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Flow and suspended sediment transport in distributary channel networks play an important role in the evolution of deltas and estuaries, as well as the coastal environment. In this study, a 1D flow and suspended sediment transport model is presented to simulate the hydrodynamics and suspended sediment transport in the distributary channel networks. The governing equations for river flow are the Saint-Venant equations and for suspended sediment transport are the nonequilibrium transport equations. The procedure of solving the governing equations is firstly to get the matrix form of the water level and suspended sediment concentration at all connected junctions by utilizing the transformation of the governing equations of the single channel. Secondly, the water level and suspended sediment concentration at all junctions can be obtained by solving these irregular spare matrix equations. Finally, the water level, discharge, and suspended sediment concentration at each river section can be calculated. The presented 1D flow and suspended sediment transport model has been applied to the Pearl River networks and can reproduce water levels, discharges, and suspended sediment concentration with good accuracy, indicating this that model can be used to simulate the hydrodynamics and suspended sediment concentration in the distributary channel networks.

Distributary channels are very common in the delta area, among which many junctions connect individual channel together to form the river networks system. Channel junctions not only play a crucial role in dividing the river discharge over distributary channels but also govern the distribution of the river sediment transportation in the form of suspended sediment. Since flow and suspended sediment transport in the distributary channels are not only highly related to the evolution of deltas and estuaries but are also related to the environment issue, it is important to understand hydrodynamics and suspended sediment transport in the distributary channels system. The 1D numerical model as an important tool has been widely used to simulate flow and sediment transport over river networks because it can accurately represent complex river network geometries and complex structures like weirs, barrages, and dams [

In the late 1970’s, Thomas and Prashum [

Most of the 1D models, however, are widely used to simulate the basic parameters, including the velocity, water level, bed elevation, and suspended sediment transport, in a single channel. Actually, 1D models can also be used to investigate hydrodynamics and sediment transport in distributary channel networks with complex planimetric structure and dynamics [

The hydrodynamic module of 1D model is based on the well-known Saint-Venant equations of the mass and momentum conservation. Consider

Suspended sediment model is based on the nonequilibrium transport equation. The continuity equation of suspended load can be expressed as

The formula for sediment carrying capacity can be expressed as

The finite-difference equations are obtained by using Preissmann’s four-point implicit difference scheme (Figure

Illustration of the flow on grid and network domains.

The hydraulic conditions at river networks junctions are reasonably assumed to satisfy two additional conditions: the quality conservation and energy conservation conditions. The quality conservation condition, which is also called discharge connection condition, means that the discharge changes are assumed to be equal to the shortage variation of discharge at a certain junction. Consider

The equation of energy conservation can be approximated using the following kinematic compatibility condition [

Finally, the finite-difference approximation of the continuity equation around the junction can be written as follows:

The values for water level can be calculated at each junction by successively applying the double sweep Thomas algorithm.

For each river section, based on the finite-difference equation (

The coefficients in (

Subsequently, the relationship between the river sections and the junction can be deduced from a single river channel by using the formula (

Substituting (

Finally, the water level and discharge at each river section of the river networks can be calculated.

For suspended sediment transport, the upwind finite-difference scheme and Preissmann’s four-point implicit difference scheme are adopted (Figure

Illustration of the suspended sediment on grid and network domains.

(i) For the downflow,

The irregular matrix equations are written as

(ii) For the upflow,

The irregular matrix equations are written as

In the tidal channel, the flow direction changes with tidal level fluctuation. The flow types of a single channel can be classified as four types (Figure

The four types of the flow at a single river channel. The types are as follows: downflow, upflow, faced-flow, and depart-flow, from the left to the right.

For the downflow, it is single direction flow. If the sediment concentration at the upboundary junction (

For the upflow, it is also single direction flow. If the sediment concentration at the downboundary junction (

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 junctions (

For the depart-flow, it is another double direction flow. First, the position of the stagnant point (

And the suspended sediment concentration at the stagnant point is

This paper also presents a junction-control method for suspended sediment in river networks.

Assuming that the erosion and deposition at the junction are small, the suspended sediment mass conservation equation is written as

Utilizing (

Solving (

The river networks in the Pearl River Delta (PRD) (Figure ^{2}. The area of the Pearl River networks cover approximately 9750 km^{2}, with a total length of over 1600 km and a coastline extending over 450 km from east to west. The Pearl River networks drain three main tributaries, Dongjiang River, Beijiang River, and Xijiang River, pass through this complex river network, and finally flow into the South China Sea through eight subestuaries that are separately called Humen, Jiaomen, Hongqimen, Hengmen, Modaomen, Jitimen, Hutiaomen, and Yamen.

Map of the Pear River networks and sampling stations.

The Pearl River network is simplified as 328 single river channels, 13 boundary rivers, 5108 computational river sections with the interval varying from 0.2 to 3.0 km, and 216 river channel junctions. Upstream boundary conditions are given by discharge and suspended sediment concentration at the five upstream boundary junctions (Shizui, Gaoyao, Shijiao, Laoyagang, and Boluo). Tidal level fluctuation and suspended sediment concentration at the downstream outlets are used as downstream boundary conditions. The Manning coefficients in the Pearl rivers are taken to be 0.01–0.05.

The distributary channel networks model has been extensively calibrated with respect to the field measurements to optimize the representation of the water level, discharge, and suspended sediment concentration over the study area. The field measurement data in 1998 and 2001 are used for calibration and validation, respectively. The Nash-Sutcliffe model efficiency (ME) which is the ratio of model error to variability in observational data is employed in this paper to evaluate the performance of the distributary channel networks model. Consider

where

(a) The calibration of water levels from July 18 to July 19, 1998. (b) The validation of water levels from February 7 to February 16, 2001.

The calibration result shows that the majority of the ME values for water levels over the Pearl River networks is over 0.65, indicating that the numerical model of the distributary channel networks can accurately simulate water level in the river networks (Figure

In terms of water discharge (Figure

(a) The calibration of discharges from July 18 to July 19, 1998. (b) The validation of discharges from February 7 to February 16, 2001.

(a) The calibration of suspended sediment concentration from July 18 to July 19, 1998. (b) The validation of suspended sediment concentration from February 7 to 16, 2001.

Figures

There are some potential reasons for errors between the simulated and observed suspended sediment concentration. Firstly, the bathymetry of the Pearl River network changes dramatically due to the intensive sand excavation during the last three decades. Therefore, the asynchronous of hydrographic and bathymetry measurement may directly lead to the inaccuracy of the simulation results. Actually, the field hydrographic measurements took place in 1998 and 2001, but the bathymetry survey happened in 1999 in our model. The asynchronous of hydrographic and bathymetry measurement should be one of the main reasons for the simulation errors. Secondly, large domain simulation needs more data and parameters, especially in suspended sediment transport simulation. However, some parameters of the suspended sediment, such as the diameter of the sediment, are regarded as relatively uniform distribution over the Pearl River network due to the limit of the data, which definitely lead to errors when simulating sediment transport. In general, the modeled results can be considered acceptable for simulating the flow and suspended sediment transport in the distributary channel networks.

A 1D hydrodynamics and suspended sediment model is developed for simulating the flow and sediment transport in the distributary channel networks. Firstly, by utilizing the finite-difference equations of the single river, as well as the mass and energy conservation at junctions, the equations of water level at junctions can be transformed to the irregular spare matrix equations. Water level and discharge at each channel section of a certain channel then can be obtained by the governing equations of the single channel. Assuming that the the erosion and deposition at the junctions are small, the nonequilibrium transport equation for suspended sediment can also be written in a matrix form. Solving the irregular spare matrix equations, suspended sediment concentration can also be obtained at all junctions. Finally, the suspended sediment concentration at each river section in river networks can be calculated.

The distributary channel networks model was applied to the Pearl River networks, one of the most complicated river networks in the world, to check the performance of the model. The model was extensively calibrated and validated against field measurements to provide an accurate representation of water level and discharge, as well as suspended sediment transport in the Pearl River networks. The calibrated and validated results show that the distributary channel networks model display an excellent performance in simulating water level and discharge. Although the performance in simulating suspended sediment concentration is not as excellent as that of water level and discharge, the model is still good enough to simulate the suspended sediment transport in the distributary channel networks model.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This research was financially supported by Commonweal Program of Chinese Ministry of Water Resources (Project number: 201301072), the Natural Science Foundation of China (NSFC, Project number: 41376094), Joint Research Projects NSFC-NWO (Project number: 51061130545), and Program for Excellent Innovative Talents of Hohai University.