River networks and estuaries are very common in coastal areas. Runoff from the upper stream interacts with tidal current from open sea in these two systems, leading to a complex hydrodynamics process. Therefore, it is necessary to consider the two systems as a whole to study the flow and suspended sediment transport. Firstly, a 1D model is established in the Pearl River network and a 3D model is applied in its estuary. As sufficient mass exchanges between the river network and its estuary, a strict mathematical relationship of water level at the interfaces can be adopted to couple the 1D model with the 3D model. By doing so, the coupled model does not need to have common nested grids. The river network exchanges the suspended sediment with its estuary by adding the continuity conditions at the interfaces. The coupled model is, respectively, calibrated in the dry season and the wet season. The results demonstrate that the coupled model works excellently in simulating water level and discharge. Although there are more errors in simulating suspended sediment concentration due to some reasons, the coupled model is still good enough to evaluate the suspended sediment transport in river network and estuary systems.
As a link between marine environments and rivers, estuaries are characterized by a variety of complex and complicated processes [
A lot of efforts have been made recently to develop coupled modelling systems, which were designed for different estuaries [
The Pearl River Estuary (PRE) and its upstream river network form the largest river system in the southern China. Historically a rich and fertile area, it has now become one of the most populated and most developed regions in China. However, as the economy grows in the region, serious problems also occur at the Pearl River network and its estuary, such as salinity intrusion [
The model coupled the 1D river network model with the 3D coastal model. It takes into consideration the complex topography of the river network and the vertical gradients of the coastal hydrodynamics. The model is applied in the PRD, which is divided into two parts. The 1D model is set up in the Pearl River network and the 3D model is applied in the PRE to investigate the transport of water flow and suspended sediment in the delta.
Based on the Saint-Venant equations and the nonequilibrium transport equation for the suspended sediment, a numerical model of junction-channel for the river network is established by using the “junction-control” method for water level and suspended sediment concentration. Firstly, the river network is schematized as river channels, junctions, and cross-sections. Secondly, the variables at each junction are calculated by solving the governing equations. Finally, the water levels, discharges, and suspended sediment concentrations at each cross-section in each river channel are calculated. More details about the hydrodynamics difference scheme and transforms of the finite-difference equations can be found in Zhang et al. [
The governing equation for the nonequilibrium transport of suspended load [
The riverbed transfiguration equation is
For suspended sediment transport equation, the upwind finite difference scheme and Preissmann four-point implicit difference scheme are employed here. According to the direction of flow, the difference equations are written as
In a tidal river, flow direction changes with ebb and flood current. The flow at a single river channel can be classified by four types (Figure
The flow direction at a single river channel changes with ebb and flood current in the tidal river. And the direction can be classified by four types (from the left to the right):
For the downflow, it is single direction flow. If the sediment concentration at the up-boundary node (
For the upflow, it is also single direction flow. If the sediment concentration at the down-boundary node (
For the faced-flow, it is double direction flow. The single river can be divided into two single direction flow river segments. If the sediment concentrations at the up- and down-boundary nodes (
For the depart-flow, it is another double direction flow. Firstly, the position of the stagnant point (
Finally, the sediment concentration at the stagnant point is
The 3D hydrodynamic and suspended sediment model is established based on ECOM model, a free-surface, fully nonlinear, primitive-equation estuarine and coastal ocean model. The equations under the orthogonal curve coordinate include water continuity equation and the momentum equations:
The diffusion process of salinity is also necessary to consider for the model. The conservation equations are described as
The transport equation of the suspended sediment is written as
The details of ECOM model can refer to Zhu et al. [
In this paper, the relationship expression of water level between 1D model and 3D model is deduced by strict mathematics method. The 1D and 3D models meet at outlets of river network and estuary, and the hydroinformation is transferred through interfaces, by which the additional hydrodynamic equation of the 1D and 3D coupled numerical model can be derived. The 1D and 3D boundary conditions at interfaces are satisfied through iteration.
The water level and discharge at the interfaces of the 1D model and 3D model can be reasonable considered equal:
Due to the difference of water levels at grids of 3D model, the down-boundary of the 1D model is the averaged water levels of the grids in the 3D model:
Based on the method of the 1D hydrodynamics model, the governing equation can be deduced to matrix of water level at junctions as below:
However, in a coupled model, the interfaced water levels are not known, which lead to
Gauss elimination method is used to simplify the coefficient matrix
Then, the water levels at junctions connected to the interfaces can be expressed by the water levels at interfaces of 1D model and 3D model:
Utilizing the relations between the water level and discharge at junctions [
Equation (
After simplifying (
Finally, taking into account (
At the beginning of the calculation, the initial discharges
As for the suspended sediment model, two additional conditions are needed to be considered. Firstly, the sediment fluxes at the interfaces of the 1D model and 3D model should be equal:
Secondly, the spatial averaged sediment concentration of 3D model should be closed to that of 1D model:
The Pearl River Delta (PRD) is located in the northern of the South China Sea. It is a dynamically complex estuarine system, which encompasses Pearl River network and PRE. The Pearl River, a subtropical river, is the second largest Chinese river in terms of annual water discharge (over 3 × 1011 m3). The channel network is formed by a large number of intricately interlaced deltaic branches, including three principal rivers: Xijiang, Beijiang, and Dongjiang, and some small rivers draining the PRD. It is a catchment area of 26,820 km2 and a total length of 1,600 km [
These fluxes pass through the river network and flow into the PRE through the eight outlets Hutiaomen and Yamen discharging into the Huangmao Bay, Modaomen and Jitimen discharging into open sea directly, and Humen, Jiaomen, Hongqimen, and Hengmen discharging into the Lingding Bay [
The model is applied to the Pearl River network and its estuary. The river network in 1D model is discretized into 347 channels, 13 boundary rivers, and 1,850 cross-sections with the interval varying from 0.2 to 3.0 km and 220 junctions. The length of the river network is about 1,600 km. The upstream boundaries include Shizui at the Tanjiang River, Gaoyao at Xijiang, Shijiao at Beijiang, Laoyagang at the Liuxi River, and Boluo at Dongjiang. The downstream boundaries include Dahu at Humen, Nansha at Jiaomen, Wanqingsha at Hongqili, Hengmen at Hengmen, Denglongshan at Maodaomen, Huangjin at Jitimen, Hutiaomen at Hutiaomen, and Huangchong at Yamen. These eight outlets are also the interfaces of the 1D and 3D model. The 3D estuarine model covers the area from the eight outlets to the −30 m isobaths (Figure
Map of the study area including
The hourly observed runoff at the upstream stations is the upper boundary conditions of the coupled model. The salinity at those stations is definitely zero. At the open sea part of the coupled model, the tidal levels are evaluated by the harmonic analysis from the most important tidal constituents of the PRE, with the uniform values of temperature and salinity from the observations. Consider the following:
The simulation is initialized with zero water levels and velocities in the bathymetry of 1998-1999 and runs about 30 days. The results of the model are used as the new initial conditions and the simulation hot-started with the results. The processes are repeated several times until the error between the last two simulations satisfies a given condition. These results are then used as the initial conditions of the coupled model. Two different periods, including July 1998 (wet season) and December 1998 (dry season), are used for model calibration. In both the 1D and 3D model domains, the nonuniform parameters, such as bed roughness parameter and particle diameter, have been adjusted in order to optimize the water level, discharge, and suspended sediment concentration over the upstream river network and its coastal waters. The specific key parameters of the coupled model are shown in Table
Parameters of the modeling.
Settings | Description | |
---|---|---|
1D | Time steps | Based on the scope of model, the time step of the 1D model is 10 s |
Roughness coefficient | This coefficient depends on the physical properties of the riverbed. At Beijiang, from upstream boundary to Sanshui | |
Particle diameter | In channel, the median particle diameter of suspended sediment is about 0.01~0.040 mm, and the median particle diameter of bed material is about 0.17~0.44 mm. | |
Sediment transport capacity |
| |
Recovery coefficient relating to the saturation | When the channels are in the deposition conditions, a value of 0.25 is applied; while, in the erosion conditions, a value of 1.0 is applied. | |
|
||
3D | Time steps |
|
Bottom roughness |
| |
Particle diameter | The median particle diameter is 0.003~0.009 mm during the spring tide period. | |
Sediment settling velocity |
|
The coupled model uses the field measurements in July 1998 (wet season) and December 1998 (dry season) at eighteen stations (Figure
This method is widely utilized by numerical modeling system [
The model skill scores for water levels are fairly high (Figures
The coupled model uses the field measurements from July 18, 1998, to July 19, 1998 (wet season), at eighteen stations as calibration. The model skill score is employed to evaluate quantitatively the model performance of water levels (a), discharges (b), and suspended sediment concentration (c) against the measured time series. The circles with the different colors represent the different performances of the model. The high scores of the water levels and the discharges show the good performance of the model, which include the contribution of the calibration of the suspended sediment concentration.
The calibration of the coupled model results with the measured time series at eighteen stations is shown, from December 19, 1998, to December 20, 1998 (dry season). The model skill score is used to evaluate the model performance of water levels (a), discharges (b), and suspended sediment concentration (c) quantitatively. The circles with the different colors represent the different performances of the model. With the high scores of the water levels and the discharges, the performances indicate the success of the model. The skill scores of the suspended sediment concentration are also good enough.
Figure
The calibration of velocity between the model results and observations at 9 stations in the Pearl River Estuary is shown. The calibration of the velocity at the surface (blue), the middle (yellow), and the bottom (green) is deployed. The result shows a good performance with the skill scores of the velocity ranging from 0.4 to 0.6.
The comparison of suspended sediment concentration for calibration at stations in the Pearl River Estuary is displayed. The skill scores of the surface (blue), the middle (yellow), and the bottom (green) show the good performance of the model with the skill scores of all the stations being above 0.2.
From Sixianjiao to Chaolianzhoutou, the annual amount of erosion and deposition in the sand excavation (up) and under the natural conditions (down) is provided in 1998. The comparison quantifies the impacts of the sand excavation in the bathymetry evolution and indicates that the amount of sand excavation has to be taken into account in the comparison between the observed and the modelled sediment erosion and deposition.
The map of the part of the Pearl River network (a) includes the locations of the main river reaches and stations. The comparison of the observed and simulated thickness of erosion or deposition (b) in 1998 is exhibited, which shows that the performance of the model can be used to evaluate sediment transport in this region.
The results show that the model skill score for sediment concentration is lower than that for water level and discharge. There are some potential reasons for the relative larger discrepancy between the simulated and observed value. First of all, more parameters in sediment simulation need to be selected than that of water level and discharge simulation. Normally, the roughness coefficient is the most important parameter in hydrodynamics simulation. However, large domain simulation in suspended sediment transport needs more data and parameters, such as the particle diameter and sediment settling rate. These parameters have large influences on the suspended sediment concentration simulation. However, due to the lack of data, some of these parameters are treated as relatively uniform distribution over the Pearl River network. This leads to error when simulating sediment transport. Secondly, the bathymetry of the Pearl River network changes dramatically due to the intensive sand excavation during the last three decades. Therefore, the asynchrony of hydrographic and bathymetry measurement may directly lead to the inaccuracy of the simulation results, especially in suspended sediment transport simulation. In fact, in our model, the field measurements were taken in 1998, but the bathymetry survey was done in 1999. The asynchrony of hydrographic and bathymetry measurement should be another reason for the simulation errors. Finally, some complex impacts, such as wind and discharge let-out by nearby reservoir, are not considered in this model, which probably affect the results of the coupled model.
This model was then used to simulate the flow division in the PRD, because flow division at some important junctions is important for the flow and sediment transport in distributary channel networks. Makou and Sanshui Stations are located at the apex of the delta. Their water discharge enters the Xijiang and the Beijiang, respectively. Table
The water flux and the diversion ratio at the two main joints in the Pearl River network: (a) Makou and Sanshui and (b) Tianhe and Nanhua (unit: ×108 m3).
Bathymetry | 1999 | |||
---|---|---|---|---|
Station | Makou | Sanshui | Tianhe | Nanhua |
Annual water flux | 2132 | 1521 | ||
Wet | 1185 [73.4%] | 406 [78.3%] | 598 [72.5%] | 515 [74.0%] |
Diversion ratio | 74.5% | 25.5% | 53.7% | 46.3% |
Dry | 429 [26.6%] | 112 [21.7%] | 227 [27.5%] | 181 [26.0%] |
Diversion ratio | 79.3% | 20.7% | 55.6% | 44.4% |
Annual | 1614 [100%] | 518 [100%] | 825 [100%] | 696 [100%] |
Diversion ratio | 75.7% | 24.3% | 54.2% | 45.8% |
The suspended sediment flux and the diversion ratio at the two main joints in the Pearl River network: (a) Makou and Sanshui and (b) Tianhe and Nanhua (unit: ×104 t).
Bathymetry | 1999 | |||
---|---|---|---|---|
Station | Makou | Sanshui | Tianhe | Nanhua |
Annual sediment flux | 1494 | 1052 | ||
Wet | 1198 [96.8%] | 253 [98.8%] | 553 [96.3%] | 461 [96.4%] |
Diversion ratio | 82.6% | 17.4% | 54.5% | 45.5% |
Dry | 40 [3.2%] | 3 [1.2%] | 21 [3.7%] | 17 [3.6%] |
Diversion ratio | 93.0% | 7.0% | 55.3% | 44.7% |
Annual | 1238 [100%] | 256 [100%] | 574 [100%] | 478 [100%] |
Diversion ratio | 82.9% | 17.1% | 54.6% | 45.4% |
The simulated flow flux and suspended sediment flux at the eight outlets in 1999.
Outlet | Humen | Jiaomen | Hongqimen | Hengmen | Maodaomen | Jitimen | Hutiaomen | Yamen | Total | |
---|---|---|---|---|---|---|---|---|---|---|
Flow flux |
Annual | 537 | 514 | 205 | 301 | 623 | 64 | 79 | 187 | 2510 |
[21.4%] | [20.5%] | [8.2%] | [12.0%] | [24.8%] | [2.5%] | [3.1%] | [7.5%] | [100%] | ||
Wet | 401 | 381 | 156 | 223 | 447 | 46 | 59 | 123 | 1836 | |
[21.8%] | [20.8%] | [8.5%] | [12.1%] | [24.4%] | [2.5%] | [3.2%] | [6.7%] | [100%] | ||
Dry | 136 | 133 | 49 | 78 | 176 | 18 | 20 | 64 | 674 | |
[20.2%] | [19.7%] | [7.3%] | [11.5%] | [26.1%] | [2.7%] | [3.0%] | [9.5%] | [100%] | ||
|
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Suspended sediment |
Annual | 208 | 199 | 90 | 115 | 289 | 17 | 24 | 41 | 983 |
[21.2%] | [20.2%] | [9.2%] | [11.7%] | [29.4%] | [1.7%] | [2.4%] | [4.2%] | [100%] | ||
Wet | 157 | 185 | 85 | 111 | 258 | 15 | 22 | 26 | 859 | |
[18.3%] | [21.5%] | [9.9%] | [12.9%] | [30.0%] | [1.8%] | [2.6%] | [3.0%] | [100%] | ||
Dry | 51 | 14 | 5 | 4 | 31 | 2 | 2 | 15 | 124 | |
[41.1%] | [11.3%] | [4.1%] | [3.2%] | [25%] | [1.6%] | [1.6%] | [12.1%] | [100%] |
In deltaic estuaries, the exchanges of the mass flux between river network and estuary require the researchers to consider these two systems as a whole. Therefore, this paper provides a mathematical method to connect the 1D river networks with the 3D estuarine model to study the flow and suspended sediment transport in this region. Based on the classic Saint-Venant equations and the nonequilibrium transport equation, 1D flow and suspended sediment model is established. Based on the orthogonal curve coordinate and the ECOM model, 3D estuarine model is established to describe the complex horizontal and vertical variability of the flow and suspended sediment transport. The relationship expression of water level at interfaces of 1D model and 3D model is strictly deduced by utilizing the relations between the water level and discharge at junctions. The 1D and 3D hydrodynamics models are then coupled by iterative computations. Finally, the 1D and 3D suspended sediment models are also coupled by adding two additional conditions. The advantage of this coupled method is that the schematisations do not overlap at the interface of the two systems, which can improve the stability of modelling.
The coupled model has been applied successful in the Pearl River network and its estuary, which is a complicated system. The simulated results are compared with the field measurements to evaluate the accuracy of the coupled model. The results show that the coupled model is capable of simulating water levels, discharges, and the suspended sediment concentration in the river network, as well as the velocity and suspended sediment at the shallow estuary. Generally speaking, the coupled model is elaborate enough to simulate water levels, discharges, and velocity in the study area. Due to the limit of the data and the simplification of the model, although the simulated suspended sediment is not as good as water level and discharge, it is still acceptable to investigate the suspended sediment transport in river network and estuary system.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was financially supported by the “Natural Science Foundation of China” (NSFC, Project nos. 41006046 and 41376094), the “Joint Research Projects NSFC-NWO” (Project no. 51061130545), and the “Commonweal Program of Chinese Ministry of Water Resources” (Project no. 201301072).