Laboratory and non-hydrostatic modelling of focused wave group evolution over fringing reef

Abstract

This paper presents physical experiments and numerical simulations to study the propagation of focused waves group across hypothetical fringing reef profiles. A wave flume is 69 m long and 1.0 m deep, and the reef cross section is made up of a reef face, a reef flat and a vertical wall. A reef crest of 0.085 m is optionally constructed on the outside to replicate the reef crown. By focusing wave trains of the JONSWAP or constant wave amplitude spectrum, the transient wave group is generated on the reef slope. Free surface elevations and flow velocity are measured over time along the flume's centreline. The focused wave process and the development of higher harmonics as a result of the nonlinear interaction over the reef face are clearly visible in the wavelet and FFT analyses of the observed free surface elevation. Low frequency wave is increasing on the reef flat while these short-period wave motions are primarily absorbed by rapid breaking on reef edge and crest. On the flat, it is discovered that reef crest has the effect of reducing short-period wave motion and increasing long-period wave motion. A numerical multi-layer non-hydrostatic wave model is employed and its ability to describe the propagation of focused wave groups over fringing reef profiles is assessed.

1. Introduction

Coral reefs exist in tropical and subtropical climate zones along the coasts. These reefs are easy to identify due to their special topography, which consists of a sloping reef face and a shallow reef platform. Significant incident wave energy is lost due to severe wave breaking that happens across the reef face or close to the reef edge. This energy is then further diminished by the bottom friction on the uneven reef flat. As a result, it has long been thought that bordering reefs can protect low-lying coastal areas from risks such wave runup, overtopping, and erosion [[1], [2], [3]]. However, during rare occurrences like tropical typhoons, wave-driven coastal risks continue to exist [4]. According to recent research, sea level rise and climate change are expected to increase the frequency and intensity of tropical cyclones, and resulting in more frequent and destructive events [5].

Extreme waves can destroy low-lying coastal settlements and coastal defenses fatally through direct impact, runup, overtopping, and subsequent flooding. Investigating the extreme wave impact on beaches has been a major effort in order to analyze, regulate, and limit the risk, especially in the wake of the disastrous tsunami that struck the Indian Ocean in 2004 and previous destructive tsunamis [[6], [7], [8]]. Since the early 1970s, solitary waves are widely used to simulate the main characteristics of tsunamis approaching the coast, as solitary waves have hydrodynamic similarities to the leading wave of a tsunami [9]. These studies [[10], [11], [12], [13], [14], [15], [16]] use solitary waves to investigate tsunami behavior under the reef environment numerically and experimentally.

Recent studies have found that the focused wave might be better at simulating extreme events during the storm [[17], [18], [19]]. The term "focused wave group" refers to a collection of discrete sinusoidal wave components that are in phase at a certain instant in time and have various amplitudes and frequencies. A wave can be classified as a rogue wave if its wave height is greater than 2.2 times the major wave height [20]. The focused waves can accurately represent the average forms of large random storms in shallow, middle and deep water [[21], [22], [23]]. Therefore, scientists and engineers are increasingly using wave focusing concept to better understand extreme wave generation, hydrodynamic characteristics and impacting loads on structures, and to study erosion on beach and overtopping on coastal defences [[24], [25], [26], [27], [28]]. We are aware of very few updates about the research on the interactions between focused wave groups and bordering reefs.

Due of the distinctive bathymetry characteristic and complicated wave hydrodynamics that arise, wave propagation across bordering reefs is challenging to numerically simulate [16]. For the focused wave considered n in this work, a numerical model should be able to accurately describe a wide range of wave frequencies across a long distance in deep water. Due to the dispersion and nonlinearity accuracy limitations, the conventionally employed Boussinesq model in reef scenarios may not succeed, and CFD (Computational Fluid Mechanics) type models require significant computational effort even though they can forecast the precise wave and flow field. Non-hydrostatic type models [[29], [30], [31], [32]], which cannot account for the viscosity effect but are fully dispersive by increasing the vertical layers and do not need to capture the violent change of the free surface, may appear to be a suitable choice when considering the compromise between model accuracy and computational cost. Recent reports on the use of non-hydrostatic wave models in coral reefs [[33], [34], [35]] have gradually increased, and it is therefore necessary to investigate whether these models can replicate focused wave propagation over bordering reefs.

The goal of the current study is to examine the evolution processes associated with waves propagating from a constant deep-water depth to the shoaling and breaking zones over reef face and reef flat/reef crest. Focused wave groups are generated from JONSWAP and constant wave amplitude wave trains. By contrasting the numerical outcomes with measurements, the competence of the multi-layer non-hydrostatic model created by the authors [35] is also assessed. The rest of this essay is structured as follows. Section 2 presents a description of the laboratory experiment, and Section 3 presents the associated results. The numerical experiments utilizing a non-hydrostatic model and a model-data comparison are shown in Section 4. Section 5 draws the findings.

2. Experiment setup

2.1. Wave flume

In the wave flume of the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, an fringing reef model was constructed. The flume is 69 m in length, 2 m in width, 1.8 m in depth, and is 1.0 m deep when empty. Glass sidewalls on one of the wave flume's lateral sides make it easier to record with a video camera and observe the progression of waves visually. The experimental wave flume's layout and equipment placement are depicted in Fig. 1. The fringing reef is located 35.6 m from the wavemaker at the flume. The reef model is 0.95 m height with a 1:4 fore slope and a 6 m wide reef flat (Fig. 2). The reef flat ends with a 0.5 m vertical wall. Smooth plexiglas covers the surface of the reef, which is securely supported by steel frames. To stop fluid penetration, silicone is filled into the seams between the lateral side walls and the reef model. Additionally, a smooth Plexiglas reef crest model with dimensions of 1.41 m in length and 0.083 m in height is available (Fig. 2(c)). According to Fig. 1, the reef crest's offshore and onshore slopes are both 1:4, much like the shoreline. The minimum water depth for these two fringing reef layouts are 0.15 m on the reef flat and 0.067 m on the reef crest, respectively.

Fig. 1.

Sketch of the wave flume and instrument location.

Fig. 2.

Front view (a), side view (b) and reef crest (c) of fringing reef model.

2.2. Test cases

The focus of this paper is to analyze the effects of different wave spectra and the presence or absence of reef flats on the propagation of focused waves on fringing reefs, as well as to calibrate the ability of the non-hydrostatic model to simulate focused waves on fringing reefs. Therefore, we will analyze the four main experimental conditions in Table 1. The focused wave group is generated by focusing 58 wave components within the JONSWAP spectrum (with the peak enhanced factor γ = 3.3) and CWA (constant wave amplitude) spectrum waves. The focusing wave amplitude A_f = 0.08 m is specified, which is defined as the linearized sum of wave components at the focal location with the absence of fringing reef model. The range of the wave frequency is defined between 0.4 and 1.0Hz, and the corresponding water depth parameter kh (k is the wave number) is mainly in the deep-water region (kh = 4.03–16.09) as shown in Table 1. For CWA spectrum waves, peak frequency (f_p) is the mean value of given frequency range. In the table, x_f is the theoretical focal position, which is fixed at x = 37.45 m to ensure a large transient wave group formed on the foreshore slope, and t_f is the theoretical focal time. Each test summarized in Table 1 is repeated three times to ensure experimental accuracy.

Table 1.

A summary of wave conditions in the experiments.

Case	Af (m)	Spectrum type	Frequency range	Peak frequency (fp)	kh range	xf (m)	tf (s)	Reef crown
1A	0.08	JONSWAP	0.5–1.0Hz	0.7 Hz	4.03–16.09	37.45	70	NO
1B	0.08	JONSWAP	0.5–1.0Hz	0.7 Hz	4.03–16.09	37.45	70	YES
2A	0.08	CWA	0.5–1.0Hz	0.75Hz	4.03–16.09	37.45	70	NO
2B	0.08	CWA	0.5–1.0Hz	0.75Hz	4.03–16.09	37.45	70	YES

2.3. Measurement apparatus

In order to obtain the wavefront processes at different locations, 32 wave gauges are used to measure the free surface elevation, and their positions are shown in Fig. 1. G1-G3 were situated 4.09, 4.69, and 5.3 m from the wavemaker, respectively. G4–G6 were set up to observe the reflected waves at the flume's flat section. G6 was precisely 35.6 m above the reef's toe. G7-G21 cover the whole reef slope and a portion of the reef flat with 0.2 m intervals. The remaining reef flat is covered by the groups G21-G28 with 0.3 m intervals and G29-G32 with 0.6 m intervals. Four ADVs (Acoustic Doppler Velocimetry, henceforth referred to as V1, V2, V3, and V4) were utilized to measure the flow velocity at the wave gauge locations of G13, G18, G27, and G30, and the ADVS probe is located about 0.05 m above the surface of the reef, all gauges were calibrated to guarantee stability and linearity. The free surface elevation and flow velocity are sampled at a rate of 50 Hz, and the experimental data from t = 0 s to t = 80 s is used for calculations to minimize the impact of reflected waves.

3. Laboratory results and discussions

3.1. Time histories of free surface elevation

The time series of free surface elevation at recorded at different gauge locations for JONSWAP and CWA spectrum waves are shown in Fig. 3 and Fig. 4. The wave components are clearly visible near the wavemaker, including higher frequency waves and long waves. CWA waves have almost equal wave amplitude for each wave component as expected. Then, influenced by wave phase and period focusing, the long-period waves gradually catch the short-period waves over the flat bottom (x < 35.60 m), inducing the higher peaks and a more compact wave envelope. The maximum crests appear near the reef edge at x = 39.0 m (G18) and reach 0.095 m for both JONSWAP and CWA spectrum waves, larger than the design value 0.08 m due to shoaling over the reef face, which also results in the focused wave peaks having a steep wave front and relatively mild back. The wave breaks violently as it plunges on the reef crest or near the reef edge. The crest curls over and impinges upon the water ahead, causing splash-up and trapping air, as shown in Fig. 5. The wave heights are highly dissipated due to breaking, they are found reform on the reef flat as turbulent bores and produce a turbulent rolling region at the front. The bores evolve significantly as they travel over the reef flat with a considerable amount of entrapped air riding on the bore heads. In Fig. 3, Fig. 4, there is an increasing trend in the low frequency period oscillations and a decreasing trend in the height of the short period oscillations on the reef flat. This will be further discussed in the next subsection in the frequency domain. The bores finally hit the vertical wall and propagate towards the wavemaker due to reflections.

Fig. 3.

Time series of free surface elevation along flume for fringing reef without (dashed lines) and with (solid lines) crown for JONSWAP spectrum waves.

Fig. 4.

Time series of free surface elevation along flume for fringing reef without (dashed lines) and with (solid lines) crown for CWA spectrum waves.

Fig. 5.

The snapshots of plunging breakers near the reef edge (a) or on the reef crest (b).

For the considered cases, the time series of free surface elevation for fringing reefs with and without reef crest almost shown no differences prior to G18, which is located at the reef ridge. The reef crown mainly affects the wave breaking events and the subsequent evolution process over reef flat. Without reef crest, the incident focused wave can penetrate further onto reef flat before breaking (see Fig. 5). The measured data from the wave gauges located on reef flat (G24, G26, G28 and G31 in Fig. 3, Fig. 4) shows that reef crest tend to cause more evident increase of mean water level and decrease of short-period wave oscillations.

3.2. The evolution of energy spectrum

The wave amplitude spectra obtained by FFT at various gauge locations along wave flume for JONSWAP spectrum waves are presented in Fig. 6. At the offshore location G4, the wave energy is mainly distributed around the peak frequency. Some low-frequency energy is also recorded, possibly due to spurious long waves being generated to compensate for the linear wavemaker transfer function [36]. As the wave train propagates over the reef face, the wave energy is transferred from the spectral peak frequency to both lower and higher frequencies due to the nonlinear interaction between wave components, which is enhanced by shoaling processes and energy focusing. Near the reef edge, G18 records the significant increase in higher harmonics and infra-gravity motion relative at the reef crest in the breaking zone, G21 records the dissipation of the high harmonics and peak frequency. Farther shoreward approximately at the middle of the reef flat (G27), most of the wave energy at the peak frequency of the incident waves is dissipated and the low frequency motion is comparable with (without crest) or higher than (with crest) high frequency motion. The presence of reef crest tends to decrease the strength of short-wave motion and increase the strength of long wave motion on the reef flat. The evolution of wave amplitude spectra along wave flume for CWA spectrum waves is basically in the same pattern as those for JONSWAP spectrum waves, as presented in Fig. 7. The downshifting of the peak (average) frequency is observed after wave breaking for CWA type waves, which is absent from JONSWAP spectrum waves.

Fig. 6.

Wave amplitude spectra at various gauge locations for JONSWAP spectrum waves without (solid lines: Case 1A) and with (dashed lines: Case 1B) reef crest.

Fig. 7.

Wave amplitude spectra at various gauge locations for CWA spectrum without (solid lines: Case 2A) and with (dashed lines: Case 2B) reef crest.

Compared with the abovementioned FFT analysis, the wavelet transform analysis is more appropriate to analyze the time series and examine the localized freak wave features in the time-frequency domain [37]. Spectrum evolution is herein further analyzed using wavelet analysis. In the present study, the Morlet wavelet is selected as the mother wavelet. Fig. 8, Fig. 9 display the wavelet spectra of Case 1 and Case 2 at four different locations. The corresponding time histories of free surface elevation is also overlayed for clarity. G3 is located 5.3 m away from the wavemaker, where the wave energy is distributed mainly around the peak frequency (Case 1) or equally distributed between frequency range (Case 2) according to the specified spectrum type, and the high frequency waves travel first in the wave train. At the instantaneous time of the maximum crest (G18), the frequency components seem to in phase approximately, and the energy of the higher harmonics becomes significant, resulting in a widening spectrum for a brief period. These short-wave motions of primary frequency band and higher harmonics are significantly dissipated due to breaking events near reef edge or reef crest (G21) and further weakened shoreward at G27. The phenomenon that reef crest decreases short-period wave motions and increases the strength of long-period wave motions on the reef flat is again confirmed.

Fig. 8.

Wavelet spectra at various gauge locations for JONSWAP spectrum without (Case 1A: (a)∼(d)) and with (Case 1B: (e)∼(h)) reef crest (solid lines denote the corresponding free surface elevation and each spectrum is nondimensionalized by the maximum value in the figure).

Fig. 9.

Wavelet spectra at various gauge locations for CWA spectrum without (Case 2A: (a)∼(d)) and with (Case 2B: (e)∼(h)) reef crest (solid lines denote the corresponding free surface elevation and each spectrum is nondimensionalized by the maximum value in the figure).

4. Numerical simulations and discussions

4.1. Non-hydrostatic model

The non-hydrostatic model developed by the authors [35] is used herein to reproduce the laboratory experiments in order to provide further insight into the measured wave behavior and to evaluate the model performance. The governing equations in the conservative from and $\sigma$ coordinate are given by Eqs. (1), (2).

$$\frac{\partial D}{\partial t}+\frac{\partial Du}{\partial x}+\frac{\partial \omega }{\partial \sigma }=0\text{,}$$ (1)

$$\frac{\partial \mathit{U}}{\partial t}+\frac{\partial \mathit{F}}{\partial x}+\frac{\partial \mathit{H}}{\partial \sigma }={\mathit{S}}_h+{\mathit{S}}_p+{\mathit{S}}_{\tau }\text{,}$$ (2)

where D = h+η is the total water depth, U = (Du, Dw) is the velocity vector, (u, w) is the primitive velocity. ω is the vertical velocity in σ coordinate and defined by Eq. (3).

$$\omega =D\frac{D\sigma }{D{t}^{*}}=D\left(\frac{\partial \sigma }{\partial t^{*}}+u\frac{\partial \sigma }{\partial x^{*}}+w\frac{\partial \sigma }{\partial z^{*}}\right)\text{,}$$ (3)

where superscript (x*, z*, t*) denotes Cartesian coordinate components. F and H are the flux vectors given by Eq. (4).

$$\mathit{F}=\left(\begin{array}{c}Duu+\frac{1}{2}g{D}^2\\ Duw\end{array}\right)\mathit{H}=\left(\begin{array}{l}u\omega \\ w\omega \end{array}\right)\text{,}$$ (4)

The source terms S_h, S_p and S_τ respectively accounts for the contribution of the hydrostatic pressure, dynamic pressure and bottom friction, as given by Eq. (5).

$${\mathit{S}}_h=\left(\begin{array}{c}gD\frac{\partial h}{\partial x}\\ 0\end{array}\right){\mathit{S}}_p=\left(\begin{array}{c}-\frac{D}{\rho }\left(\frac{\partial p}{\partial x}+\frac{\partial p}{\partial \sigma }\frac{\partial \sigma }{\partial x^{*}}\right)\\ -\frac{1}{\rho }\frac{\partial p}{\partial \sigma }\end{array}\right){\mathit{S}}_{\tau }=-C_{\tau }{\mathit{u}}_b\left|{\mathit{u}}_b\right|\text{,}$$ (5)

where C_τ is the bed roughness coefficient controlled by the Manning coefficient and water depth in the form of C_τ = gn²/h^1/3. u_b = (u_b, w_b) is the velocity vector at the bottom layer.

The vertical velocity should satisfy the kinematic boundary at the water surface and seabed, which is defined by Eq. (6).

$$\begin{array}{l}\mathrm{w}{|}_{\mathrm{z}=\mathrm{\eta }}=\frac{\partial \mathrm{\eta }}{\partial \mathrm{t}}+\mathrm{u}\frac{\partial \mathrm{\eta }}{\partial \mathrm{x}}\\ \mathrm{w}{|}_{\mathrm{z}=‐\mathrm{h}}=‐\frac{\partial \mathrm{h}}{\partial \mathrm{t}}‐\mathrm{u}\frac{\partial \mathrm{h}}{\partial \mathrm{x}}\end{array}\text{,}$$ (6)

In non-hydrostatic type models, the free surface is defined as a single-valued function of horizontal position (disable to handle plunging overturning waves). Integrating Eq. (1) from 0 to 1 in σ coordinate and using the boundary conditions Eq. (6) leads to Eq. (7).

$$\frac{\partial D}{\partial t}+\frac{\partial }{\partial x}\left(D{\int }_0^{1}ud\sigma \right)=0\text{,}$$ (7)

The main steps of numerical implementation are summarized here for completeness, the details are referred to Fang et al. [35]. The governing equations are discretized using rectangle cells in $\sigma$ coordinate. A hybrid finite-volume/finite-difference method is employed to create shock-capturing scheme, with the aim of enhancing model stability and capturing breaking waves as discontinuities without relying on empirical formulations. In contrast, shock-capturing Boussinesq model [38,39] and depth-integrated non-hydrostatic model [40] usually contain some tunable parameters to mimic wave breaking. The convective terms are calculated using finite volume scheme with a central upwind flux function while the rest are discretized using second order finite difference method. The explicit Euler one-step method is adopted for time stepping. Each time step is decomposed into a predictor stage and a corrector stage. In the predictor stage, the intermediate velocity field is obtained by solving the momentum equations with the known pressure field. In the corrector stage, the pressure difference is obtained by solving Poisson-type equations, which is then used to update the final velocity field.

4.2. Parameter settings and boundary conditions

The wave flume shown in Fig. 1 is discretized using uniform △x = 0.02 m horizontal grids and 10 vertical layers after the convergence test. The incident wave signal including free surface elevation and velocities is sent into the computational domain via left inflow boundary using linear wave theory. For solid boundaries such as the vertical wall and fringing reef surface, the free slip boundary conditions are used, and the dynamic pressure at the free surface is zero. A minimum water depth of 0.001 m was used in the numerical simulations to distinguish the wet and dry cells to simply treat moving shorelines that possibly occur on the reef crest. Bottom friction is neglected.

4.3. Model-data comparisons

The predicted time histories of free surface elevation at selected gauge locations for four cases are presented in Fig. 10, Fig. 11, Fig. 12, Fig. 13. As is seen from these figures, the model is able to describe the focusing process that occurs during the long distance propagation from wavemaker (G1) to the end of reef face (G18), denoting the dispersion accuracy of the model is sufficient to reproduce each wave component embodied in the JONSWAP and CWA spectra. The notable discrepancies mainly exist after wave breaking events. As abovementioned, the incident focused wave group breaks on the reef edge/crest and reforms as turbulent bores, their evolution on reef flat involves significant change of free surface elevation, turbulence generation and dissipation and bubble entrainment. However, all these aspects are not well addressed in the numerical model. We thus cannot expect the model to capture fine details of breaking and post-breaking waves in a wave-by-wave manner. In addition to this defect, the model underestimates the wave crest at G21 for crested-reef cases, namely, Case 1B (Fig. 11) and Case2B (Fig. 13), partly because wave gauges record the maximum value of plunging breakers characterized by multi-values in vertical direction whilst the numerical model only simulates the free surface as a single value of the horizontal coordinate. The computed time series of flow velocities at four ADV locations for four cases are also given in Fig. 10, Fig. 11, Fig. 12, Fig. 13, they are found in reasonable agreements with the measurements again regarding the velocity amplitude, phase and variation trend.

Fig. 10.

Comparison of time histories of free surface elevation and flow velocity between measured data (dashed lines) and simulated results (solid lines) for Case 1A.

Fig. 11.

Comparison of time histories of free surface elevation and flow velocity between measured data (dashed lines) and simulated results (solid lines) for Case 1B.

Fig. 12.

Comparison of time histories of free surface elevation and flow velocity between measured data (dashed lines) and simulated results (solid lines) for Case 2A.

Fig. 13.

Comparison of time histories of free surface elevation and flow velocity between measured data (dashed lines) and simulated results (solid lines) for Case 2B.

The computed spectra by the model at G4, G18, G21 and G27 are compared with the experimental data in Fig. 14 at the offshore region (G4), the reef edge (G18), active breaking zone (G21) and the middle of reef flat (G27). In the offshore region, the model slightly over-predicts the spectral amplitude, which possibly because the model does not consider friction of flume bottom and sidewalls. On the reef face (G18), the wave energy transfer from primary frequency to both higher harmonics and low-frequency band are well captured by the model for JONSWAP spectrum waves. However, at the same position, the model underestimates the amplitude of the higher harmonics and low-frequency band for CWA spectrum waves. After a careful check on the video camera for this case, we found wave front becomes very steep at G18 and approaches wave breaking, whilst this is not the case for JONSWAP spectrum waves. Accurate modelling of this highly nonlinear and critical moment might exceed the model's capability range. In the active breaking zone (G21) and in the middle of reef flat (G27), the spectrum amplitudes around the peak frequency are over-predicted but the further dissipation of high-frequency motion and increase of low-frequency motion are still reasonably captured. The downshifting of peak frequency for CWA spectrum waves is also well predicted.

Fig. 14.

Comparison of measured (symbols) and simulated (lines) wave spectra at selected gauges for Case 1 (a)∼(d) and Case 2 (e)∼(f). (Solid lines: Case 1A and Case 2A; Dashed lines: Case 1B and Case 2B; Solid circles: Case 1A and Case 2A; Hollow circles: Case 1B and Case 2B).

5. Conclusions

The propagation and transformation of focused wave groups over typical fringing reef profiles with and without reef crest have been studied in laboratory tests. The nonlinear interaction is enhanced by the processes of energy concentration and shoaling as the wave progresses over the reef face, causing the energy to move from the peak frequency to both lower and higher frequencies. In comparison to the offshore gauge, the higher harmonics and infra-gravity movements are also increasing significantly. Violent plunging breakers that are close to the reef edge or reef flat dissipate the majority of the wave energy in the incident-wave frequency band and higher harmonics. The amplitude of low-frequency wave increases in comparison to or exceeds that of high-frequency wave motion as wave moves closer to the shore. It has been discovered that reef crest has an impact on reef flat that reduces short-period wave motion and increases long-period wave motion.

A multi-layer non-hydrostatic wave model was used for numerical simulations. The non-hydrostatic model is unable to deal with breaking waves because it does not account for wave breaking turbulence. However, the overall performance of the model is not too bad. It can capture the evolution of free surface height and flow velocity across the reef profile, as well as the complicated variation in the wave spectrum caused by wave breaking and non-linear energy transfer. Since there are no ad hoc factors in the model, such as empirical energy dissipation terms or onset/cease criteria for wave breaking, some of the uncertainty caused by these tuneable parameters is reduced. In light of this, we draw the conclusion that the multi-layer non-hydrostatic model is a viable tool for simulating focused wave group propagation along reef-fronted coastlines. Additional parameter research will be carried out using various wave parameters and bathymetry combinations. Future work will also include adding a turbulence closure model to the current model and investigating the scale effect of focused wave group.

Ethics

Not applicable.

Data availability statement

Data generated and utilized for analyses of results presented in this manuscript are available from the corresponding author on reasonable requests.

Funding statement

This work was supported by National Key Research and Development Program of China (2022YFC3106101), and the National Natural Science Foundation of China (52071057, 52171247), and Open Research Project of Hebei Marine Ecological Restoration and Smart Ocean Monitoring Engineering Research Center (HBMESO2316).

CRediT authorship contribution statement

Ping Wang: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Formal analysis, Data curation. Lixin Gong: Writing – original draft, Visualization, Validation, Investigation, Data curation. Kezhao Fang: Writing – review & editing, Writing – original draft, Supervision, Software, Project administration, Formal analysis. Li Xiao: Writing – original draft, Validation, Investigation, Formal analysis, Data curation. Long Zhou: Visualization, Validation, Data curation. Daxun Gou: Visualization, Resources, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.