The Humen Estuary, one of the largest outlets of the Pearl River, is a long and wide tidal channel with a considerable tidal flow every year. Storm surges, always superposing spring tide, travel from the estuary and endanger the safety of people living around the river. However, little research has quantified the relationship between the hydraulic characteristics and the geometry features in this estuary. In this regard, an analytical model, combined with a numerical model, is applied to investigate the characteristics of tidal waves and surge propagations in the estuary. Given the geometric, topographic, and tidal parameters at the mouth of the estuary, the tidal damping and wave celerity can be computed. The numerical results were used to calibrate and verify the analytical model. The results indicate that the analytical model can describe the astronomical tidal dynamics very well in correspondence with the numerical results. However, the analytical model cannot predict the tide well when a tropical cyclone-induced surge is superimposed on the astronomical tide. The reason is that this model does not take the wind stress and the pressure depression into account. After reducing Manning’s coefficient, we found that the analytical results could be close to the numerical results. Finally, we analyzed the characteristics of the tidal wave in the Humen Estuary using the analytical solution and its parameters.

Tidal waves are a major hydrodynamic factor that influences the flooding, ecosystems, transport, and morphological evolution in estuaries. In contrast to tidal waves in deep oceans, which are driven by astronomical forces with a high degree of predictability, waves propagating along estuaries tend to adjust their amplitude, celerity, and shape during interactions with topography, friction, and other secondary factors such as wind stress and runoff. A tidal wave in a shallow estuary has the characteristics of amplification and damping, which alternate along the estuary. The tidal amplitude is influenced by two dominant processes: amplification due to convergent cross sections with a decrease in depth in the landward direction and damping due to bottom friction. If the former process dominates over the latter, the wave is amplified; otherwise, the wave is damped. The celerity of propagation is also influenced by the processes of tidal damping and amplification. If the tidal wave is damped, the celerity is decreased. Conversely, if the tidal wave is amplified, the celerity is increased [

To understand the mechanism of tidal wave propagation along an estuary, vast efforts have been made to induce and solve the estuary hydrodynamic model. Generally, these works can be divided into two methods: analytical solutions and numerical simulations. With advances in computational technology, tidal wave propagation can be accurately simulated by numerical models [

The Humen Estuary, one of the major accesses for a tidal wave from the South China Sea entering the Pearl River network, has a significant effect on flooding and inundation in Guangzhou city, which is the capital and economic center of Guangdong Province. However, limited measured data in the Humen Estuary restrict the understanding of tidal wave propagation along the Humen Estuary in the upstream direction. Although some previous numerical simulations have been performed [

With the questions mentioned above, the objectives of the study are as follows: 1. to compose and validate a method of analysis that combines a classical analytical solution and the numerical results and is able to correctly reflect the characteristics of tide propagation in the Humen Estuary; 2. to check and verify a way to adapt the method of analysis to the context of tidal wave and surge propagation associated with tropical cyclones; and 3. to extract insight into the hydrodynamic features and factors in the Humen Estuary. Thus, we apply Savenije’s analytical solution to the Humen Estuary in conjunction with numerical simulation results to describe and analyze the characteristics of the tidal wave in the Humen Estuary, Pearl River. A series of tests are conducted to answer the above questions in this paper.

The sections are organized as follows. First, some background information about the Humen Estuary in the Pearl River network is introduced in

The Pearl River network, located in South China, delivers a large amount of fresh water (ranging from 20,000 m^{3}/s in the wet summer to 3600 m^{3}/s in the dry winter) into the northern South China Sea through eight outlets (

The shapes of most alluvial estuaries are similar all over the world. The width and the area of the cross section decreases in the upstream direction, resulting in a convergent (funnel-shaped) estuary. The main geometric parameters of the convergent estuary can be described by exponential functions along the estuary axis with the origin at the mouth:_{0}, _{0}, and _{0} are the same variables at the estuary mouth;

The parameters of Equations (1)–(3) can be obtained by regression on the topographic data. From the digital elevation model (DEM) of the Pearl River Delta, 54 cross sections were extracted to obtain the cross-sectional area, width, and depth (

The tidal dynamics in an estuary can be described by the following Saint–Venant equations:

After the scaling of Equations (4) and (5) and under the assumption of a harmonic wave traveling from the estuary mouth to the upstream reach, the following dimensionless parameter can be obtained:_{0} is the classical wave celerity of a frictionless progressive wave,

Using the above dimensionless parameters in Equations (6)–(11), the scaling form of Equations (4) and (5) can be solved on the basis of the equations for the phase lag:

The Finite Volume Community Ocean Model (FVCOM), an unstructured-grid finite-volume, three-dimensional primitive equation coastal ocean model developed originally by Chen et al. [

The forces driving the model include tidal waves from the South China Sea and surges caused by meteorological forces such as storms, cyclones, and rainfalls. In this paper, we consider only tropical cyclone. The semi-empirical parametric cyclone model is integrated into the ocean model to drive the surge. The advantage of the parametric cyclone model is that it does not require as much meteorological data as the dynamic model to drive the model. The only data needed contain the track of the cyclone, the center pressure drop, the forward speed, and the maximum wind radius, most of which are available on weather forecast websites except for the maximum wind radius, which should be obtained using a statistical formula and then adjusted according to the surge results. Here, the cyclone No.1822 (

We used the Humen Estuary geometry presented in

The model was further verified with the numerical results on 16–17 September 2018. The reason for choosing this period is that Super Typhoon Mangosteen approached and made landfall on the coast of Guangdong Province during this time. Thus, at first, we only simulated the astronomical tide without exerting a wind force in the numerical model. Through this simulation, the analytical result was compared with the numerical result assuming no cyclone landfall. From

Then, we simulated the typhoon-surge scenario by setting the cyclone model and by exerting the wind and pressure forces on the surface of the tidal flow. The analytical result was compared with the numerical result. It is shown in

From Equation (16), we can find that the effect of the positive wind stress term, which caused a maximum surge, is equivalent to a reduction in the Manning coefficient:

Therefore, we can make the analytical solution close to the numerical result by tuning Manning’s coefficient to be less. The analytically calculated tidal amplitudes before and after tuning the coefficient are shown in

Savenije’s solution describes the variation of the four dimensionless parameters

The hydrodynamic analysis, as with the geometric analysis, indicates that there are three distinct segments for the mainstream of the Humen estuary.

To investigate the difference made by the storm surge compared with the normal tidal wave, we depicted the calibrated parameter curves in the middle section under the storm surge. As expected, the curves under the surge move slightly toward the zone with less friction from the original curves under the astronomical tide. This is in agreement with the analysis of the results in the former section. Previous studies have indicated that runoff can increase the friction for wave propagation in an estuary; however, this study shows that storm surge can reduce the friction for the wave propagation while exaggerating the wave amplitude.

The Humen Estuary is so complicated that it can be divided into three sections. Any section demonstrates its distinct features compared with the others. To better understand the property, we compared them with other typical estuaries, which have been analyzed by Savenije et al. [

In this study, Savenije’s solution was applied for the first time to the Humen Estuary. Due to the scarcity and low resolution of the measured data, we used the numerical results to calibrate and verify the analytical model. The merit of using an analytical model is that it can provide direct insight into relationships among the tidal properties, such as velocity amplitude, the tidal damping rate, and wave celerity; the geometry indicator; friction; and the tidal forces. This analytical model demonstrated good accuracy when it was applied to an estuary where the tide dominates in comparison with the river discharge. The results indicate that the analytical model can predict the astronomical tide well in the Humen Estuary after calibration. However, it cannot predict the tide well when a tropical cyclone-induced surge is superimposed onto the astronomical tide. The reason may lie in the fact that Savenije’s solution does not take the wind forces into account. After reducing Manning’s coefficient, we found that the analytical result could be close to the numerical results. This means that the loss of the wind forcing can partly be compensated by adjusting the friction.

By analyzing the tidal wave propagation along the Humen Estuary, we found that the characteristics of the three sections—the mouth section (0–8.7 km), the middle section (8.7–30.4 km), and the upstream section (30.4–36 km)—are not alike at all. The mouth section is a typical riverine estuary with a nearly constant cross section. The tidal wave traveling there is in the form of a progressive wave and with a nearly classical celerity in a frictionless state. In contrast, the upstream section is a typical oceanic estuary with a short convergence length. The tidal wave there is in the form of a standing wave with a nearly infinite celerity. The middle section is in the intermediate zone of the two solution families. The tidal wave is first amplified and then damped, with a transition point that is the location of the maximum tidal amplitude. Finally, a comparison was conducted between the Humen Estuary and other estuaries.

Conceptualization, Z.Z. and F.G.; methodology, Z.Z.; validation, Z.Z.; formal analysis, D.Z.; investigation, Z.Z.; resources, D.H.; data curation, D.H.; writing—original draft preparation, Z.Z.; writing—review and editing, F.G.; visualization, D.Z.; supervision, D.Z.; project administration, F.G.; funding acquisition, F.G. All authors have read and agreed to the published version of the manuscript.

This paper was supported by the National Key R&D Program of China (grant No. 2018YFB0505500 and 2018YFB0505502) and by the National Natural Science Foundation of China (grant No. 41771421, 41771447, and 41571386).

Not applicable.

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No report any data.

The authors declare no conflict of interest.

The location of the outlets of the Pearl River network.

The deployment of the cross sections along the Humen Estuary.

The regression lines for the cross-sectional area ^{2}), width

The domain and grids of the Pearl River network model.

Verification of the numerical model in four stations: Nansha, Wanqinsha, Henmeng, and Neigang.

Comparison of the analytical results for (

Comparison of the analytical results for (

Comparison of the analytical tidal amplitude before (solid line) and after (dash line) tuning Manning’s coefficient, and numerical simulation for verification under tide and surge during 16–17 September 2018.

The relation between four parameters: (

Positioning of the Humen (red line), Schelde (yellow squares), and Hau (pink triangles) Estuaries in the damping number (

Shape characteristics of the Humen Estuary.

Subsections | Range (km) | A (km) | B (km) | D (km) |
---|---|---|---|---|

Mouth | 0–8.7 | 166.7 | 333.3 | 333.3 |

Middle | 8.7–30.4 | 25 | 71.4 | 40.0 |

Upstream | 30.4–36 | 20 | 8.3 | 208.3 |

The parameters of the Typhoon Mangosteen (two days before landfall).

Time | Latitude (N) | Longitude (E) | Pressure (hPa) | Maximum Wind Speed (m/s) |
---|---|---|---|---|

00:00 14/09 | 16 | 126.9 | 905 | 56.6 |

06:00 14/09 | 16.7 | 125.7 | 905 | 56.6 |

12:00 14/09 | 17.4 | 124.1 | 905 | 56.6 |

18:00 14/09 | 18 | 122.3 | 905 | 56.6 |

00:00 15/09 | 18 | 120.5 | 940 | 46.3 |

06:00 15/09 | 18.5 | 119.7 | 940 | 46.3 |

12:00 15/09 | 19.2 | 118.3 | 950 | 43.7 |

18:00 15/09 | 19.8 | 117 | 955 | 41.2 |

00:00 16/09 | 20.6 | 115.3 | 960 | 38.6 |

06:00 16/09 | 21.7 | 113.5 | 960 | 38.6 |

12:00 16/09 | 22.2 | 111.6 | 970 | 33.4 |

18:00 16/09 | 22.7 | 109.7 | 980 | 28.3 |

Parameters used for analytical model.

Subsections | Storage Width Ratio_{s} |
Value Range | Manning’s Coefficient ^{−1/3}s) |
||
---|---|---|---|---|---|

Astronomical Spring Tide | Considering Cyclone Surge | Value Range | |||

Mouth | 1 | 1–2 | 0.005 | 0.005 | 0.017–0.06 |

Middle | 1.8 | 1–2 | 0.031 | 0.018 | 0.017–0.06 |

Upstream | 1.5 | 1–2 | 0.035 | 0.015 | 0.017–0.06 |