# Development of a Two-Dimensional Hybrid Sediment-Transport Model
## 1 Introduction  
Sediment transport, defined as sediments driven by water and moving with the water, is one of the most important processes when studying morphological and environmental problems. Sediment transport may result in sediment depositions in lakes, reservoirs [1, 2] and coastal wetlands [3, 4]; erosion of riverbanks [5, 6], coastlines [7, 8], and downstream of dams [9, 10]; local scour downstream of hydraulic structures [11, 12]; gully erosion [13, 14]; channel evolution [15, 16]; adsorption/de-adsorption and resuspension [17], etc. In addition to conventional physical models, with the advancement of computer technology and numerical methods, numerical models have become powerful tools to study sediment transport in rivers, lakes, reservoirs, and coastal regions. In natural rivers, sediment in the water can be described as a two-phase flow [18, 19], in which the sediment phase and the water phase are governed by the continuity and the momentum equations and interact with each other all the time [20, 21]. In the conventional single-phase flow method, sediment transport is described as a diffusion phenomenon using the momentum equation and the transport equations: the suspended load moves in the form of a suspension in the water column, while the bed load moves by sliding, rolling, or saltation along or nearthe bed. Despite the advancement of the two-phase flow method [21; 22; 23] in recent years, the single-phase flow method [20; 24; 25; 26] is still dominant in sediment transport modeling due to its relative simplicity and higher computational efficiency. Sediment transport models may be categorized according to the dimension of study domains (one dimensional (1D), two dimensional (2D), or three dimensional (3D)), flow conditions (steady or unsteady), uniformity of sediment particles (single-sized or multiple-sized), transport mode of sediment (equilibrium or nonequilibrium), and the cohesion of sediment materials (noncohesive or cohesive). In natural rivers, nonuniform and noncohesive sediments are dominant, and the flows are unsteady and turbulent. Moving sediments interact with the channel and can both change channel geometry and be influenced by channel geometry. The dynamic interactions between flow and sediments imply that global equilibrium sediment transport (the sediment transport rate equals the transport capacity) is rare. Local transport may be temporarily in equilibrium with the flow, however, nonequilibrium sediment transport is much more common in natural channels [18]. The 1D sediment transport models (e.g., [25]; CCHE1D [27]; MIKE 11 [28]; HEC-RAS [29]; and GSTAR-1D [30]) were developed for averaged solutions with high computing efficiency for long-term simulations in large-scaled domains, while 3D models (e.g., CCHE3D [31]; Delft3D [32]) are for highly-sophisticated solutions of short-term simulations in local small domains. The 2D models (e.g., [19]; CCHE2D [24]; SRH-2D [26]; [33]) are in between 1D and 3D models with respect to computing efficiency and numerical accuracy. Theoretically, sediment transport is a 3D phenomenon and 3D models should be used. However, in practice for different problems, model selection needs to balance computing efficiency and numerical accuracy. Unlike hydrodynamic flow models, there are more uncertainties and challenges with the sediment transport models since numerous semiempirical and empirical formulas have been developed, covering all aspects of the sediment transport process, such as the sediment settling velocity, sediment incipient motion, mobile bed roughness, critical shear stress, suspended-load transport capacity, and bed-load transport capacity. A good review of some of those formulas can be found in [20]. Most of those formulas were derived based on physical laws using experimental data under steady flow conditions, and application of them to truly unsteady sediment transport has been a concern [21]. Each formula has its own advantages, limitations, and application ranges.