Influence Mechanism of Geomorphological Evolution in a Tidal Lagoon with Rising Sea Level

Abstract

A tidal lagoon system has multiple environmental, societal, and economic implications. To investigate the mechanism of influence of the geomorphological evolution of a tidal lagoon, the effect of critical erosion shear stress, critical deposition shear stress, sediment settling velocity, and initial bed elevation were assessed by applying the MIKE hydro- and morpho-dynamic model to a typical tidal lagoon, Qilihai Lagoon. According to the simulation results, without sediment supply, an increase of critical erosion, deposition shear stress, or sediment settling velocity gives rise to tidal networks with a stable terrain. Such an equilibrium state can be defined as when the change of net erosion has little variation, which can be achieved due to counter actions between the erosion and deposition effect. Moreover, the influence of the initial bed elevation depends on the lowest tidal level. When the initial bed elevation is below the lowest tidal level, the tidal networks tend to be fully developed. A Spearman correlation analysis indicated that the geomorphological evolution is more sensitive to critical erosion or deposition shear stress than sediment settling velocity and initial bed elevation. Exponential sea level rise contributes to more intensive erosion than the linear or the parabolic sea level rise in the long-term evolution of a tidal lagoon.

1. Introduction

As a unique landform on the coast, lagoons can be divided into three categories, i.e., tidal lagoons [1], reef lagoons [2,3], and coral atoll lagoons [4]. The number of lagoons is declining at an alarming rate. For instance, there were 251 lagoons in China in 1979, but 19 lagoons disappeared in 31 years, due to human activities or changes of natural conditions [5]. Lagoons provides many ecosystem services, such as habitats for fish and shell fish [6]. Therefore, it is vital to prevent the disappearance of lagoons, due to their ecological and economic benefits [7]. As a result, the mechanism of the influence of geomorphological evolution in lagoons has been widely investigated [8,9,10,11].

The main type of lagoons, tidal lagoons, are generated from sea level changes and sediment supply, and their evolution relies on both hydrodynamic and geomorphological conditions [12,13,14]. In a tidal lagoon system, the tidal channel connects the lagoon with the open sea, and dominates the sediment supply and the water exchange, so that it determines the geomorphological stability of the system [15,16]. In general, research on geomorphological stability can be classified into short-term and long-term. The short-term studies are mainly based on field observation and physical modelling, while the long-term studies often depend on process-based numerical models. Roelvink et al. [17] studied Kate Lagoon, using both physical modelling and numerical modelling. In their investigation, the physical model simulated the erosion and deposition process in the tidal channel well, but the numerical model showed a low quality in simulating the erosion process on the tidal shoals owing to the tide and waves. Through a physical model, Tambroni et al. [18] found that the apparent tidal asymmetry plays an important role and showed that the ebb tide determines scour in the tidal channel, which was similar to the experimental results from a study on an ebb-dominated tidal channel by Price [19].

Apart from physical modelling, numerical modelling is also an effective tool for investigations on geomorphological evolution. Cayocca [20] constructed a two-dimensional model and simulated the dynamic geomorphological evolution of a tidal channel in the Arcachon Basin, France. It was found that the tidal current enforces the generation of new tidal creeks and takes sediment into the tidal channel. Moreover, either migration or closure of tidal channels occurs on coasts dominated by weak tidal waves, along with unsteady hydrodynamic conditions. If the hydrodynamic conditions are relatively complicated, three-dimensional models are necessary for simulations. For example, Lam et al. [21] used Delft3D to simulate the periodical geomorphological evolution of a tidal channel, where the seasonal runoff and waves were the main influence factors.

In addition to the evolution of the tidal channel, the generation of tidal networks should also be highlighted as representative of the evolution in a lagoon. In general, tidal networks are generated from the lagoon entrance and extend to the center of the lagoon. Therefore, tide is the primary hydrodynamic force that brings about the tidal shoals and bifurcated tidal creeks, rather than runoff and waves [22]. Specifically, the generation of tidal networks mainly results from the variation in bed elevation, and the headward erosion dominated by the ebb tide develops the creeks. For intricate tidal networks, multiple creeks develop simultaneously, and combinations among creeks occur from time to time [23,24,25]. The development of tidal networks implies that the geomorphological evolution will eventually reach a dynamic equilibrium state, which has been studied by many researchers [26,27]. For instance, Stefanon et al. [28] constructed a physical model to investigate the geomorphological evolution with different tidal amplitudes, tidal channel shapes, and initial bed elevations. The headward erosion was emphasized as key to lagoon evolution. In addition, if the tidal networks develop rapidly and the lagoon stays in an erosion state, there is a linear relation between the width and depth of the sub-creeks, according to their numerical results. However, even with the same experimental conditions, the resultant terrain varies a lot due to the stochastic disruption on the initial bed elevation. Thus, the mean bed elevation is more susceptible to the mean water level than the tidal amplitudes or the tidal cycles.

According to the aforementioned previous research, the geomorphological evolution of a tidal lagoon system is influenced by the tidal channel, which determines the tidal conditions and the tidal networks, which indicate the geomorphological evolution trends.

Research on sediment distribution in estuaries started in the 19th century. Reynolds [29,30,31] conducted a series of experiments using physical models to investigate geomorphological evolution and found that the development direction of tidal shoals and sand ridges was perpendicular to the direction of the tidal current. However, the evolution did not reach an equilibrium state, even after 16,000 tidal cycles. Generally, the temporal and spatial change of sediment transport is hard to simulate, especially the nonlinear interactions among hydrodynamic factors, sediment characteristics, and biological influences. Thus, empirical equations are widely utilized to simulate sediment transport under specific conditions [32,33,34,35,36]. For instance, Kleinhans et al. [37] arranged a tilted terrain as the initial condition to study sediment transport, and found it had a positive influence on the seaward bed load transport under gravity. Furthermore, the settling velocity of the suspended load was considered by Carl et al. [38], and the suspension was proven to be controlled by the bed shear stress. An ideal model was established for investigation of the geomorphological evolution in a tidal lagoon by Marciano et al. [39]. It took a decade to generate an ebb delta, and the tidal networks achieved an equilibrium state after 30 years.

Nowadays, it is feasible to adopt a geomorphological acceleration factor to reduce the CPU costs for effective simulation of long-term geomorphological evolution [40]. With such an acceleration factor, Vlaswinkel and Cantelli [41] simulated the generation of tidal networks, and it required only 5 days to attain an equilibrium state. They found that the geomorphological evolution develops rapidly at the very beginning and that headward erosion of ebb tide plays an important role in the evolution. Besides the acceleration factor, the model scale is also important to the CPU costs. Iwasaki et al. [42] constructed a physical model in a relatively small flume (0.9 m in width and 0.8 m in length) to investigate geomorphological evolution. The system attained an equilibrium state in just 2 h, which shows that the CPU time costs depend on the model scale.

The impacts of sea level rise on the coast have attached increased attention from researchers. Particularly, sea level rises would have a great influence on estuaries; not only on the hydrodynamic conditions such as tidal convergence and reflection, but also on the geomorphological conditions in a basin, tidal flat, or tidal inlet [43,44]. Aside from climate change, sea level rises can result from other natural factors, such as wind over the lagoon [45]. Research on sea level rises in lagoons has focused on the ecosystem [46,47] and the geomorphological evolution [48,49]. As a long-term variation, studies on sea level rise emphasized more on the rise process, rather than the final sea level. For instance, both linear and parabolic growth of sea level rise were considered by Parker et al. [50] for coastal management purposes.

In terms of CPU time costs and model scale, numerical modelling is superior to physical modelling. To investigate the mechanism of influence of geomorphological evolution in a tidal lagoon, a typical lagoon was selected to provide the real data for the simulation. Then, based on the simulation results in real conditions, four potential controlling factors were assessed separately as the single variables for analysis, i.e., the critical erosion shear stress (CESS), critical deposition shear stress (CDSS), sediment settling velocity (SSV), and initial bed elevation (IBE). Terrain patterns were analyzed to show the geomorphological evolution, especially the generation of tidal networks. Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) were used for quantitative analysis of the impacts of the four individual controlling factors and the correlation among the variables. Sea level rise (SLR) was taken into account as an external factor of the geomorphological evolution.

The objective of this study was to determine the impacts of internal factors on the geomorphological evolution and to provide guidance for the subsequent restoration of tidal lagoons based on the variable importance analysis. In addition, it aimed to offer an approach for predicting geomorphological evolution under different variations in sea level rise.

2. Field Site and Methodology

2.1. Selection of a Typical Tidal Lagoon

A lagoon is a unique type of coastal wetland, covering a closed or semi-closed water area with some upstream rivers and one, or a few, tidal channel [51]. To investigate geomorphological evolution, a typical tidal lagoon is essential, to ensure that the findings are applicable to other sites. As one of major lagoons in North China, Qilihai Lagoon is the largest located in the Bohai Bay [52] (Figure 1a). It has a typical terrain as a tidal lagoon, with a tidal channel (Xinkaikou), generated in 1833 by a flood [53], connecting with the Bohai Sea, and four upstream rivers (Figure 1b). Sun [51] classified lagoon evolution into a growth phase, old phase, and death phase. Qilihai Lagoon is at the growth phase at present, which means that it is in an equilibrium erosion state. The upstream rivers are relatively small, so little sediment can be carried into the lagoon. In addition, an adequate tidal prism promotes effective water exchange with the open sea through the tidal channel. Considering these circumstances, Qilihai Lagoon is qualified to represent tidal lagoons as a typical one, with appealing geomorphological and hydrodynamic conditions. Hence, an ideal model of Qilihai Lagoon will be established next for the investigation of its geomorphological evolution.

2.2. The Ideal Model

Ideal models, also called exploratory models, have been widely used to study the mechanism of influence [54,55]. Here, the two coupled hydrodynamics and morphodynamics modules in the MIKE suite were used to study the geomorphological evolution of Qilihai Lagoon. More detailed information about the model can be found in our previous paper [56] and the official website of MIKE (https://www.mikepoweredbydhi.com/, accessed on 13 January 2022) [57].

The ideal model of Qilihai Lagoon was based on the profile recorded from a remote-sensing image in 2018 and a field survey in 2016 [58]. With cooperation from the Tianjin Exploration Center of Marine Geology, the bathymetry was measured using the VRS (virtual reference station) technique, RTK (real-time kinematic) positioning, and SOKKIA total station. The current and sediment concentration were provided by the Eighth Geological Brigade, Hebei Geological Prospecting Bureau, and the data were collected using an ADCP (Acoustic Doppler Current Profiler, Nortek, Norway). In addition, the grain-size of sediment samples in the bottom surface layer was measured using a laser particle size analyzer. According to the data, the mean width and length of the tidal channel are $150 \mathrm{m}$ and 1800 m (Figure 1b,c). The lagoon is $2000 \mathrm{m}$ in length, perpendicular to the tidal channel, and $1000 \mathrm{m}$ in width, parallel to the tidal channel. The four rivers that flow into the lagoon were set with mean dimensions, respectively $50 \mathrm{m}$ in width and $1000 \mathrm{m}$ in length (Figure 1b). The numerical model contains 3870 grid nodes and 7044 triangle meshes, with a grid size from $10 \mathrm{m}$ to $30 \mathrm{m}$ (Figure 1c).

2.3. Model Set Up

2.3.1. Control Group

A control group was set up to simulate and capture the most important driving forces of the geomorphological evolution in the realistic scenario and to estimate the CPU time costs to attain an equilibrium state. Manning number was set as $60{\mathrm{m}}^{1/3}/\mathrm{s}$. The tide data recorded in two continuous tidal cycles was collected at the Xinkaikou tide station in 2017 (Figure 2), indicating that the mean, highest, and lowest tidal levels are $0 \mathrm{m}$, $0.32 \mathrm{m}$, and $-0.56 \mathrm{m},$ respectively. The medium tide level of $0 \mathrm{m}$ was used as the water level in the ideal model. The discharge of each of the 4 adjacent rivers was equally set as $1{\mathrm{m}}^3/\mathrm{s}$, as the mean annual discharge. The water level and the initial flow velocity in the lagoon were set as $0 \mathrm{m}$ and $0 \mathrm{m}/\mathrm{s}$, respectively.

It was assumed that the sediment characteristics are the same as those in the Qilihai Lagoon. To simplify the ideal model, only a suspended load was considered in this study. The settling velocity (SSV) of the suspended load was $0.008 \mathrm{m}/\mathrm{s}$. The critical erosion shear stress (CESS) and the critical deposition shear stress (CDSS) were $0.20{ \mathrm{N}/\mathrm{m}}^2$ and $0.09{ \mathrm{N}/\mathrm{m}}^2$, respectively. The bed roughness was $0.001 \mathrm{m}$. The initial bed elevation (IBE) was set as the mean elevation measured, that is $-0.5 \mathrm{m}$. Without sediment input from the upstream rivers into the lagoon, the boundary sediment concentration in the tidal inlet is $0.03{ \mathrm{kg}/\mathrm{m}}^3$, and the sediment concentration inside the lagoon is $0.01{ \mathrm{kg}/\mathrm{m}}^3$. The sediment layer thickness at the bed was set as $10 \mathrm{m}$. The morphological evolution model acceleration factor was set at 100, which means that it would take the model a year running in real time to simulate the evolution in a century.

In practice, wind may have considerable effect on the geomorphological evolution in the Bohai Sea, due to its seasonal, interannual, and decadal variations [59], which is neglected in this study. Tide and waves are two remaining driving forces of sediment transport. The wind data at 10 m height above mean sea level collected from 1900 to 2018 can be found in the ERA-Interim and ERA-20C databases. The mean wind velocity is $0.27 \mathrm{m}/\mathrm{s}$ with the direction of $244°$ (WSW) in the Bohai Sea. Based on the relationship between wind and the drag force on the water surface in Equations (1) and (2), the wind shear stress on water surface can be calculated as $0.00012{ \mathrm{N}/\mathrm{m}}^2$. Under the mean annual wind velocity, the mean significant wave height is $0.001 \mathrm{m}$, which equals $~0.2\%$ of the mean water depth, and the mean wave radiation stress in the lagoon is ${10}^{-5}{ \mathrm{N}/\mathrm{m}}^2$.

$${\tau }_w={\tau }_s={\rho }_a{c}_w{u}_w{}^2$$

(1)

$$c_w=\{\begin{array}{cc}\hfill c_a,& u_w<w_a\hfill \\ \hfill c_a+\frac{c_b-c_a}{w_b-w_a}\left(u_w-w_a\right),& w_a\le u_w<w_b\hfill \\ \hfill c_b,& u_w\ge w_b\hfill \end{array}$$

(2)

where ${\rho }_a$ is the atmospheric density; $c_w$ is the wind drag force coefficient; $u_w$ is the wind velocity at 10 m height above mean sea level; $c_a$ and $c_b$ are the empirical drag force coefficients, 0.001255 and 0.002425, respectively; $w_a$ and $w_b$ are the empirical critical wind velocities, $7 \mathrm{m}/\mathrm{s}$ and $25 \mathrm{m}/\mathrm{s}$, respectively.

2.3.2. Sediment Transport

To focus on the sediment transport within the lagoon system, sediment supply from the open sea was also neglected in the model simulations. Then based on the model set-up for the control group, the effects of sediment transport parameters including CESS, CDSS, SSV, and IBE, can be investigated individually. All of the model variables were selected within appropriate ranges around the corresponding mean values chosen for the control group in the simulation.

Based on the control group model run, after the ideal model attains an equilibrium state, the maximum bed shear stress is about $0.24{ \mathrm{N}/\mathrm{m}}^2$, and the mean bed shear stress is around $0.12{ \mathrm{N}/\mathrm{m}}^2$. Accordingly, the CESS is seen to change from $0.10{ \mathrm{N}/\mathrm{m}}^2$ to $0.30{ \mathrm{N}/\mathrm{m}}^2$, with an increment of $0.02{ \mathrm{N}/\mathrm{m}}^2$, representing 11 CESS conditions. If the bed shear stress is greater than CESS, then erosion occurs, which can be calculated from Partheniades’s formula [60],

$$S_E=E\left(\frac{{\tau }_b}{{\tau }_{ce}}-1\right)$$

(3)

where the erosion term $S_E$ represents erosion term; $E$ is the erosion coefficient set as an empirical value ${10}^{-4 }{\mathrm{kg}/\mathrm{m}}^2/\mathrm{s}$; ${\tau }_b$ is the bed shear stress; ${\tau }_{ce}$ is the CESS. If the bed shear stress is equal to or less than the CDSS, suspended particles start to settle down and cause deposition. If the bed shear stress is greater than the CDSS, the suspended particles will move with the ambient flow. According to the observation data of Qilihai Lagoon, the CDSS is found to change from $0.02{ \mathrm{N}/\mathrm{m}}^2$ to $0.20{ \mathrm{N}/\mathrm{m}}^2$, with an increment of $0.02{ \mathrm{N}/\mathrm{m}}^2$, resulting in 10 CDSS conditions. The deposition can be calculated using Krone’s formula [61],

$$S_D={\omega }_{s}c\left(1-\frac{{\tau }_b}{{\tau }_{cd}}\right)$$

(4)

where $S_D$ is deposition term; ${\omega }_s$ is the sediment settling velocity; $c$ is the suspended sediment concentration; ${\tau }_{cd}$ is the CDSS. Third, SSV, i.e., ${\omega }_s$, largely determines the CPU time costs for suspended sediment to settle on the bed. According to the bathymetric survey in 2016, the median grain-size of sediments in the bottom surface layer of Qilihai Lagoon is from $0.00245 \mathrm{mm}$ to $0.314 \mathrm{mm}$. However, if the grain-size is smaller than 0.03 mm, flocculation should be considered. Then the SSV of the cohesive sediment would be treated the same as the SSV of the sediment with a grain-size ten times larger than the single particle before flocculation [62]. Accordingly, the median grain-size is assumed to range between $0.0245 \mathrm{mm}$ and $0.314 \mathrm{mm},$ with a Stokes’ settling velocity [63] from $0.0005 \mathrm{m}/\mathrm{s}$ to $0.09 \mathrm{m}/\mathrm{s}$. The 7 SSV values, i.e., $0.0001 \mathrm{m}/\mathrm{s}$, $0.0005 \mathrm{m}/\mathrm{s}$, $0.001 \mathrm{m}/\mathrm{s}$, $0.005 \mathrm{m}/\mathrm{s}$, $0.01 \mathrm{m}/\mathrm{s}$, $0.05 \mathrm{m}/\mathrm{s}$, and $0.1 \mathrm{m}/\mathrm{s}$ are used for the model simulation.

The last variable, IBE, related to water depth, plays an important role in the evolution, due to its effect on the bed shear stress (Equations (5) and (6)).

$${\tau }_b=\sqrt{{\tau }_{bx}{}^2+{\tau }_{by}{}^2}={\rho }_0{c}_b{U}^2$$

(5)

$$c_b=\frac{g}{{\left(M{h}^{1/6}\right)}^2}$$

(6)

where ${\rho }_0$ is the density of fluid; $c_b$ is the frictional resistance coefficient; $U$ is the flow velocity; $M$ is the Manning number, $h$ is the water depth. The mean bed elevation of Qilihai Lagoon is $-0.5 \mathrm{m}$ relative to the mean sea level, so the IBE is shown to increase from $-1.0 \mathrm{m}$ to $-0.1 \mathrm{m}$, with an increment of $0.1 \mathrm{m}$, resulting in 10 IBE conditions.

2.4. Variable Importance Analysis

In this research, there are 4 independent variables and dependent variables, such as erosion amount (EA), deposition amount (DA), and net erosion amount (NEA). To show the importance of each variable, a variable importance analysis was carried out. Both Pearson correlation coefficient and Spearman correlation coefficient are widely used for this type of evaluation. The Pearson correlation coefficients $R_P$ is given by [64]

$$R_P=\frac{cov\left(X,Y\right)}{{\sigma }_X{\sigma }_Y}$$

(7)

where $cov\left(X,Y\right)$ is the covariance of $X$ and $Y$; ${\sigma }_X$ and ${\sigma }_Y$ are the standard deviation of $X$ and $Y$. The stability of the Pearson correlation coefficient is sensitive to data discretization. To minimize the influence from the discretization of the SSV [65], the Spearman correlation coefficient was utilized in this study [66],

$$R_S=1-\frac{6{\displaystyle \sum }{d}_i{}^2}{n\left(n^2-1\right)}$$

(8)

$$d_i=P_{X_i}-P_{Y_i}$$

(9)

where $R_S$ is the correlation coefficients; sorting $X$ and $Y$, $P_{X_i}$ and $P_{Y_i}$ represent the positions of data $X_i$ and $Y_i$ in order; $n$ is the amount of data. Spearman correlation coefficients in the range of 0.0 to 0.2, 0.2 to 0.4, 0.4 to 0.6, 0.6 to 0.8, and 0.8 to 1.0, represent barely any correlation, little correlation, medium correlation, close correlation, and great correlation, respectively.

3. Model Results and Analysis

In this section, we will analyze the five groups of simulation results: a control group and four experimental groups, with different CESS, CDSS, SSV, and IBE. We will focus on the representative terrain patterns during the evolution and regional erosion or deposition amount, to examine the mechanism of influence on geomorphological evolution in the tidal lagoon.

3.1. Control Group

The evolution results driven by the mean annual wind velocity after 100 years are shown in Figure 3, without wind, with wind, and with wind-included waves, where the wave is generated by the local wind. As shown in Figure 3, erosion occurs in the tidal channel, and sediment settles in the lagoon. The tidal channel generates a main creek in the lagoon entrance, which bifurcates into two sub-creeks, extending to the river mouths. The final tidal networks are similar for the aforementioned three conditions. Thus, the local wind has little effect on the long-term evolution, therefore, the wind will be neglected in the following simulations, for simplicity.

EA, DA, and net erosion or deposition amount (NEDA) per unit area during the simulation of the control group were calculated by the bed layer thickness and the dry sediment density and shown in Figure 4. Positive and negative NEDA indicate that the lagoon is under deposition and erosion conditions. Figure 4 shows that the EA increases during the first 5 years and then decreases after the 5th year and attains an equilibrium value around $75{ \mathrm{kg}/\mathrm{m}}^2$. Due to the sediment input from the tide inlet, the DA keeps increasing, but with a decreasing change rate, which is below $1{ \mathrm{kg}/\mathrm{m}}^2/\mathrm{y}$ after the 36th year. Meanwhile, the NEDA decreased in the first few years, and then increased with decreasing rate, which was also below $1{ \mathrm{kg}/\mathrm{m}}^2/\mathrm{y}$ in the 36th year.

Zhou et al. [67] defined that, ignoring sediment input, if the net sediment transport amount becomes constant, then the evolution reaches an equilibrium state. In the control group, there was sediment input from the tidal inlet, so it is different from the definition by Zhou et al. Considering the sediment input, the equilibrium state can be defined as the condition where the change of the NEDA is below $1{ \mathrm{kg}/\mathrm{m}}^2/\mathrm{y}$. Accordingly, the ideal model attained an equilibrium state in 36 years for the control group.

According to the interannual variation of the maximum erosion depth (Figure 5), there are two peaks in the process. After the second peak in the 20th year, the maximum erosion depth starts to decline with a decreasing rate, which is below $0.01 \mathrm{m}/\mathrm{y}$ after the 50th year. Similarly, the mean flow velocity declines after the second peak in the 6th year, whose change was around $-{10}^4 \mathrm{m}/\mathrm{s}/\mathrm{y}$ after the 50th year. In the conditions set for the control group, the evolution was relatively intensive in the first decade, and after the 50th year, the ideal model attained an equilibrium state, in terms of the geomorphological and hydrodynamic conditions.

The representative terrain patterns of the ideal model in the 1st, 10th, 50th, and 100th year were chosen for analysis (Figure 6). During geomorphological evolution, the tidal channel is under erosion, and creek A was generated in the lagoon entrance initially, which bifurcated into creek B and C inside the lagoon later. After the 10th year, creek D and E appeared at the end of creek C. Meanwhile, creek B and north side of the tidal channel changed to a deposition state. According to the terrain in the 50th and 100th year, this evolution can still be seen at the end of creek E, but the terrain is stable overall, which means that the system attained an equilibrium state within 100 years.

For quantitative analysis purposes, Figure 7 shows the locations and elevations of the observation points T1, T2, T3, and T4. T1 is in the tidal channel; T2 is located in the northern shoal near the lagoon entrance; T3 and T4 are set at the bifurcations of creek A and creek C, respectively (Figure 7a). As is shown, T1 suffered from erosion at first, where the maximum erosion depth reached $-2.50 \mathrm{m}$ in the 20th year, and then was subject to accretion owing to deposition. T2 was under deposition with a decreasing rate, which reached a maximum bed elevation of $0.08 \mathrm{m}$ and stayed that way after the 5th year, indicating it had achieved an equilibrium state. In addition, the bed elevation at T3 rose to $-0.33 \mathrm{m}$ in the 2nd year, and erosion dominated the evolution afterwards. By the 43th year, the bed elevation remained around $-0.92 \mathrm{m}$. T4 was generally under deposition, where the elevation eventually attained $-0.20 \mathrm{m}$.

It is evident from Figure 7 that the geomorphological evolution was relatively active in the tidal channel and the lagoon entrance, while in the lagoon center, the evolution was hysteretic and inactive. On the other hand, the tidal shoals attained an equilibrium state more easily, which depended on their location.

3.2. Impacts of CESS

The terrain patterns of the ideal model for different CESS after 100 years is shown in Figure 8. When the CESS was around the mean bed shear stress of $0.12{ \mathrm{N}/\mathrm{m}}^2$, the erosion in the tidal channel was intensive, and tidal networks were generated with several sub-creeks. For a CESS over $0.12{ \mathrm{N}/\mathrm{m}}^2$, the location of creek A was fixed, but the erosion depth was reduced. Meanwhile, the number of sub-creeks of creek C decreased considerably. Once the CESS was over the maximum value of $0.24{ \mathrm{N}/\mathrm{m}}^2$, as in real-world conditions, the bifurcation of creek A extended farther from the lagoon entrance. In this condition, with increase of the CESS, creek B tended to be shallow, and the sub-creeks of creek C almost disappeared.

In brief, for the lagoon system, erosion decreases with increasing CESS. For the tidal networks, the generation of sub-creeks was quite sensitive to CESS compared with the results in the control group.

Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different CESS after 100 years are illustrated in

Table 1. Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different CESSs after 100 years.

Dependent Variables	CESS (N/m2)
	0.10	0.12	0.14	0.16	0.18	0.20	0.22	0.24	0.26	0.28	0.30
EA (kg/m2)	197.1	183.3	167.9	159.6	151.2	144.0	138.7	130.8	120.2	114.6	111.1
DA (kg/m2)	101.8	100.8	95.3	92.2	90.0	89.3	87.3	84.7	78.7	76.1	74.8
NEA (kg/m2)	95.3	82.5	72.6	67.4	61.2	54.7	51.3	46.1	41.5	38.5	36.3

. Neglecting the sediment input into the lagoon, the settled sediment comes from the previous bed erosion. When the CESS increases from $0.10{ \mathrm{N}/\mathrm{m}}^2$ to $0.30{ \mathrm{N}/\mathrm{m}}^2$, the EA decreases by $86.0{ \mathrm{kg}/\mathrm{m}}^2$, the DA decreases by $27.0{ \mathrm{kg}/\mathrm{m}}^2$, and the NEA decreases by 59.0 kg/m². The EA is more susceptible to the increase of CESS due to the direct influence of CESS described by Equation (3), while the DA also decreases, owing to the reduced suspended sediment from bed erosion.

3.3. Impacts of CDSS

Figure 9 shows the terrain patterns of the ideal model under different CDSS after 100 years. As long as the CDSS is lower than $0.10{ \mathrm{N}/\mathrm{m}}^2$, the overall terrain patterns are similar to each other, in that the tidal network starts from creek A at the lagoon entrance, and bifurcates into creek B and C in the lagoon center. Once the CDSS reaches $0.10{ \mathrm{N}/\mathrm{m}}^2$, a circular shoal appeared inside creek A, and creek C bifurcates into two sub-creeks. With a further increase of CDSS over 0.16 N/m², the tidal shoal inside creek A disappeared, but the location of creek A was fixed. Meanwhile, creek C relocated to the lagoon center, and the length was greatly reduced. It is evident that the increase of CDSS intensified the deposition and suppressed the generation of the tidal network.

Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different CDSS after 100 years are shown in

Table 2. Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different CDSSs after 100 years.

Dependent Variables	CDSS (N/m2)
	0.02	0.04	0.06	0.08	0.10	0.12	0.14	0.16	0.18	0.20
EA (kg/m2)	149.5	148.2	145.9	144.7	142.1	140.7	134.9	129.0	123.8	118.9
DA (kg/m2)	94.0	92.7	91.0	89.9	88.8	87.7	83.3	80.3	78.0	76.8
NEA (kg/m2)	55.5	55.6	54.9	54.9	53.4	52.9	51.6	48.7	45.8	42.1

. According to Equation (4), with higher CDSS, the deposition amount should increase, but the EA and the DA is reduced in Table 2. Due to the increase of CDSS from the minimum to the maximum values, the variations of EA and DA were $30.6{ \mathrm{kg}/\mathrm{m}}^2$ and $17.2{ \mathrm{kg}/\mathrm{m}}^2$, respectively. On one hand, with the intensive deposition effect, the erosion effect was limited as a result, so that the sediment could not be suspended from the bed erosion. On the other hand, with less suspended sediment, the DA was reduced. Consequently, even though the NEA decreased due to higher CDSS, the lagoon system still suffered erosion.

Considering the combined influences from CESS and CDSS, neither erosion term nor deposition term changed independently from each other in response to the variation of the controlling factors, such as CESS and CDSS. The deposition effect and erosion effect would counteract each other, and drive the geomorphological evolution, to achieve an equilibrium state.

3.4. Impacts of SSV

The terrain pattern of the ideal model for different SSV after 100 years is shown in Figure 10. If the SSV was as low as $0.0001 \mathrm{m}/\mathrm{s}$, creek A was generated along the side of the lagoon, and bifurcated far from the lagoon entrance. Simultaneously, with very little deposition, overall, the lagoon system suffered from erosion, especially at the tidal channel. With the increase of SSV to $0.01 \mathrm{m}/\mathrm{s}$, tidal shoals appeared and brought about apparent bifurcations of the tidal network. Under this circumstance, the sediment from bed erosion settles immediately on both sides of the tidal creeks. Although the development of tidal shoals relocated creek C to the lagoon center, with a further increase of the SSV, the tidal networks tended to be more stable. Hence, SSV plays an important role in the generation of a tidal network.

Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different SSV, after 100 years, are shown in

Table 3. Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different SSVs, after 100 years.

Dependent Variables	SSV (m/s)
	0.0001	0.0005	0.001	0.005	0.01	0.05	0.1
EA (kg/m2)	179.0	159.1	153.0	149.2	141.3	139.6	138.5
DA (kg/m2)	109.7	98.0	94.4	94.3	86.8	86.0	85.7
NEA (kg/m2)	69.4	61.1	58.6	54.9	54.5	53.6	52.8

. Similar to the CDSS, the increase of SSV intensified the deposition, but the EA and the DA decreased, due to the aforementioned mutual restriction of erosion and deposition. When the SSV varied from $0.0001 \mathrm{m}/\mathrm{s}$ to $0.001 \mathrm{m}/\mathrm{s}$, the NEA decreased by $10.8{ \mathrm{kg}/\mathrm{m}}^2$; however, with a further increase of the SSV to 0.1 m/s, the NEA only declined by $5.8{ \mathrm{kg}/\mathrm{m}}^2$. This implies that low SSV has a greater influence on geomorphological evolution.

3.5. Impacts of IBE

Terrain patterns of the ideal model under different IBE, after 100 years, are shown in Figure 11. When the IBE decreased from $-0.1 \mathrm{m}$ to $-0.5 \mathrm{m}$, the tidal networks were well formed, in terms of scale, and more deposition occurred on the tidal shoals. Then the tidal networks experienced significant change, with more sub-creeks when the IBE was $-0.6 \mathrm{m}$. If the IBE further decreased from $-0.6 \mathrm{m}$ to $-1.0 \mathrm{m}$, the tidal shoals fully developed, which suppressed the generation of tidal networks in both scale and depth. The water level for the ideal model of the lagoon was based on the lowest tidal level, which is $-0.56 \mathrm{m}$; therefore, when the IBE was above −0.56 m, tidal shoals appeared at the very beginning. However, if the IBE was below $-0.56 \mathrm{m}$, the lagoon was submerged entirely, where the erosion was intensive enough to dominate the evolution. Thus, the influence of IBE on geomorphological evolution is dependent on the lowest tide level. Tidal networks were properly generated and developed when the IBE was below the lowest tide level, particularly with a low water depth.

Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different IBE after 100 years are shown in

Table 4. Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different IBEs, after 100 years.

Dependent Variables	IBE (m)
	−0.1	−0.2	−0.3	−0.4	−0.5	−0.6	−0.7	−0.8	−0.9	−1.0
EA (kg/m2)	120.4	127.3	133.2	137.2	144.0	130.9	123.2	113.9	105.6	98.4
DA (kg/m2)	15.2	29.3	50.2	70.7	89.3	85.5	82.3	77.1	72.1	68.0
NEA (kg/m2)	105.2	98.0	83.0	66.6	54.7	45.4	40.9	36.8	33.5	30.3

. With the decreasing of IBE from $-0.1 \mathrm{m}$ to $-1.0 \mathrm{m}$, the EA and the DA increased at first and then decreased. Both EA and DA reached the maximum when the IBE was at $-0.5 \mathrm{m}$. If the IBE decreases beyond $-0.5 \mathrm{m}$, the DA increases further, so that the NEA decreases in response. However if the IBE moves below $-0.5 \mathrm{m}$, the EA declines further, which reduces the NEA as well.

In summary, when the IBE is above the lowest tide level, the variation of IBE mainly affects the DA, but if the IBE is below the lowest tide level, the EA is more sensitive to the variation of IBE than DA. In terms of NEA, the rise of IBE would make the lagoon suffer from more intensive erosion.

4. Discussions

The influence of four physical factors on the geomorphological evolution in a tidal lagoon has been investigated using an ideal model. Based on the model results, three issues should be considered. First of all, the reliability and universality of the results should be checked by comparison with previous studies. Second, the relative importance of each variable should be assessed using Spearman correlation coefficients. Finally, we mainly focused on the internal contributing factors of the lagoon evolution in the simulation, because external factors are hard to estimate; and both human activities and climate changes are likely to have significant effects on the geomorphological evolution in a tidal lagoon. Based on the field observation data, however, the sea level rise (SLR) can be estimated roughly as an external factor, so that its influence on the geomorphological evolution of the lagoon can be investigated.

4.1. Reliability of Model Results

During the evolution, the erosion effect was intensive at the beginning in the control group (Figure 5). According to the study carried out by Stefanon et al. [28], and also proven by the laboratory experiments, the tidal networks generated multilevel creeks, tidal shoals, and tidal channel confluences. Moreover, they found that the increased mean water level led to a significant influence on the mean bed elevation. The water depth is a critical factor for sediment transport over intertidal mudflats according to Whitehouse et al. [23], and on a creek system in the Wash according to Symonds et al. [24]. Similarly, the water depth was embedded in the IBE in this study, and unlike the previous study, we revealed that the relationship between the lowest tidal level and the IBE had a dominant effect on the evolution, and that the increase of water level led to more deposition, by either weakening the erosion effect or intensifying the deposition effect. In addition, the generation of tidal networks depends on both hydrodynamic and geomorphological conditions, as highlighted by Kleinhams et al. [37] and Vlaswinkel et al. [41]. In the control group, the erosion effect in the tidal channel was more intensive than that in the lagoon, and the maximum erosion depth was close to the right side of the channel, due to the Coriolis force. This phenomenon was also found in the Lignanon tidal inlet by Petti et al. [15] and in the Arcachon Basin by Cayocca [20], especially for the tidal channel dominated by an ebb tide. Then, Equations (3) [60] and (4) [61] were utilized to calculate the erosion and deposition independently, but the results showed a great difference, whereby erosion and deposition would counteract each other to drive the evolution to an equilibrium state [68]. In addition, Carl et al. [38] emphasized the effect of SSV on the formation of tidal networks in the Venice Lagoon.

In summary, the numerical results show some general features of lagoon evolution, and the ideal model provided a good representation of the mechanism of influence of the internal factors. According to our findings, it is feasible to predict the evolution, maintain the equilibrium, and promote the restoration of a tidal lagoon. To achieve effective coastal management of a lagoon, it is important to assess the correlations among different factors and their relative importance.

4.2. Variable Importance Analysis

Table 5. Spearman correlation coefficients among key variables.

Dependent Variables	Independent Variables				Dependent Variables
	CESS	CDSS	SSV	IBE	EA	DA	NEA
EA	0.613	0.533	0.291	0.110		0.928	0.724
DA	0.479	0.526	0.352	0.024	0.928		0.455
NEA	0.590	0.357	0.228	0.625	0.724	0.455
Average	0.561	0.472	0.290	0.253	0.826	0.692	0.590

shows the Spearman correlation coefficients among CESS, CDSS, SSV, IBE, EA, DA, and NEA. As shown in the table, the EA has a good correlation with the DA, because without sediment input to the lagoon system, the settled sediment is from the bed erosion. Moreover, there is a close correlation between the EA and the NEA.

Among independent variables, the SSV has the smallest correlation with NEA, therefore, less influence on the overall geomorphological evolution. In addition, the IBE has a close correlation with the NEA, because it dominates the water depth, which in turn affects the hydrodynamic conditions significantly. The CESS may influence the EA considerably, as discussed in Section 2.3.2; thus, there is a close correlation between these two variables, as shown by Table 5. Moreover, the CESS also has a medium correlation with both DA and NEA. In other words, the CESS is a crucial factor in the geomorphological evolution compared with the others. Furthermore, the CDSS has a similar correlation with both the EA and the DA. The reason for this has been mentioned earlier, that the deposition effect counteracts the erosion effect, so that the DA is unlikely to increase or decrease independently of the EA. According to the average correlation coefficients in the bottom row, the EA has the highest correlation with other variables, and the DA has the second highest correlation with the other variables. The CESS and the CDSS showed a more direct effect on the geomorphological evolution than the SSV and the IBE.

4.3. Influences of SLR

SLR is relatively easy to estimate for the long-term evolution, because it results from continuous climate changes. To model the process of SLR adequately, three types of SLR variation pattern were chosen for the investigation: linear variation, parabolic variation, and exponential variation. The simulation of the time evolution of SLR was based on the medium tidal level, plus the variation of sea level predicted by the tidal level data collected at the Tanggu tide station indicated in Figure 1 from 1950 to 2018 (Figure 12a), where the slope of the fitting line was $0.0034 \mathrm{m}/\mathrm{a}$. Therefore, the initial sea level was set as $0.00 \mathrm{m}$, and the final sea level after 100 years was set as $0.34 \mathrm{m}$. The variations of sea level rise are shown in Figure 12b. Another case was set with a constant sea level for comparison.

The terrain patterns of the ideal model under three different sea level variations after 100 years are shown in Figure 13. The erosion effect in the tidal channel was more intensive with SLR, especially under the exponential variation of SLR, where the lagoon suffered from more erosion, with wider tidal creeks. Meanwhile, according to the increased deposition area in the lagoon, the sea level rise would also lead to more depositions. The tidal shoals were higher and larger under the parabolic variation of SLR scenario.

Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for three different sea level rise processes after 100 years are shown in

Table 6. Erosion amount (EA), deposition amount (DA), and net erosion amount (NEA) per unit area for different sea level rise processes after 100 years.

Dependent Variables	Sea Level Rise Scenarios
	Constant	Exponential Variation	Linear Variation	Parabolic Variation
EA (kg/m2)	145.01	151.37	149.27	148.85
DA (kg/m2)	90.30	97.72	99.54	103.29
NEA (kg/m2)	54.71	53.65	49.73	45.56

. First, even with a constant sea level, the ideal model was in an erosion state. Second, the exponential variation of SLR led to over 4% more EA compared with the constant sea level, with both the linear and the parabolic variation of SLR being about 3% more than the constant sea level. The influence on the erosion effect of the three different types of rise were similar to each other. Third, the increases of DA due to the exponential, the linear, and the parabolic variations of SLR were about 8%, 10%, and 14%, respectively, of the DA for the constant sea level. Hence, the sea level rise had more effect on the deposition effect in a lagoon than the erosion effect. Last, the NEA for the exponential, the linear, and the parabolic variation of SLR were around 98%, 91%, and 83% of that for the constant sea level. This result indicates that the exponential variation of SLR has more influence on the erosion in a lagoon compared with the linear variation and the parabolic variation of SLR.

The aforementioned influence of SLR on the geomorphological evolution would further deteriorate the local ecosystem and hinder the development of a lagoon, as Ward [69] found in his study of Arctic coastal wetlands. Here, we aimed to concentrate on the terrain, and one of our findings, that SLR would promote the accretion in a tidal lagoon, was also found by Bruneau et al. [48] in Obidos Lagoon, Portugal, and Lodder et al. [49] in the Wadden Sea tidal basins. The proportional relations from the quantitative analysis show the impacts on a tidal lagoon from different types of SLR variation processes, which provides us with a robust technique for estimating lagoon evolution under different climate change scenarios.

5. Conclusions

To investigate the mechanism of influence of geomorphological evolution in a tidal lagoon, Qilihai Lagoon was selected as a typical tidal lagoon, due to its sustainable geomorphological and hydrodynamic conditions. An ideal model of this typical lagoon was established in the system based on MIKE suite. A control group was set up using the observation data of Qilihai Lagoon. According to the simulation of the control group, it took around 50 years for the ideal model to attain an equilibrium state. Based on the conditions set for the control group, except for the sediment supply, the influence on the geomorphological evolution from four internal factors, i.e., critical erosion shear stress (CESS), critical deposition shear stress (CDSS), sediment settling velocity (SSV), and initial bed elevation (IBE) were investigated. The terrain patterns during the evolution and three dependent variables, erosion amount (EA), deposition amount (DA), and net erosion amount (NEA), were shown in both quantitative and qualitative analyses. Finally, a variable importance analysis was applied to compare the relative importance of these factors. In addition, the influence of an external factor, sea level rise (SLR), and its variation patterns was also quantified. The key findings of the geomorphological evolution in a tidal lagoon are as follows:

• The lagoon geomorphological evolution is active in the tidal channel, but hysteretic in the lagoon. The generation of tidal networks promotes the evolution towards reaching an equilibrium state. An increase of CESS, CDSS, SSV, or water depth (due to the descent of IBE) has a beneficial effect on the evolution.
• The erosion effect and the deposition effect counteract each other, so that the lagoon terrain eventually attains the equilibrium state when the change of net erosion amount per unit area remains within $1{ \mathrm{kg}/\mathrm{m}}^2/\mathrm{y}$.
• The influence by the IBE mainly depends on the lowest tidal level. If the IBE is below the lowest tidal level, the deposition effect is more sensitive to the variation of IBE. However, if the IBE is above the lowest tidal level, the variation of IBE causes more erosion.
• According to the variable importance analysis, EA is highly correlated with other variables. In addition, CESS and CDSS showed a more direct effect on the geomorphological evolution than SSV and IBE. Thus, it is more effective to alter the evolution by changing CESS or CDSS.
• SLR is considered the only external contributing factor for lagoon evolution that can be estimated reasonably well. This indicates that an exponential variation of SLR would give rise to more intensive erosion in a lagoon in the long-term compared with linear variation and parabolic variation of SLR.

With these findings, we are able to predict the geomorphological evolution in a tidal lagoon under the influence of these factors and provide effective approaches to manage the lagoon’s evolution. In the near future, we will focus more on better understanding the hydrodynamic factors of a lagoon system, especially those sensitive to climate changes or human activities.