(1) The Level-1 model

The governing equations of the HDM in a Level-1 model can be regarded as an extended version of the SWEs by inserting additional terms, mainly including the density gradient terms and the terms related to the ∂*zb*/∂*<sup>t</sup>* (*zb* is riverbed elevation). However, the e ffects of these additional terms are still open issues. Some researchers [47,48] included both of the two kinds of additional terms in their models. Wu [49] pointed out that the e ffect of the ∂*zb*/∂*<sup>t</sup>* term, added into the continuity equation, is dominant relative to the e ffect of other additional terms. This point is supported in Cao et al. [50], where only the enhanced continuity equation is used together with the momentum equations from the original SWEs. Generally, the Level-1 model is mainly used when the flow, sediment transport, and morphological evolution are strongly coupled to each other (the rate of bed deformation being considerable compared to that of flow evolution), such as the dam-break flows on a moveable riverbed.
