Articles | Volume 6, issue 4 
            
                
                    
            
            
            https://doi.org/10.5194/esurf-6-989-2018
                    © Author(s) 2018. This work is distributed under 
the Creative Commons Attribution 4.0 License.
                the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esurf-6-989-2018
                    © Author(s) 2018. This work is distributed under 
the Creative Commons Attribution 4.0 License.
                the Creative Commons Attribution 4.0 License.
Morphodynamic model of the lower Yellow River: flux or entrainment form for sediment mass conservation?
                                            Department of Hydraulic Engineering, State Key Laboratory of
Hydroscience and Engineering, Tsinghua University, Beijing, China
                                        
                                    Andrew J. Moodie
                                            Department of Earth, Environmental and Planetary Sciences, Rice
University, Houston, TX, USA
                                        
                                    Hongbo Ma
                                            Department of Earth, Environmental and Planetary Sciences, Rice
University, Houston, TX, USA
                                        
                                    
                                            Department of Hydraulic Engineering, State Key Laboratory of
Hydroscience and Engineering, Tsinghua University, Beijing, China
                                        
                                    Yuanfeng Zhang
                                            Yellow River Institute of Hydraulic Research, Zhengzhou, Henan, China
                                        
                                    Kensuke Naito
                                            Department of Civil and Environmental Engineering, Hydrosystems
Laboratory, University of Illinois, Urbana-Champaign, IL, USA
                                        
                                    Gary Parker
                                            Department of Civil and Environmental Engineering, Hydrosystems
Laboratory, University of Illinois, Urbana-Champaign, IL, USA
                                        
                                    
                                            Department of
Geology, Hydrosystems Laboratory, University of Illinois, Urbana-Champaign,
IL, USA
                                        
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 - Grain Size‐Specific Engelund‐Hansen Type Relation for Bed Material Load in Sand‐Bed Rivers, With Application to the Mississippi River C. An et al. 10.1029/2020WR027517
 - Theory of delayed response in river morphodynamics: Applicability and limitations C. An & X. Fu 10.1016/j.ijsrc.2021.07.004
 - Autocyclic Secondary Channels Stabilize Deltaic Islands Undergoing Relative Sea Level Rise G. Salter & M. Lamb 10.1029/2022GL098885
 - Sediment transport on rippled beds O. Guevara et al. 10.1063/5.0236116
 - Impact of the Xiaolangdi Reservoir Operation on Water–Sediment Transport and Aquatic Organisms in the Lower Yellow River During Flood Events X. Zhang et al. 10.3390/su17188136
 - Effect of Sediment Supply on Morphodynamics of Free Alternate Bars: Insights from Hydrograph Boundary Layer H. Dai et al. 10.3390/w13233437
 - Modeling Deltaic Lobe‐Building Cycles and Channel Avulsions for the Yellow River Delta, China A. Moodie et al. 10.1029/2019JF005220
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 - Effect of grain-sorting waves on alternate bar dynamics: implications of the breakdown of the hydrograph boundary layer S. Tanabe & T. Iwasaki 10.5194/esurf-13-723-2025
 - Flood Control through Engineered Avulsions and Floodways in the Lower Yellow River L. Chen & B. Hobbs 10.1061/(ASCE)WR.1943-5452.0001151
 - The Effect of Sediment Supply on Pool‐Riffle Morphology Y. Lei et al. 10.1029/2023WR035983
 - An advection-dispersion model for routing suspended sediment down the river network A. Haddadchi & C. Rose 10.1016/j.envsoft.2025.106417
 - An advanced check‐dam sedimentation module: Laboratory validation and implementation in a distributed sediment yield model for field application G. Zhang et al. 10.1002/esp.5714
 - Fluvial landscape evolution controlled by the sediment deposition coefficient: Estimation from experimental and natural landscapes L. Guerit et al. 10.1130/G46356.1
 - Creation of Cadastral Maps of Flooding Based on Numerical Modeling A. Klikunova et al. 10.14529/jcem190201
 - A new large-scale suspended sediment model and its application over the United States H. Li et al. 10.5194/hess-26-665-2022
 - The Longitudinal Profile of a Prograding River and Its Response to Sea Level Rise W. Gao et al. 10.1029/2020GL090450
 - The Migration of the Erosion Center Downstream of the Three Gorges Dam, China, and the Role Played by Underlying Gravel Layer S. Zheng et al. 10.1029/2022WR034152
 - Stability index for the planview morphology of alluvial rivers and a case study of the Lower Yellow River Y. Liu et al. 10.1016/j.geomorph.2021.107853
 - Characterizing braided rivers in two nested watersheds in the Source Region of the Yangtze River on the Qinghai-Tibet Plateau Z. Li et al. 10.1016/j.geomorph.2019.106945
 - Numerical Investigation on the Adaptation of Dam-Break Flow-Induced Bed Load Transport to the Capacity Regime over a Sloping Bed P. Hu et al. 10.2112/JCOASTRES-D-19-00120.1
 - Stability of Aquatic Nitrogen Cycle Under Dramatic Changes of Water and Sediment Inflows to the Three Gorges Reservoir L. Pang et al. 10.1029/2022GH000607
 
Latest update: 02 Nov 2025
Short summary
            In most models of river morphodynamics, sediment mass conservation is described by the Exner equation, which may take either the flux form or the entrainment form. Here we compare the two forms of the Exner equation under conditions typical of the lower Yellow River. We find that when using a single sediment grain size, there is little difference between the two forms. But when considering sediment mixtures, the two forms will show very different patterns of grain sorting.
            In most models of river morphodynamics, sediment mass conservation is described by the Exner...