < 0.50 PBIAS > ±55

Water 2021, 13, x FOR PEER REVIEW 8 of 23

WaterFigure2021, 13 4., 106 Observed (dot red line) and simulated (solid blue line) vertical averaged current velocity and current direction 8 of 23 during neap tide (a–c current velocity in m·s−1; d–f current direction in degree) and spring tide (g–i current velocity in m·s−1; j–l current direction in degree) at the C1~C3 stations.

Water 2021, 13, x FOR PEER REVIEW 9 of 23

Table 3. RSR and NSE of flow and salinity, PBIAS of SSC at the C1~C3 stations.

Flow Salinity SSC Station Neap Spring Neap Spring Neap Spring RSR NSE RSR NSE RSR NSE RSR NSE PBIAS (%) PBIAS (%) C1 0.40 0.84 0.36 0.87 0.41 0.83 0.57 0.68 6.65 20.02 FigureFigure 5. 5. ObservedObserved (dot red line)line) andand simulatedsimulated (solid (solid blue blue line) line) vertical vertical averaged averaged salinity salinity (PSU) (PSU) during during (a– c(a)– neapc) neap tide tide and C2and (d–f) spring 0.22 tide at 0.95the C1~C3 stations.0.28 0.92 0.17 0.97 0.54 0.71 11.30 24.04 C3(d –f) spring 0.44 tide at the0.81 C1~C3 stations.0.51 0.74 0.50 0.75 0.69 0.52 −47.36 −31.27 Table 2. General performance ratings [49].

Figure 6. ObservedObserved (dot (dot red red line) line) and and simulated simulated (solid (solid blue blue line) line) bottom bottom suspended suspended sediment sediment concentration concentration (kg·m (kg−3)·m dur-−3) ingduring (a–c ()a neap–c) neap tide tide and and (d–f ()d spring–f) spring tide tide at C1~C3 at C1~C3 stations. stations.

2.4. Experimental Design Based on the ORE model, several experiments are designed to study the response of the turbidity maximum to a rapid-change discharge, which are summarized in Table 4. Taking the year 2007 as an example, a PRD with a peak discharge over 1000 m3·s−1 occurred nine times and the maximum discharge reached 7310 m3·s−1, which is approximately one order greater than the multiyear average value (442 m3·s−1 by Song et al., [33]). A PRD event with a 1590 m3·s−1 peak discharge (return period is about 13 years) was captured during field measurements (from 25 to 27 April, day of the year 113~142, Figure 7a). The daily average river discharge from 2005 to 2015 at the Xuren hydrologic station (Figure 1a) shows that the duration of a PRD event is usually less than 2 days in the ORE. Thus, the flooding duration is set to 2 days in some experiments. In contrast to Run 0, wind and NR are ignored in the other cases to focus on the Ou River PRD. Run 1 represents the low- discharge condition of a constant 500 m3·s−1 (the solid blue line in Figure 7b), according to the multiyear average value of 442 m3·s−1 [33]. Runs 2 and 3 are experiments in which the 3-day PRD measured during the observational period (Figure 7a) is given during neap tide and spring tide, respectively (Table 4). Run 4 is the same as Run 1 except that the river SSC is set to 0. The river SSC during PRD is set to 0 in Runs 5~10. Runs 5~7 have the same total river discharge volume during PRD but with different duration. Runs 8~10 have the same PRD duration (2 days) as Run 5, but have a different peak discharge. According to

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Table 2. General performance ratings [49].

Performance Rating RSR NSE PBIAS (%) for Sediment Very Good 0 ≤ RSR ≤ 0.50 0.75 ≤ NSE ≤ 1 PBIAS < ±15 Good 0.50 < RSR ≤ 0.60 0.65 ≤ NSE < 0.75 ±15 < PBIAS < ±30 Satisfactory 0.60 < RSR ≤ 0.70 0.50 ≤ NSE < 0.65 ±30 < PBIAS < ±55 Unsatisfactory RSR > 0.70 NSE < 0.50 PBIAS > ±55

Table 3. RSR and NSE of ﬂow and salinity, PBIAS of SSC at the C1~C3 stations.

Flow Salinity SSC Station Neap Spring Neap Spring Neap Spring PBIAS PBIAS RSR NSE RSR NSE RSR NSE RSR NSE (%) (%) C1 0.40 0.84 0.36 0.87 0.41 0.83 0.57 0.68 6.65 20.02 C2 0.22 0.95 0.28 0.92 0.17 0.97 0.54 0.71 11.30 24.04 C3 0.44 0.81 0.51 0.74 0.50 0.75 0.69 0.52 −47.36 −31.27

The performance rating of the PBIAS for sediment is listed in Table2. PBIASs of SSC are concluded in Table3, and all values reach a satisfactory level, indicating the model can reproduce suspended sediment dynamics. Note that the river SSC during ﬂooding can rise an order compared to a low-discharge condition [33], so the lack of observed river SSC may be the reason that SSC simulations are comparatively inaccurate. Overall, this numerical model is able to describe the hydrodynamics and suspended sediment transport in the ORE.

2.4. Experimental Design Based on the ORE model, several experiments are designed to study the response of the turbidity maximum to a rapid-change discharge, which are summarized in Table4. Taking the year 2007 as an example, a PRD with a peak discharge over 1000 m3·s−1 occurred nine times and the maximum discharge reached 7310 m3·s−1, which is approximately one order greater than the multiyear average value (442 m3·s−1 by Song et al., [33]). A PRD event with a 1590 m3·s−1 peak discharge (return period is about 13 years) was captured during ﬁeld measurements (from 25 to 27 April, day of the year 113~142, Figure7a). The daily average river discharge from 2005 to 2015 at the Xuren hydrologic station (Figure1a) shows that the duration of a PRD event is usually less than 2 days in the ORE. Thus, the ﬂooding duration is set to 2 days in some experiments. In contrast to Run 0, wind and NR are ignored in the other cases to focus on the Ou River PRD. Run 1 represents the low-discharge condition of a constant 500 m3·s−1 (the solid blue line in Figure7b), according to the multiyear average value of 442 m3·s−1 [33]. Runs 2 and 3 are experiments in which the 3-day PRD measured during the observational period (Figure7a) is given during neap tide and spring tide, respectively (Table4). Run 4 is the same as Run 1 except that the river SSC is set to 0. The river SSC during PRD is set to 0 in Runs 5~10. Runs 5~7 have the same total river discharge volume during PRD but with different duration. Runs 8~10 have the same PRD duration (2 days) as Run 5, but have a different peak discharge. According to the daily average OR discharge collected from 2005 to 2015, the maximum discharge was 10,900 m3·s−1, which was recorded in August 2014. Therefore, in Runs 8, 5, 9, and 10, the peak discharge is set to increase from 2500 m3·s−1 (return period is about 30 years) to 10,000 m3·s−1 (return period is about 3500 years) during spring tide with 2500 m3·s−1 intervals to examine the impact of discharge volume on the ETM. Runs 11~14 use the same PRD duration (2 days) as Run 5, but have a different peak discharge and the river SSC during PRD is set to 0.4 kg·m−3. Water 2021, 13, 106 10 of 23

Table 4. Experiment conﬁguration and the SSC and location of the ETM core in the along-channel section (the red line in Figure1b with the red triangle indicating 0 km).

Peak Discharge PRD Occurrence PRD Duration River SSC during ETM Core SSC ETM Core Run (m3·s−1) Time (Day) PRD (kg·m−3) (kg·m−3) Location (km) Run 0 Real type - - - - - Run 1 500 - - 0.2 1.61 16.07 Run 2 Real type Neap Tide 3 0.2 0.56 25.36 Run 3 Real type Spring Tide 3 0.2 1.41 20.20 WaterRun 2021 4, 13, x FOR PEER 500 REVIEW - - 0 1.38 16.2410 of 23 Run 5 5000 Spring Tide 2 0 1.16 26.74 Run 6 3500 Spring Tide 3 0 1.15 28.11 Run 7 2750 Spring Tide 4 0 1.16 26.54 Run 8 2500the daily Spring average Tide OR discharge 2 collected from 02005 to 2015, the 1.38maximum discharge 20.38 was Run 9 750010,900 Spring m3·s−1 Tide, which was recorded 2 in August 2014. 0 Therefore, in 1.07 Runs 8, 5, 9, and 28.11 10, the Run 10 10,000peak discharge Spring Tide is set to increase 2 from 2500 m3·s− 01 (return period is 1.01 about 30 years) 30.71to 10,000 Run 11 2500 Spring Tide 2 0.4 1.44 20.38 m3·s−1 (return period is about 3500 years) during spring tide with 2500 m3·s−1 intervals to Run 12 5000 Spring Tide 2 0.4 1.24 26.74 Run 13 7500examine Spring the Tide impact of discharge 2 volume on the 0.4 ETM. Runs 11~14 1.28 use the same 28.11PRD du- Run 14 10,000ration Spring (2 days) Tide as Run 5, but have 2 a different peak 0.4 discharge and the 1.23 river SSC during 30.71 PRD is set to 0.4 kg·m−3.

FigureFigure 7. ((aa)) River River discharge discharge of of the the OR OR duri duringng the the in-situ measurement. measurement. ( (bb)) Two Two types types of of river river discharge discharge (blue (blue lines) lines) in in experimentexperiment runs: runs: the the solid solid line line is is for for low-discharge, low-discharge, the dashed line with squares is for PRD.

Table 4. Experiment configuration and the SSC and location of the ETM core in the along-channel section (the red line in Figure 1b with the red triangle3. Resultsindicating 0 km). 3.1. Saltwater Intrusion Peak Discharge PRD Occurrence PRD Duration River SSC during ETM Core SSC ETM Core Loca- Run (m3·s−1) 3.1.1. Spring-NeapTime Modulation(Day) PRD (kg·m−3) (kg·m−3) tion (km) Run 0 Real type The distribution- of the salinity- during spring- and neap tides- at the bottom- layer of Run 1 500 the ORE under - the low-discharge - condition 0.2 is shown in Figure 1.61 8a–d. The saltwater 16.07 at Run 2 Real type the bottom Neap layer Tide is more easily 3 extended landward 0.2 than at 0.56 the surface [1]. 25.36 Therefore, Run 3 Real type Spring Tide 3 0.2 1.41 20.20 Run 4 500 - - 0 1.38 16.24 Run 5 5000 Spring Tide 2 0 1.16 26.74 Run 6 3500 Spring Tide 3 0 1.15 28.11 Run 7 2750 Spring Tide 4 0 1.16 26.54 Run 8 2500 Spring Tide 2 0 1.38 20.38 Run 9 7500 Spring Tide 2 0 1.07 28.11 Run 10 10,000 Spring Tide 2 0 1.01 30.71 Run 11 2500 Spring Tide 2 0.4 1.44 20.38 Run 12 5000 Spring Tide 2 0.4 1.24 26.74 Run 13 7500 Spring Tide 2 0.4 1.28 28.11 Run 14 10,000 Spring Tide 2 0.4 1.23 30.71

Water 2021, 13, x FOR PEER REVIEW 11 of 23

3. Results 3.1. Saltwater Intrusion 3.1.1. Spring-Neap Modulation Water 2021, 13, 106 The distribution of the salinity during spring and neap tides at the bottom layer11 of of 23 the ORE under the low-discharge condition is shown in Figure 8a–d. The saltwater at the bottom layer is more easily extended landward than at the surface [1]. Therefore, this sec- tionthis shows section the shows location the locationof the salt-wedge of the salt-wedge by the salinity by the at salinity the bottom at the layer. bottom The layer.tidal cycle The selectedtidal cycle during selected the spring during and the neap spring tides and is neap the last tides tidal is the cycle last during tidal cyclethe flooding. during theAt highﬂooding. water At slack, high the water salt-wedge slack, the of salt-wedge the ORE is of closer the ORE to the is closerJiang-Xin-Si to the Jiang-Xin-Si during spring during tide thanspring during tide thanneap during tide. At neap high tide. water At slack, high th watere salinity slack, isoline the salinity of 1 PSU isoline is mainly of 1 PSU in the is areamainly of Yang-Fu-Shan in the area of Yang-Fu-Shan to Zhuang-Yuan to Zhuang-Yuan or Wu-Niu during or Wu-Niu the spring during and the neap spring tides, and while neap thetides, salinity while isolines the salinity of 2 isolinesto 5 PSU of during 2 to 5 PSUthe neap during tide the are neap more tide intensive are more than intensive during than the springduring tide the spring(Figure tide 8a,b). (Figure At low8a,b). water At low slack, water as slack,the main as the channel main channelof runoff, of runoff,the area the of Yang-Fu-Shanarea of Yang-Fu-Shan to Zhuang-Yuan to Zhuang-Yuan to Long-Wan to Long-Wan is generally is generally covered covered with freshwater with freshwater during neapduring tide, neap and tide, the andsalinity the salinityisoline of isoline 5 PSU of is 5 located PSU is near located Qi-Li-Gang near Qi-Li-Gang (Figure 8c). (Figure During8c). springDuring tide, spring the tide,salt-wedge the salt-wedge shifts to the shifts east to of the the eastQi-Li-Gang; of the Qi-Li-Gang; at this moment, at this west moment, of the Qi-Li-Gang,west of the Qi-Li-Gang, only part of only the partdeeper of the areas deeper keeps areas some keeps saltwater some saltwaterwith salinity with of salinity about of 1 PSUabout (Figure 1 PSU 8d). (Figure 8d).

Figure 8. Distribution diagram of bottom salinity (ﬁlled(filled contour, unit: PSU) under (a–d) the low-dischargelow-discharge conditioncondition andand (e–h) PRD condition at high water slack and low water slack. The salinity is in 1-PSU intervals. Left panels are during (e–h) PRD condition at high water slack and low water slack. The salinity is in 1-PSU intervals. Left panels are during neap neap tide, and right panels are during spring tide. White areas indicate tidal flat. tide, and right panels are during spring tide. White areas indicate tidal ﬂat.

During both springspring andand neapneap tides,tides, PRD PRD moves moves the the salt-wedge salt-wedge seaward seaward (Figure (Figure8e–h). 8e– h).At highAt high water water slack, slack, during during the the neap neap tide, tide in, thein the runoff runoff main main channel channel of of Yang-Fu-Shan Yang-Fu-Shan to toZhuang-Yuan Zhuang-Yuan to Long-Wan,to Long-Wan, the the 1 PSU 1 PSU isoline isoline shifts shifts between between Zhuang-Yuan Zhuang-Yuan and Long-Wanand Long- Wan(Figure (Figure8e). At 8e). high At waterhigh water slack, slack, during during the spring the spring tide, thetide, salt-wedge the salt-wedge is more is more landward land- wardthan thethan neap the neap tide, andtide, the and head the head of the of 1 the PSU 1 PSU salinity salinity isoline isoline is about is about 1.2 km1.2 westkm west of the of theZhuang-Yuan Zhuang-Yuan (Figure (Figure8f). 8f). Since Since the the branch branch of of Yang-Fu-Shan Yang-Fu-Shan to to Wu-Niu Wu-Niu is is not not the the main main channel of runoff, the change of salt-wedge location is not obvious whether there is PRD or not (Figure8f). At low water slack, the PRD pushes the salt-wedge downstream to the sea, and the salinity value near the Qi-Li-Gang is about 2 to 3 PSU during neap tide (Figure8g). At the low water slack, under the PRD, 1 PSU salinity isoline is pushed near the Huang-Hua, except for areas with high water depth during spring tide (Figure8h). Water 2021, 13, x FOR PEER REVIEW 12 of 23

or not (Figure 8f). At low water slack, the PRD pushes the salt-wedge downstream to the sea, and the salinity value near the Qi-Li-Gang is about 2 to 3 PSU during neap tide (Figure 8g). At the low water slack, under the PRD, 1 PSU salinity isoline is pushed near the Huang-Hua, except for areas with high water depth during spring tide (Figure 8h).

3.1.2. Stratification Dyer [50] proposes a method for calculating the stratification intensity and classify- ing the mixing type called the stratification index, which is calculated by dividing the difference between surface and bottom salinity ΔS by the vertically averaged seawater salinity S . According to Dyer [50], when the stratification index is less than 0.15, it is well- mixed; the indicator is partially mixed when between 0.15 and 0.32, and stratified when greater than 0.32. Figure 9 shows a distribution of the tidally averaged stratification index Water 2021, 13, 106 on the along-channel section during spring and neap tides. The along-channel section12 se- of 23 lects the position with the largest along-channel flow velocity, while the section also covers the area where the ETM may occur. Under the low-discharge condition, since the spring tide amplitude is stronger than the neap tide, the stratification during the spring 3.1.2. Stratification tide is obviously weaker than during the neap tide. During neap tide, the stratification indexDyer is always [50] proposes greater than a method 0.32 (solid for calculating blue line in the Figure stratification 9) seaward intensity from 16.4 and classifyingkm, indi- thecating mixing that typethe water called theis stratified. stratification During index, spring which tide, is calculated the stratification by dividing index the is difference mostly betweenlower than surface 0.32 and and sometimes bottom salinity even lower∆S by than the 0.15 vertically (dashed averaged blue line seawater in Figure salinity9), indi-S. Accordingcating that tothe Dyer water [50 has], whenchanged the from stratification stratified indexduring is neap less thantide to 0.15, partially it is well-mixed; mixed or theeven indicator mixed during is partially spring mixed tide. when between 0.15 and 0.32, and stratified when greater thanUnder 0.32. Figure the PRD,9 shows the tidally a distribution averaged of stratifi the tidallycation averaged decreases stratification from the landward index onhead the along-channelto 21.7 km during section neap duringtide (the spring red solid and line neap compared tides. The to the along-channel blue solid line section in Figure selects 9) theand positionto 20.9 km with during the largestspring tide along-channel (the red dashed flow velocity,line compared while to the the section blue dashed also covers line thein Figure area where 9), but the theETM PRD maycannot occur. alter Underthe mixi theng low-dischargetype. This is because condition, the PRD since pushes the spring the tidesalt-wedge amplitude seaward, is stronger the position than thewhere neap it has tide, a thesignificant stratification stratification during at the the spring head of tide the is obviouslysalt-wedge weaker under thanthe low-discharge during the neap condition, tide. During but is neap mostly tide, covered the stratification with well-mixed index is alwaysfreshwater greater under than the 0.32 PRD (solid and bluebecomes line inmixed. Figure In9 )these seaward areas from where 16.4 the km, stratification indicating thatin- thedex waterincreases, is stratified. the maximum During stratification spring tide, index the stratificationrises from 0.76 index (solid is blue mostly line lowerin Figure than 0.329) to and0.97 sometimesduring the neap even tide lower (solid than red 0.15 line (dashed in Figure blue 9), lineand the in Figure maximum9), indicating stratification that theindex water rises has from changed 0.37 (dashed from stratified blue line duringin Figure neap 9) to tide 0.42 to during partially the mixed spring or tide even (dashed mixed duringred line spring in Figure tide. 9).

FigureFigure 9. 9.Stratiﬁcation Stratification indexindex onon the along-channel section (the (the red red line line in in Figure Figure 1b1b with with the the red red triangle triangle indicating indicating 00 km) km) duringduring neap neap tidetide (colored(colored solidsolid lines)lines) andand spring tide (colored dashed lines). lines). Black Black dashed dashed lin lineses indicate indicate the the thresholds thresholds of of 0.15 and 0.32, respectively. 0.15 and 0.32, respectively.

Under the PRD, the tidally averaged stratification decreases from the landward head to 21.7 km during neap tide (the red solid line compared to the blue solid line in Figure9) and to 20.9 km during spring tide (the red dashed line compared to the blue dashed line in Figure9), but the PRD cannot alter the mixing type. This is because the PRD pushes the salt-wedge seaward, the position where it has a significant stratification at the head of the salt-wedge under the low-discharge condition, but is mostly covered with well-mixed freshwater under the PRD and becomes mixed. In these areas where the stratification index increases, the maximum stratification index rises from 0.76 (solid blue line in Figure9) to 0.97 during the neap tide (solid red line in Figure9), and the maximum stratification index rises from 0.37 (dashed blue line in Figure9) to 0.42 during the spring tide (dashed red line in Figure9).

3.2. Estuarine Turbidity Maximum 3.2.1. Spring-Neap Modulation The distribution of the tidally averaged SSC during spring and neap tides at the bottom of the ORE is shown in Figure 10a–d. Since the most signiﬁcant part of the ETM is Water 2021, 13, x FOR PEER REVIEW 13 of 23

3.2. Estuarine Turbidity Maximum 3.2.1. Spring-Neap Modulation The distribution of the tidally averaged SSC during spring and neap tides at the bottom of the ORE is shown in Figure 10a–d. Since the most significant part of the ETM is Water 2021, 13, 106 13 of 23 located at the bottom, the location of the ETM is better reflected by the bottom SSC. Under the low-discharge condition, the ETM at the ORE is mainly located between the Yang-Fu- Shan and Long-Wan, with the core area located near Long-Wan, which is consistent with previouslocated observations at the bottom, [51]. the location The stratification of the ETM is betterinhibits reflected the vertical by the bottom diffusion SSC. and Under therefore the low-discharge condition, the ETM at the ORE is mainly located between the Yang-Fu- contributesShan and to Long-Wan, the SSC withtrapping. the core However, area located althou neargh Long-Wan, the stratification which is consistent during withneap tide is largerprevious than that observations during spring [51]. The tide, stratification the resuspended inhibits the sediment vertical diffusion caused andby the therefore tidal current decreasescontributes during to the neap SSC tide, trapping. leading However, to a smaller although core the stratificationSSC of the duringETM. During neap tide neap is tide, the largermaximum than that SSC during at the spring bottom tide, theof the resuspended ETM is sediment0.77 kg·m caused−3 (Figure by the 10a), tidal currentwhile during springdecreases tide, it during can reach neap 1.61 tide, kg·m leading−3 (Figure to a smaller 10b). core Under SSC of the the PRD, ETM. the During ETM neap shifts tide, seaward the maximum SSC at the bottom of the ETM is 0.77 kg·m−3 (Figure 10a), while during during the spring and neap tides, and the SSC of the ETM core is reduced compared to spring tide, it can reach 1.61 kg·m−3 (Figure 10b). Under the PRD, the ETM shifts seaward the low-dischargeduring the spring condition, and neap tides,as the and large the amou SSC ofnt the of ETM water core carried is reduced by the compared PRD dilutes to the ETM.the During low-discharge neap tide, condition, the area as the enclosed large amount by the of 0.55 water kg·m carried−3 SSC by theisoline PRD under dilutes the PRD is significantlyETM. During reduced neap tide, compared the area enclosedto the low-discharge by the 0.55 kg·m condition−3 SSC isoline (red under lines the in PRDFigure is 10a,c); the coresignificantly location reduced also shifts compared downstream to the low-discharge from the near condition Long-Wan (red lines (Fig inure Figure 10a) 10 a,c);to near Qi- Li-Gangthe core (Figure location 10c) also by shiftsPRD. downstreamDuring spring from tide, the nearthe area Long-Wan enclosed (Figure by the 10a) 1.35 to near kg·m−3 SSC Qi-Li-Gang (Figure 10c) by PRD. During spring tide, the area enclosed by the 1.35 kg·m−3 isoline is significantly reduced under the PRD than under the low-discharge condition SSC isoline is significantly reduced under the PRD than under the low-discharge condition (red(red lines lines in Figure in Figure 10b,d), 10b,d), and and the corecore location location of theof the ETM ETM shifts shifts about about 6 km downstream6 km downstream by theby thePRD PRD (Figure (Figure 10b,d). 10b,d).

Figure 10.Figure Distribution 10. Distribution diagram diagram of tidally of tidally averaged averaged bottom bottom SSCSSC (ﬁlled (filled contour, contour, unit: unit: kg·m kg·m−3) under−3) under (a,b) the(a,b low-discharge) the low-discharge conditioncondition and (c, andd) PRD (c,d) PRDcondition. condition. Upper Upper panels panels are are during during neapneap tide, tide and, and lower lower panels panels are during are during spring spring tide. White tide. White areas indicateareas indicate tidal flat. tidal ﬂat.

FigureFigure 11 11shows shows the the tidally tidally averagedaveraged SSC SSC (filled (filled contour contour and redand isolines) red isolines) and the and the tidally averaged salinity (blue isolines) on the along-channel section during the spring and tidallyneap averaged tides, aswell salinity as the (blue residual isolines) flow along on the the along-channel section. The residual section flow during is calculated the spring by and neapa movingtides, as average well as through the residual a time window flow along of a lunar the day.section. During The neap residual tide, under flow the is low- calculated by adischarge moving condition,average through the ETM is a located time window 15~20 km, of mainly a lunar near day. the 2~4During PSUsalinity neap tide, isolines under the low-discharge(Figure 11a). condition, Figure 11b showsthe ETM the verticalis located structure 15~20 of km, the residualmainly flow,near the the upper-layer 2~4 PSU salinity isolineswater (Figure with less 11a). salinity Figure or smaller 11b shows density the is mainly vertical seaward, structure and theof the lower-layer residual seaward flow, the up- runoff coverages with landward density-driven flow to form a stagnation point with zero per-layer water with less salinity or smaller density is mainly seaward, and the lower- residual flow velocity. The location of the ETM is near the position of the stagnation point. layerUnder seaward the PRD, runoff both coverages the locations with of thelandward ETM and density-driven the salt-wedgeshift flow towards to form the a sea,stagnation pointand with the corezero location residual of theflow ETM velocity. shifts about The 8location km downstream of the ETM (Figure is near11c). Thethe locationposition of the stagnationof the ETM point. is approximately Under the PRD, the same both as the that lo ofcations the 5~7 of PSU the salinity ETM and isolines, the whilesalt-wedge the shift towardsstagnation the sea, point and also the shifts core downstream location of near the the ETM ETM shifts (Figure about 11c,d). 8 km downstream (Figure 11c). The location of the ETM is approximately the same as that of the 5~7 PSU salinity isolines, while the stagnation point also shifts downstream near the ETM (Figure 11c,d).

Water 2021, 13, x FOR PEER REVIEW 14 of 23

The location of the ETM during spring tide is similar to that during neap tide under the low-discharge condition, which is approximately the same as the position of the 1~2 PSU salinity isolines (Figure 11e). The stagnation point during spring tide is about 8 km downstream from the position during neap tide, and this seaward movement is due to the weaker stratification during spring tide compared with neap tide and the weakening of saltwater intrusion (Figure 11f). Under the PRD, during spring tide, the core ETM shifts about 5 km towards the sea, roughly near the 1~2 PSU salinity isolines position (Figure 11g). Meanwhile, the stagnation point is about 2 km downstream compared to the low- discharge condition, roughly at the head of the 3 PSU salinity isoline (Figure 11h). It is noteworthy that there is a relatively large SSC belt (with a maximum SSC of 0.44 kg·m−3) near the upstream part of the section (0~8 km) under the PRD during neap tide (Figure 11c). The formation of this belt is mainly because the PRD inputs a high amount of sediment in a short time into the channel, while the upstream water sediment transport is too weak to immediately move it downstream, resulting in the temporary suspended sediment storage (Figure 11c). However, under the PRD, during spring tide, such characteristics are not significant (Figure 11g) because the river SSC experiment design does not take into account that the river SSC increases during PRD [33] in Run 3, and SSC during spring Water 2021, 13, 106 tide is higher than neap tide. As a result, the temporary suspended sediment14 storage of 23 is not obvious during spring tide. This will be further discussed in Section 4.2.

FigureFigure 11. (left 11. (leftpanels) panels) Tidally Tidally averaged averaged SSC SSC (red (red lines lines and filledfilled contour, contour, unit: unit: kg ·kg·mm−3)− and3) and salinity salinity (blue (blue lines, lines, unit: unit: PSU) PSU) distributiondistribution on the on thealong-channe along-channell section section during during neap neap tide ((aa,c,c)) and and during during spring spring tide tide (e,g ).(e The,g). SSCThe isSSC in 0.1is in kg ·0.1m− 3kg·m−3 intervalsintervals and andthe thesalinity salinity is is in in 1-PSU 1-PSU intervals.intervals. (right (right panels) panels Along-channel) Along-channel residual residual flow velocity flow (filledvelocity contour, (filled unit: contour, m·s−1) unit: m·s−1)distribution distribution on on the the along-channel along-channel section section during during neap tide neap (b,d )tide and ( duringb,d) and spring during tide (fspring,h). Positive tide indicates(f,h). Positive seaward. indicates seaward. The location of the ETM during spring tide is similar to that during neap tide under 3.2.2.the Sediment low-discharge Transport condition, which is approximately the same as the position of the 1~2 PSU salinity isolines (Figure 11e). The stagnation point during spring tide is about 8 km downstreamThe mean from SSC theflux position through during a unit-width neap tide, cross and this section seaward can movement be calculated is due as to the weaker stratification during spring tide compared with neap tide and the weakening of saltwater intrusion (Figure 11f). Under the PRD, during spring tide, the core ETM shifts about 5 km towards the sea, roughly near the 1~2 PSU salinity isolines position (Figure 11g). Meanwhile, the stagnation point is about 2 km downstream compared to the low-discharge condition, roughly at the head of the 3 PSU salinity isoline (Figure 11h). It is noteworthy that there is a relatively large SSC belt (with a maximum SSC of 0.44 kg·m−3) near the upstream part of the section (0~8 km) under the PRD during neap tide (Figure 11c). The formation of this belt is mainly because the PRD inputs a high amount of sediment in a short time into the channel, while the upstream water sediment transport is too weak to immediately move it downstream, resulting in the temporary suspended sediment storage (Figure 11c). However, under the PRD, during spring tide, such characteristics are not significant (Figure 11g) because the river SSC experiment design does not take into account that the river SSC increases during PRD [33] in Run 3, and SSC during spring tide is higher than neap tide. As a result, the temporary suspended sediment storage is not obvious during spring tide. This will be further discussed in Section 4.2. Water 2021, 13, 106 15 of 23

3.2.2. Sediment Transport The mean SSC ﬂux through a unit-width cross section can be calculated as

1 Z T Z h T0 = Ucdzdt (16) T 0 0 where T is one or more tidal cycles, U is the horizontal ﬂow vector, c is the SSC, h is the depth of water which changes with the tide level, and z is the vertical coordinate depth (0 for the bottom; h for the surface). Uncles and Jordan [52] suggested that the factors in Equation (16) can be decomposed into h = h0 + ht (17) 0 U = U0 + Ut + U (18) 0 c = c0 + ct + c (19) where the subscript “0” represents the tidally averaged value, the subscript “t” denotes the deviations from the tidally averaged value, a bar denotes a depth-mean value, and a prime denotes the deviations from the depth-mean value. Thus, Equation (16) can be rewritten as

D 0 0E T0 = h0U0c0 + c0 htUt + hUtct + Uthhtcti + hU c (20) | {z } | {z } | {z } T1 | {z } T2 T3 T4

where T0 is the net sediment transport, T1 represents the Eulerian transport, the tidally averaged SSC transport by the Eulerian residual flow, and T2 represents the Stokes-drift transport. T3 represents the coupling between the SSC and the hydrodynamics, which changes with the tide. This is because the phase of water depth, flow, and SSC are not fully orthogonal with the changes of tide, i.e., the tidal pumping effect. T4 represents the transport of SSC caused by coupling between the vertical shear of the flow and the vertical difference of the SSC. T1 and T2 are together known as Lagrangian transport. During both spring and neap tides, the sediment transport is mainly controlled by the Eulerian transport and the Stokes-drift transport. Figure 12 shows the mean suspended sediment flux through a unit-width along the section. Under the low-discharge condition, during neap tide, sediment transport is generally seaward from the landward head to 26 km, while on the remaining part of the section, sediment transport is mostly landward, together forming a convergence area of sediment transport around 26 km (red line in Figure 12a). The sediment transport T0 magnitude is 0~0.67 kg·s−1·m−1, and the Eulerian transport T1 magnitude is 0~0.77 kg·s−1·m−1, which is the largest component. In addition, the T2 magnitude is 0.03~0.12 kg·s−1·m−1, the T3 magnitude is 0~0.08 kg·s−1·m−1, and the T4 magnitude is 0~0.04 kg·s−1·m−1 (Figure 12a). Similar to neap tide, sediment transport converges around approximately 23 km during spring tide (Figure 12b). During spring tide, the sediment transport T0 magnitude is 0~3.34 kg·s−1·m−1, and the Eulerian transport T1 magnitude is 0~3.62 kg·s−1·m−1, which is also the largest part of the magnitude. In addition, the T2 magnitude is 0.22~0.80 kg·s−1·m−1, the T3 magnitude is 0~0.48 kg·s−1·m−1, and the T4 magnitude is 0~0.13 kg·s−1·m−1 (Figure 12b). During both the spring and neap tides, the convergence area of sediment transport is generally downstream from the position of the ETM and stagnation point (Figure 11). Because Equation (16) calculates the vertical averaged sediment transport, and the largest part of the SSC in the ETM is near the bottom, the area of the vertical averaged sediment transport convergence and the ETM position will not be accurately consistent. Additionally, Stokes-drift transport is always landward. The landward sediment transport during spring tide (seaward from 23 km) is mainly attributed to Stokes-drift transport (Figure 12b). Water 2021, 13, x FOR PEER REVIEW 16 of 23

the magnitude of T0 is 0~1.50 kg·s−1·m−1 during neap tide, and the magnitude of T0 is 0~3.76 kg·s−1·m−1 during spring tide (Figure 12c,d). It is noteworthy that the maximum net sediment transport during neap tide under the PRD is 0~8 km on the along-channel section, which is different from that under the low-discharge condition (Figure 12c). Consid- ering the temporary suspended sediment storage (Figure 11e), on the along-channel section at 0~8 km, the PRD increases the average sediment transport from 0.40 kg·s−1·m−1 un- Water 2021, 13, 106 16 of 23 der the low-discharge condition to 0.91 kg·s−1·m−1. Meanwhile, it more easily transports the stored suspended sediment downstream (Figure 12c).

FigureFigure 12. Tidally 12. Tidally averaged averaged SSC SSC transport transport and and its its decomposed decomposed terms onon the the along-channel along-channel section section under under (a,b )(a the,b) low- the low- dischargedischarge condition condition and and (c,d ()c ,PRDd) PRD condition. condition. Upper Upper panels panels are are during neap neap tide, tide, and and lower lower panels panels are are during during spring spring tide. tide. PositivePositive value value means means seaward seaward transport. transport.

4. DiscussionIn general, the PRD drives the Eulerian transport (T1) seaward, and by contrast, the changes of the remaining terms are not signiﬁcant, so the pattern of the main control 4.1. Sediment Source to Form ETM sediment transport mechanism remains the same (Figure 12). For example, under the PRD, theThe magnitude suspended of T0 sediment is 0~1.50 from kg·s− river1·m−1 dischargeduring neap cannot tide, andaffect the the magnitude location ofof T0ETM. is Re- sults0~3.76 (Section kg·s− 13,·m Figure−1 during 11) spring indicate tide that (Figure ET 12Msc,d). are It isin noteworthy similar positions that the maximumand have net similar responsesediment characteristics transport during to neap PRD tide during under theneap PRD and is 0~8 spring km on tides. the along-channel However, section,the ETM is strongerwhich isin differentspring tide from and that is under thus thediscussed low-discharge further. condition Figure (Figure13 shows 12c). a Consideringtidally averaged SSCthe distribution temporary suspendedwith the same sediment total storage amount (Figure of PRD 11e), but on under the along-channel different PRD section durations at 0~8 km, the PRD increases the average sediment transport from 0.40 kg·s−1·m−1 under and under a low-discharge condition, without taking into account the river SSC. Under the low-discharge condition to 0.91 kg·s−1·m−1. Meanwhile, it more easily transports the thestored low-discharge suspended condition, sediment downstream when the river (Figure is 12 noc). longer supplying sediment, the ETM position (Figure 13a) is similar to when the river is supplying sediment (Run 1, Figure 11e),4. Discussionlocated at approximately 15~20 km of the section. However, the SSC of the ETM without4.1. Sediment river suspended Source to Form sediment ETM supply is lower than that with river suspended sediment supply.The suspended Taking the sediment ETM fromcore riveras an discharge example, cannot the SSC affect at thethe locationcore with of ETM.river sus- pendedResults sediment (Section3 supply, Figure (Run11) indicate 1) can that reach ETMs 1.55 are kg·m in similar−3 (Figure positions 11a), and while have the similar SSC of the ETMresponse core without characteristics river suspended to PRD during sediment neap supply and spring (Run tides. 4) decreases However, to 1.38 the ETMkg·m is−3 (Fig- urestronger 13a). It inindicates spring tide the andsediment is thus discussedsource of further.ETM in Figure the Ou 13 River shows is a mainly tidally averagedderived from SSC distribution with the same total amount of PRD but under different PRD durations the resuspension of the seabed. and under a low-discharge condition, without taking into account the river SSC. Under the low-discharge condition, when the river is no longer supplying sediment, the ETM position (Figure 13a) is similar to when the river is supplying sediment (Run 1, Figure 11e), located at approximately 15~20 km of the section. However, the SSC of the ETM without river suspended sediment supply is lower than that with river suspended sediment supply. Taking the ETM core as an example, the SSC at the core with river suspended sediment supply (Run 1) can reach 1.55 kg·m−3 (Figure 11a), while the SSC of the ETM core without river suspended sediment supply (Run 4) decreases to 1.38 kg·m−3 (Figure 13a). It indicates the sediment source of ETM in the Ou River is mainly derived from the resuspension of the seabed.

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FigureFigure 13. Tidally 13. Tidally averaged averaged SSC SSC (red (red lines lines and and filled ﬁlled contour, unit: unit: kg kg·m·m−3−)3) and and salinity salinity (blue (blue lines, lines, unit: unit: PSU) PSU) distribution distribution on theon along-channel the along-channel section section during during spring spring tide tide when when river river SSC SSC is is set set to 0 under ((aa)) the the low-discharge low-discharge condition, condition, (b) ( ab) a 2- day-PRD2-day-PRD duration, duration, (c) a (3-day-PRDc) a 3-day-PRD duration duration and and (d (d) )a a 4-day-PRD 4-day-PRD duration.duration. The The SSC SSC is in is 0.1 in kg0.1·m kg·m−3 intervals−3 intervals and the and the salinitysalinity is in is1-PSU in 1-PSU intervals. intervals.

TheThe large large amount amount of of water water broughtbrought by by the the PRD PRD has has two two effects effects on ETM: on ETM: (1) the (1) water the water broughtbrought by by the the PRD PRD into into the seasea dilutesdilutes the the ETM; ETM; (2) (2) that that water water can can change change the water the water velocityvelocity and and then then change change the bottom shear shear stress, stress, such such that that the the seabed seabed may may provide provide more more suspended sediment into the water. Taking a peak discharge of the PRD with 5000 m3·s−1 suspended sediment into the water. Taking a peak discharge of the PRD with 5000 m3·s−1 (return period is about 170 years) as an example, while the PRD pushes both the ETM (returnandsalt-wedge period is about seaward, 170 years) the SSC as of an the example, ETM core while is reduced the PRD to pushes 1.16 kg both·m−3 the(Run ETM 5, and salt-wedgeFigure 13 b)seaward,compared the with SSC that of the under ETM the core low-discharge is reduced conditionto 1.16 kg·m (Run−3 (Run 4, Figure 5, Figure 13a). 13b) comparedFigure 14 with shows that the under bottom the shear low-discharge stress, and the condition net sediment (Run flux 4,E bFigurewhich 13a). represents Figure 14 showsthe SSC the fluxbottom of the shear seabed, stress, under and the the low-discharge net sediment condition flux Eb (Runwhich 4) andrepresents the PRD the condi- SSC flux of tionthe seabed, (Run 5) withoutunder the river low-discharge suspended sediment condition supply (Run during 4) and the the PRD. PRD PRD condition decreases (Run 5) withoutboth the river bottom suspended shear stress sediment and the supply net sediment during flux theEb PRD.during PRD flood decreases tide and increases both the bot- them during ebb tide (Figure 14). During the 2-day PRD, the average net sediment flux tom shear stress and the net sediment flux Eb during flood tide and increases them during of Run 5 is 4.84 × 10−5 kg·m−2·s−1 (Figure 14d) on the along-channel section, which in- ebb tide (Figure 14). During the 2-day PRD, the average net sediment flux of Run 5 is 4.84 creases compared with that under the low-discharge condition (Run 4, Figure 14b) of −5 −2 −1 × 104.52 kg·m× 10−s5 kg (Figure·m−2·s− 14d)1, indicating on the along-channel that the seabed section, resuspends which more increases SSC to compared the water with thatduring under the the PRD. low-discharge This has also beencondition observed (Run in Delaware4, Figure River 14b) Estuary,of 4.52 Trenton,× 10−5 kg·m New−2 Jer-s−1, indi- catingsey, USA,that the by Sommerfieldseabed resusp andends Wong more [53 ]SSC that to during the water a PRD during the seabed the PRD. can be This eroded has also beenmore observed severe, whichin Delaware can last forRiver several Estuary, tidal cycles.Trenton, The New white Jersey, dashed USA, lines inby Figure Sommerfield 14 andindicate Wong the [53] ETM that location during under a PRD the the low-discharge seabed can condition. be eroded The more strongest severe, seabed which resus- can last forpension several area, tidal providing cycles. The the largest white SSC dashed into water, lines isin not Figure located 14 where indicate theETM the developsETM location under(Figure the 14 low-discharge). This suggests condition. that the SSC The resuspended strongest seabed from seabed resuspension needs to bearea, transported providing the by the estuarine circulation to develop the ETM. The difference in bottom shear stress largest SSC into water, is not located where the ETM develops (Figure 14). This suggests caused by different PRDs is another factor affecting the ETM. Generally, when the PRD thatpeak the dischargeSSC resuspended is smaller, from the ETM seabed is more needs landward. to be transported When the by total the volume estuarine of PRD circulation is to thedevelop same, the the durationETM. The is longer,difference and thein botto peakm discharge shear stress is smaller. caused The by total different amount PRDs of is anotherPRD in factor Figure affecting 13c,d is equalthe ETM. to that Generally, in Figure 13whenb; meanwhile, the PRD peak the PRD discharge in Run 6is lasts smaller, for the ETM3 days is more (Figure landward. 13c) and When the PRD the in total Run volume 7 lasts for of 4PRD days is (Figurethe same, 13d). the Taking duration the SSCis longer, andisolines the peak of 0.6~1.0 discharge kg·m is−3 smaller.in Figure The 13b–d total as indicators,amount of the PRD ETM in becomesFigure 13c,d more is landward equal to that in asFigure peak 13b; discharge meanwhile, decreases. the Meanwhile, PRD in Run the 6 SSC lasts at thefor core3 days of the (Figure ETM varies13c) and according the PRD in Runto 7 different lasts for PRD 4 days durations. (Figure The13d). SSC Taking at the the core SSC of isolines the ETM of during 0.6~1.0 3-day kg·m PRD−3 in (RunFigure 6, 13b– Figure 13c) is slightly lower than that during 2-day PRD (Run 5, Figure 13b) and 4-day d as indicators, the ETM becomes more landward as peak discharge decreases. Mean- PRD (Run 7, Figure 13d), but with a difference of less than 0.02 kg m−3. while, the SSC at the core of the ETM varies according to different PRD durations. The SSC at the core of the ETM during 3-day PRD (Run 6, Figure 13c) is slightly lower than that during 2-day PRD (Run 5, Figure 13b) and 4-day PRD (Run 7, Figure 13d), but with a difference of less than 0.02 kg m−3.

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FigureFigure 14. Time 14. Time series series diagram diagram of of(left) (left) bottom bottom shear shear stress (filled(filled contour, contour, unit: unit: N· mN·m−2)− and2) and (right) (right) net net sediment sediment flux (filledflux (filled contour,contour, unit: unit: ×10−×4 kg·m10−4 kg−2s·−m1) −on2·s the−1) onalong-channel the along-channel section section during during spring spring tide tide when when river river SSC SSC is is set set to 00 underunder ( a(,ac),c) the low-dischargethe low-discharge condition condition and (b, andd) a ( b2-day,d) a 2-dayPRD. PRD.White White dashed dashed lines lines indicate indicate ETM ETM location location under under the the low-discharge low-discharge condition.condition. Shadows Shadows indicate indicate flood tide. flood tide.

4.2. ETM Recovery Time 4.2. ETM Recovery Time PRDPRD imports imports a ahigh high amount amount ofof suspendedsuspended sediment sediment in ain short a short time time and and the upstream the upstream waterwater sediment sediment transport transport is is too too weak weak to to move move it it seaward seaward in time. As a result, thethe sedi-sediment broughtment broughtby the byPRD the is PRD temporarily is temporarily stored stored in the in the upstream upstream channel. channel. Subsequently, Subsequently, this sedimentthis sediment can be can transported be transported downstream downstream by by estuarine estuarine circulation. circulation. Figure 15 15 shows shows the recoverythe recovery of the of stored the stored suspended suspended sediment sediment in in the the channel channel with PRDPRD with with a rivera river SSC SSC of −3 3 −1 0.4of kg·m 0.4 kg−3 ·andm aand peak a peak discharge discharge of of5000 5000 m m3·s−·1s (Run(Run 12). 12). Since Since the the river river SSCSSCis is set set to to the multiyearthe multiyear plum-rainy/typhoon plum-rainy/typhoon season season average, average, it is it isdifficult difficult to to distinguish distinguish the storedstored sus- suspended sediment in the channel during the spring tide with PRD (Run 3, Figure 11g). pended sediment in the channel during the spring tide with PRD (Run 3, Figure 11g). Previous work [33] on the river SSC of the Ou River during flooding shows that the river PreviousSSC during work PRD [33] can on bethe an river order SSC greater of the than Ou the River average. during Therefore, flooding despite shows the that lack the of river SSCriver during SSC measurementPRD can be an during order PRD, greater in the than experiment the average. design, Therefore, it is reasonable despite to set the the lack of riverriver SSC SSC measurement during PRD as during twice thePRD, multiyear in the expe plum-rainy/typhoonriment design, it season is reasonable average. to The set the riverdistribution SSC during of tidally PRD averagedas twice SSCthe multiyear during PRD plum-rainy/typhoon with enhanced river SSCseason is shown average. in The distributionFigure 15a. ofCompared tidally averag to the 5000ed SSC m3 ·sduring−1 peak PRD discharge with PRDenha withoutnced river river SSC suspended is shown in Figuresediment 15a. supplyCompared (Run 5,to Figurethe 5000 13b), m the3·s− SSC1 peak of thedischarge ETM core PRD with without river suspended river suspended sed- sedimentiment supply supply (Run (Run 12, 5, Figure Figure 15 13b),a) is higher,the SSC and of thethelocation ETM core is closer with toriver the suspended location of sed- imentthe ETMsupply under (Run the 12, low-discharge Figure 15a) is condition higher, (Runand the 1, Figure location 11e). is Additionally,closer to the sedimentlocation of the storage occurs at 0~5 km of the along-channel section in Run 12 (Figure 15a), but does not ETMoccur under in Run the 5 low-discharge without river suspended condition sediment (Run 1, supply Figure (Figure 11e). Additionally,13b), which has sediment the same stor- agePRD occurs volume at 0~5 as Run km 12, of indicatingthe along-channel that the sediment section storage in Run is due12 (Figure to the river 15a), suspended but does not occursediment in Run supply. 5 without One river day after suspended the PRD, sediment the stored supply suspended (Figure sediment 13b), nearwhich the has section the same PRDlandward volume side as Run is gradually 12, indicating transported that downstream,the sediment and storage the ETM is due and to salt-wedge the river suspended move sedimentupstream supply. by the density-drivenOne day after flowthe PRD, (Figure the 15 b).stored The storedsuspended suspended sediment sediment near and the the section landwardETM converge side is at gradually the location transported of the ETM underdownstream, the low-discharge and the ETM condition, and salt-wedge at which mo- move upstreamment, the by SSC the of density-driven the ETM core is stillflow smaller (Figur thane 15b). that The under stored the low-discharge suspended conditionsediment and the(Figure ETM converge 11e) but in at the the same location order of (2 the days ETM after under the PRD, the low-discharge Figure 15c). Subsequently, condition, at the which SSC of the ETM core gradually increases to the value under the low-discharge condition moment, the SSC of the ETM core is still smaller than that under the low-discharge con- and eventually recovers to normal. For example, in Run 12, the SSC of the ETM core 3 days ditionafter (Figure the PRD 11e) is close but toin thethe SSC same under order the (2 low-discharge days after the condition PRD, Figure (Figure 15c). 15d). Subsequently, the SSC of the ETM core gradually increases to the value under the low-discharge condition and eventually recovers to normal. For example, in Run 12, the SSC of the ETM core 3 days after the PRD is close to the SSC under the low-discharge condition (Figure 15d).

Water 2021, 13, x FOR PEER REVIEW 19 of 23 Water 2021, 13, 106 19 of 23

FigureFigure 15. Tidally 15. Tidally averaged averaged SSC SSC (red (red lines lines and and filled ﬁlled contour, unit: unit: kg kg·m·m−3−)3) and and salinity salinity (blue (blue lines, lines, unit: unit: PSU) PSU) distribution distribution on theon along-channel the along-channel section section duri duringng spring spring tide tide with with the the 5000 5000 m m33·s·s−−1 1peakpeak discharge discharge PRD whenwhenthe the river river SSC SSC is is set set to to 0.4 kg·m−0.43 (Run kg·m 12),−3 (Run and 12),the tidal and the cycle tidal is cycle(a) the is last (a) the during last during PRD, ( PRD,b) a day (b) a later day laterthan than(a), ( (ca)), two (c) twodays days later later than than (a), ( aand), (d) three anddays (d later) three than days (a later). The than SSC (a). is The in 0.1 SSC kg·m is in− 0.13 intervals, kg·m−3 intervals, and the andsalinity the salinity is in 1-PSU is in 1-PSU intervals. intervals.

In InEquation Equation (14), thethe NSE, NSE, which which is closer is closer to 1, the to precision1, the precision of the simulation of the issimulation higher, is higher,is used is toused evaluate to evaluate the ETM the recovery ETM including recovery both including position both and magnitude.position and When magnitude. the observation value Xobs and the simulation value Xmodel in Equation (14) are replaced by When the observation value Xobs and the simulation value Xmodel in Equation (14) are re- the tidally averaged SSC value on each vertical layer under the low-discharge condition placedand theby PRD,the tidally respectively, averaged the NSE SSC indicates value on a measureeach vertical for the layer recovery under of thethe ETM low-discharge from conditionthe disturbed and the state PRD, by the respectively, PRD to the low-dischargethe NSE indicates condition. a measure When thefor NSE the recovery calculated of the ETMafter from the PRDthe disturbed is close enough state by to 1,the the PRD ETM to affectedthe low-discharge by the PRD iscondition. considered When to have the NSE calculatedrecovered after to the the low-discharge PRD is close condition.enough to To1, the determine ETM affected the effect by of the river PRD suspended is considered to sedimenthave recovered supply onto the recovery low-discharge time, Figure condit 16a showsion. To the determine NSE after the the differenteffect of peakriver sus- pendeddischarge sediment PRDs (2-daysupply duration) on recovery without time, river Fi suspendedgure 16a shows sediment the supplyNSE after (Runs the 5 anddifferent peak8~10); discharge Figure PRDs16b is (2-day similar duration) to Figure 16 witha, butout the river PRD suspended has river suspendedsediment supply sediment (Runs 5 andsupply 8~10); (Runs Figure 11~14). 16b is Comparisons similar to Figure of these 16a, experimental but the PRD results has showriver thatsuspended whether sediment the river suspended sediment supply or not, the NSE affected by PRD initially decreases from supply (Runs 11~14). Comparisons of these experimental results show that whether the 1 and then gradually increases after the end of the PRD (Figure 16). The NSE increases riverslowly suspended after it reaches sediment 0.90, supply so 0.90 isor taken not, asthe the NSE threshold affected to determineby PRD initially whether decreases or not the from 1 andETM then recovers gradually to a low-discharge increases after condition the end (Figure of the 16 ).PRD Table (Figure5 shows 16). the ETMThe NSE recovery increases slowlytime after differentit reaches peak 0.90, discharge so 0.90 is PRDs, taken with as the and threshold without river to determine suspended whether sediment or not thesupply. ETM recovers Under the to river a low-discharge without suspended conditio sedimentn (Figure supply, 16). the Table recovery 5 shows time ofthe the ETM ETM recov- − eryis time 111.8~142.8 after different h after the peak 2500~10,000 discharge m PRDs3·s 1 peak, with discharge and without PRDs. river Generally, suspended the larger sediment supply.the peak Under discharge the river is, the without longer thesuspended recovery timesediment will be. supply, However, the the recovery recovery time time of the ETMincreases is 111.8~142.8 slowly after h after the peak the discharge2500~10,000 reaches m3·s a− threshold.1 peak discharge For example, PRDs. the Generally, recovery the times of Run 9 and Run 10 are similar (Table5). The river can supply the sediment to the larger the peak discharge is, the longer the recovery time will be. However, the recovery diluted ETM and reduce the recovery time. Under the river with suspended sediment timesupply, increases the recovery slowly timeafter of the the peak ETM discharge is 85.0~110.7 reaches h after a the threshold. 2500~10,000 For mexample,3·s−1 peak the re- coverydischarge times PRDs. of Run Meanwhile, 9 and Run the 10 recovery are similar time (Table with river 5). The suspended river can sediment supply supply the sediment is to shorterthe diluted than thatETM without and reduce river suspended the recovery sediment time. supply Under (Table the5 ).river Figure with 16b suspended shows that sedi- mentNSE supply, has a larger the recovery ﬂuctuation time during of the the ETM PRD (0~48is 85.0~110.7 h) than that h after after the the 2500~10,000 end of PRD, exceptm3·s−1 peak dischargefor Run 11PRDs. due toMeanwhile, the small peak the discharge.recovery time This with suggests river that suspended the suspended sediment sediment supply is shortersupplied than by that PRD without contributes river to thesuspended increase of se NSEdiment to 1 orsupply a reduction (Table in the5). recoveryFigure 16b time shows thatof NSE the ETM. has a In larger addition, fluctuation previous studiesduring also the foundPRD (0~48 that the h) spring-neap than that after modulation the end [31 of] PRD, and the antecedent discharge conditions [30] may affect the ETM recovery time through except for Run 11 due to the small peak discharge. This suggests that the suspended sed- affecting the salinity distribution. iment supplied by PRD contributes to the increase of NSE to 1 or a reduction in the recovery time of the ETM. In addition, previous studies also found that the spring-neap modulation [31] and the antecedent discharge conditions [30] may affect the ETM recovery time through affecting the salinity distribution.

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Figure 16. Recovery times of the ETM indicated by the NSE when (a) the river SSC is set to 0 and (b) the river SSC is set to −3 0.4 kg·m kg·m−.3 Dashed. Dashed lines lines indicate indicate 0.90. 0.90. Note Note the the vertical vertical axis axis range range differs. differs.

Table 5. Recovery time (unit: hour) of the ETM after PRD with peak discharge (unit: m3·s−1) shown Table 5. Recovery time (unit: hour) of the ETM after PRD with peak discharge (unit: m3·s−1) shown in the parentheses. in the parentheses. Run 8 Run 5 Run 9 Run 10 RiverRiver SSC SSC during during PRD PRD (kg·m−3) Run 8 Run 5 Run 9 Run 10 (kg·m−3) (2500)(2500) (5000)(5000) (7500)(7500) (10,000)(10,000) 0 111.8 138.7 142.7 142.8 0 111.8 138.7 142.7 142.8 Run 11 Run 12 Run 13 Run 14 RiverRiver SSC SSC during during PRD PRD (kg·m−3) Run 11 Run 12 Run 13 Run 14 (kg·m−3) (2500)(2500) (5000)(5000) (7500)(7500) (10,000)(10,000) 0.4 85.0 94.7 97.3 110.7 0.4 85.0 94.7 97.3 110.7 5. Conclusions 5. Conclusions Small/medium-sized rivers are more likely to have PRDs during the plum-rainy/ty- Small/medium-sized rivers are more likely to have PRDs during the plum-rainy/typhoon phoon season, which becomes important to study its impact on the hydrodynamic and season, which becomes important to study its impact on the hydrodynamic and sediment sediment dynamics as the global warming-induced inundation risks rise and terrestrial dynamics as the global warming-induced inundation risks rise and terrestrial sediment sediment sequestration increases. Based on some in-situ measurements including tidal el- sequestration increases. Based on some in-situ measurements including tidal elevation, evation, tidal current, salinity, and SSC, the numerical model of the ORE is validated. tidal current, salinity, and SSC, the numerical model of the ORE is validated. Under the low-discharge condition, the stratification during spring tide is obviously Under the low-discharge condition, the stratification during spring tide is obviously weaker than that during neap tide, and the PRD generally makes the stratification weaker than that during neap tide, and the PRD generally makes the stratification stronger. stronger. During spring tide, the turbidity maximum in the ORE is larger than that during During spring tide, the turbidity maximum in the ORE is larger than that during neap tide. neap tide. Although stronger stratification during neap tide would facilitate sediment Although stronger stratification during neap tide would facilitate sediment trapping, the trapping,stronger tidal the stronger current during tidal current spring tideduring resuspended spring tide more resuspended sediment than more that sediment during neapthan thattide. during In addition, neap tide. the positionsIn addition, of thethe ETMpositi duringons of the spring ETM tide during and neapspring tide tide are and similar. neap tideWhile are the similar. PRD pushesWhile the the PRD ETM pushes downstream, the ETM it alsodownstream, dilutes the it ETMalso dilutes by bringing the ETM a large by bringingamount ofa large water. amount of water. Based on on the the mechanism mechanism decomposition decomposition of ofsediment sediment transport, transport, during during both both neap neap and springand spring tides, tides, the sediment the sediment transport transport is most isly mostly induced induced by Eulerian by Eulerian transport transport and Stokes- and driftStokes-drift transport. transport. Generally, Generally, the PRD the drives PRD drivesan additional an additional seaward seaward Eulerian Eulerian transport transport sea- seaward, and by contrast, the changes of the remaining terms are not significant and the

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pattern of the main control sediment transport mechanism remains unchanged. As a result, the ETM in the ORE is generally induced by residual current, or the sediment convergence of the seaward river flow and landward density-driven flow. The sediment source of the ETM in the ORE is mainly derived from the sediment resuspension from the seabed. The PRD changes the bottom shear stress, so that the seabed can provide more suspended sediment into the water. In addition, the suspended sediment brought by the PRD contributes to the recovery of the diluted ETM after the PRD, or the ETM affected by the PRD can recover to a low- discharge condition more quickly. The suspended sediment brought by the PRD will be temporarily stored in the upstream channel, because the upstream water sediment transport is too weak to move it downstream in time. Subsequently, this stored sediment can be transported downstream by estuarine circulation. With river suspended sediment supply, the recovery times are 85.0~110.7 h under PRDs with a peak discharge of 2500~10,000 m3·s−1, and the larger the peak discharge is, the longer the recovery time will be. Since the vertical mixing during neap tide is weaker than that during spring tide, we speculate that the ETM recovery time to PRD is slightly longer than that during spring tide. The morphological evolution of small/medium- sized river estuaries due to extreme weather conditions is not yet sufficiently understood. Therefore, the impact of the PRD on the morphological evolution, the transport, and the fate of the Ou River’s watershed suspended particulate matter in the ORE or the East China Sea will be further explored.

Author Contributions: Conceptualization, D.S.; methodology, Y.Y. and D.S.; writing—original draft preparation, Y.Y.; writing—review and editing, D.S. and N.W.; supervision, X.B. All authors have read and agreed to the published version of the manuscript. Funding: This research is funded by National Natural Science Foundation of China (Grant No. 41876088), Shandong Provincial Natural Science Foundation, China (Grant No. ZR2019MD010) and Fundamen- tal Research Funds for the Central Universities, China (Grant No. 201913020). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Geyer, W.R.; MacCready, P. The estuarine circulation. Annu. Rev. Fluid Mech. 2014, 46, 175–197. [CrossRef] 2. Maccready, P.; Geyer, W.R. Advances in estuarine physics. Annu. Rev. Mar. Sci. 2012, 2, 35–58. [CrossRef][PubMed] 3. Burchard, H.; Schuttelaars, H.M.; Ralston, D.K. Sediment Trapping in Estuaries. Annu. Rev. Mar. Sci. 2018, 10, 371–395. [CrossRef] [PubMed] 4. Milliman, J.D. Sediment discharge to the ocean from small mountainous rivers: The New Guinea example. Geo Mar. Lett. 1995, 15, 127–133. [CrossRef] 5. Hibma, A.; Schuttelaars, H.M.; de Vriend, H.J. Initial formation and long-term evolution of channel-shoal patterns. Cont. Shelf Res. 2004, 24, 1637–1650. [CrossRef] 6. Xie, D.; Pan, C.; Gao, S.; Wang, Z.B. Morphodynamics of the Qiantang Estuary, China: Controls of river flood events and tidal bores. Mar. Geol. 2018, 406, 27–33. [CrossRef] 7. Olabarrieta, M.; Geyer, W.R.; Coco, G.; Friedrichs, C.T.; Cao, Z. Effects of density-driven flows on the long-term morphodynamic evolution of funnel-shaped estuaries. J. Geophys. Res. Earth 2018, 123, 2901–2924. [CrossRef] 8. Rodrigues, M.; Fortunato, A.B.; Freire, P. Saltwater intrusion in the upper Tagus Estuary during droughts. Geosciences 2019, 9, 400. [CrossRef] 9. Weng, X.; Jiang, C.; Zhang, M.; Yuan, M.; Zeng, T. Numeric Study on the Influence of Sluice-Gate Operation on Salinity, Nutrients and Organisms in the Jiaojiang River Estuary, China. Water 2020, 12, 2026. [CrossRef] 10. Hirabayashi, Y.; Mahendran, R.; Koirala, S.; Konoshima, L.; Yamazaki, D.; Watanabe, S.; Kim, H.; Kanae, S. Global flood risk under climate change. Nat. Clim. Chang. 2013, 3, 816–821. [CrossRef] 11. Schubel, J.R. Turbidity maximum of the northern Chesapeake Bay. Science 1968, 161, 1013–1015. [CrossRef][PubMed] 12. Meade, R.H. Landward transport of bottom sediments in estuaries of the Atlantic coastal plain. J. Sediment Res. 1969, 39, 222–234. Water 2021, 13, 106 22 of 23

13. Song, D.; Wang, X.H.; Kiss, A.E.; Bao, X. The contribution to tidal asymmetry by different combinations of tidal constituents. J. Geophys. Res. Oceans 2011, 116, C12007. [CrossRef] 14. Uncles, R.J.; Elliott, R.C.A.; Weston, S.A. Dispersion of salt and suspended sediment in a partly mixed estuary. Estuaries 1985, 8, 256–269. [CrossRef] 15. Postma, H. Transport and accumulation of suspended matter in the Dutch Wadden Sea. Neth. J. Sea Res. 1961, 1, 148–190. [CrossRef] 16. Jay, D.A.; Musiak, J.D. Particle trapping in estuarine tidal flows. J. Geophys. Res. Oceans 1994, 99, 20445–20461. [CrossRef] 17. Geyer, W.R. The importance of suppression of turbulence by stratification on the estuarine turbidity maximum. Estuaries 1993, 16, 113–125. [CrossRef] 18. Bartholdy, J. Processes controlling import of fine-grained sediment to tidal areas: A simulation model. In Coastal and Estuarine Environments: Sedimentology, Geomorphology and Geoarchaeology; Pye, K., Allen, J.R.L., Eds.; Special Publications of the Geological Society: London, UK, 2000; Volume 175, pp. 13–29. 19. Burchard, H.; Flöser, G.; Staneva, J.V.; Badewien, T.H.; Riethmüller, R. Impact of density gradients on net sediment transport into the Wadden Sea. J. Phys. Oceanogr. 2008, 38, 566–587. [CrossRef] 20. Scully, M.E.; Friedrichs, C.T. Sediment pumping by tidal asymmetry in a partially mixed estuary. J. Geophys. Res. Oceans 2007, 112, C07028. [CrossRef] 21. Winterwerp, J.C. Fine sediment transport by tidal asymmetry in the high-concentrated Ems River: Indications for a regime shift in response to channel deepening. Ocean Dyn. 2011, 61, 203–215. [CrossRef] 22. Ralston, D.K.; Geyer, W.R.; Warner, J.C. Bathymetric controls on sediment transport in the Hudson River estuary: Lateral asymmetry and frontal trapping. J. Geophys. Res. Oceans 2012, 117, C10013. [CrossRef] 23. Hudson, A.S.; Talke, S.A.; Jay, D.A. Using satellite observations to characterize the response of estuarine turbidity maxima to external forcing. Estuar. Coast. 2017, 40, 343–358. [CrossRef] 24. Fugate, D.C.; Friedrichs, C.T.; Sanford, L.P. Lateral dynamics and associated transport of sediment in the upper reaches of a partially mixed estuary, Chesapeake Bay, USA. Cont. Shelf Res. 2007, 27, 679–698. [CrossRef] 25. McSweeney, J.M.; Chant, R.J.; Sommerfield, C.K. Lateral variability of sediment transport in the Delaware Estuary. J. Geophys. Res. Oceans 2016, 121, 725–744. [CrossRef] 26. Le Hir, P.; Ficht, A.; Jacinto, R.S.; Lesueur, P.; Dupont, J.-P.; Lafite, R.; Brenon, I.; Thouvenin, B.; Cugier, P. Fine sediment transport and accumulations at the mouth of the Seine estuary (France). Estuaries 2001, 24, 950–963. [CrossRef] 27. Traykovski, P.; Geyer, R.; Sommerfield, C. Rapid sediment deposition and fine-scale strata formation in the Hudson estuary. J. Geophys. Res. Earth 2004, 109, F02004. [CrossRef] 28. Mitchell, S.; Akesson, L.; Uncles, R. Observations of turbidity in the Thames Estuary, United Kingdom. Water Environ. J. 2012, 26, 511–520. [CrossRef] 29. Song, D.; Wang, X.H.; Cao, Z.; Guan, W. Suspended sediment transport in the Deepwater Navigation Channel, Yangtze River Estuary, China, in the dry season 2009: 1. Observations over spring and neap tidal cycles. J. Geophys. Res. Oceans 2013, 118, 5555–5567. [CrossRef] 30. Sanford, L.P.; Suttles, S.E.; Halka, J.P. Reconsidering the physics of the Chesapeake Bay estuarine turbidity maximum. Estuaries 2001, 24, 655–669. [CrossRef] 31. Ralston, D.K.; Geyer, W.R. Episodic and long-term sediment transport capacity in the Hudson River estuary. Estuar. Coast. 2009, 32, 1130–1151. [CrossRef] 32. Yan, Y.; Song, D.; Bao, X.; Ding, Y. The Response of Lateral Flow to Peak River Discharge in a Macrotidal Estuary. Water 2020, 12, 3571. [CrossRef] 33. Song, L.; Xia, X.M.; Liu, Y.F.; Cai, T.L. Variations in water and sediment fluxes from Oujiang River to estuary. J. Sediment Res. 2012, 1, 46–52. (In Chinese) 34. Shang, S.; Fan, D.; Yin, P.; Burr, G.S.; Zhang, M.; Wang, Q. Late Quaternary environmental change in Oujiang delta along the northeastern Zhe-Min Uplift zone (Southeast China). Palaeogeogr. Palaeoclimatol. Palaeoecol. 2018, 492, 64–80. [CrossRef] 35. Zhang, M.Y.; Fan, D.D.; Wu, G.X.; Shang, S.; Chen, L.L. Palynological characters of late Quaternary in the South flank of the Oujiang River delta and their paleoclimate implications. Quat. Sci. 2012, 6, 182–195. (In Chinese) 36. Xie, Q.C.; Li, B.G.; Xia, X.M.; Li, Y.; Van Weering, T.C.E.; Berger, G.W. Spatial and temporal variations of tidal flat in the Oujiang estuary in China. Acta Geograph. Sin. 1994, 49, 509–516. (In Chinese) 37. Zuo, L.Q.; Lu, Y.; Li, H. Further study on back silting and regulation of mouth bar in Oujing estuary. Hydro Sci. Eng. 2012, 3, 6–13. (In Chinese) 38. Chen, C.; Liu, H.; Beardsley, R.C. An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: Application to coastal ocean and estuaries. J. Atmos. Ocean. Technol. 2003, 20, 159–186. [CrossRef] 39. Chen, C.; Beardsley, R.C.; Cowles, G. An Unstructured Grid, Finite-Volume Coastal Ocean Model (FVCOM) System. Oceanography 2006, 19, 78–89. [CrossRef] 40. Song, D.; Wang, X.H. Suspended sediment transport in the Deepwater Navigation Channel, Yangtze River Estuary, China, in the dry season 2009: 2. Numerical simulations. J. Geophys. Res. Oceans 2013, 118, 5568–5590. [CrossRef] 41. Kumar, M.; Schuttelaars, H.M.; Roos, P.C. Three-dimensional semi-idealized model for estuarine turbidity maxima in tidally dominated estuaries. Ocean Model. 2017, 113, 1–21. [CrossRef] Water 2021, 13, 106 23 of 23

42. Wang, X.H.; Byun, D.; Wang, X.; Cho, Y. Modelling tidal currents in a sediment stratified idealized estuary. Cont. Shelf Res. 2005, 25, 655–665. [CrossRef] 43. Wang, X.H. Tide-induced sediment resuspension and the bottom boundary layer in an idealized estuary with a muddy bed. J. Phys. Oceanogr. 2002, 32, 3113–3131. [CrossRef] 44. Mellor, G.L.; Yamada, T. A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers. J. Atmos. Sci. 1974, 31, 1791–1806. [CrossRef] 45. Ariathurai, R.; Krone, R.B. Finite element model for cohesive sediment transport. J. Hydr. Eng. Div. 1976, 102, 323–338. 46. Mehta, A.J.; McAnally, W.H. Fine-grained sediment transport. In Sedimentation Engineering: Processes, Measurements, Modeling, and Practice; Garcia, M.H., Ed.; American Society of Civil Engineers: New York, NY, USA, 2008; pp. 253–306. 47. Yao, S.; Li, S.; Liu, H.; Lu, Y.; Zhang, C. Experiment study on effects of waterway regulation structures on flood capacity of river. Port Waterw. Eng. 2010, 6, 120–126. (In Chinese) 48. Passerotti, G.; Massazza, G.; Pezzoli, A.; Bigi, V.; Zsoter, E.; Rosso, M. Hydrological Model Application in the Sirba River: Early Warning System and GloFAS Improvements. Water 2020, 12, 620. [CrossRef] 49. Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 2007, 50, 885–900. [CrossRef] 50. Dyer, K.R. Estuaries: A Physical Introduction, 2nd ed.; Wiley: London, UK, 1997; p. 195. 51. Zhang, X.; Chen, X.; Dou, X.; Zhao, X.; Xia, W.; Jiao, J.; Xu, H. Study on formation mechanism of turbidity maximum zone and numerical simulations in the macro tidal estuaries. Adv. Water Sci. 2019, 30, 86–94. (In Chinese) 52. Uncles, R.J.; Jordan, M.B. Residual fluxes of water and salt at two stations in the Severn Estuary. Estuar. Coast. Mar. Sci. 1979, 9, 287–302. [CrossRef] 53. Sommerfield, C.K.; Wong, K.C. Mechanisms of sediment flux and turbidity maintenance in the Delaware Estuary. J. Geophys. Res. 2011, 116, C01005. [CrossRef]