1. Rhine, Netherlands, flood 4 Nov 1998 (Wilbers & Ten Brinke, 2003) The Impact of Variability in Dune Dimensions on Sediment Sorting and Morphodynamics Astrid Blom University of Twente US National Center for Earth-surface Dynamics (NCED) km bed level m NAP

2. Blom et al., WRR, 2003

5. Developments Sediment continuity framework by Parker, Paola & Leclair (2000): active bed described by PDF of bed surface elevationsSediment continuity framework by Parker, Paola & Leclair (2000): active bed described by PDF of bed surface elevations Extension to dunes (Blom, 2003, Blom & Parker, 2004)Extension to dunes (Blom, 2003, Blom & Parker, 2004) Present research: extension to aggradational / degradational casesPresent research: extension to aggradational / degradational cases Continuity of non-uniform sediment Existing bed layer models (e.g., Hirano, 1971) Useful, but…Useful, but… Inadequate description of sediment fluxesInadequate description of sediment fluxes Ellipticity of set of equationsEllipticity of set of equations Problematic definition of active layerProblematic definition of active layer

6. Case study The Ribberink (1987) aggradation experiment Three sediment continuity models: A.The Hirano active layer model B.The sorting evolution model with regular dunes C.The sorting evolution model with irregular dunes Flow described using formulation backwater curveFlow described using formulation backwater curve Simple power-based and surface-based sub-model of sediment transport (Ribberink, 1987)Simple power-based and surface-based sub-model of sediment transport (Ribberink, 1987)

7. c b sediment concentration within the bed (c b = 1 - porosity) F mi volume fraction content of size fraction i in the active layer F ai volume fraction content of size fraction i in the transported sediment F Ii volume fraction content of size fraction i at the interface q a sediment transport rate  thickness of active layer η I elevation of interface between active layer and substrate Sediment continuity of active layer: The Hirano active layer model (1971) substrate active layer ηIηI  F mi F ai q a F Ii

8. C i concentration of size fraction i at level z (C i = c b P s F i ) P s probability that the bed level is higher than z F i volume fraction content of size fraction i at level z D ei E ei deposition and entrainment densities of size fraction i at level z c b sediment concentration within the bed (c b = 1 - porosity) aa x z z PsPs z FiFi coarse fine The sorting evolution model (Blom, 2003) based on Parker-Paola-Leclair (2000) framework

9. lee q top stoss z x Apply the Einstein step length formulation (Einstein, 1950) to the stoss face:Apply the Einstein step length formulation (Einstein, 1950) to the stoss face: deterministic step lengths At the lee face entrainment neglected. Lee face deposition determined by a lee sorting function.At the lee face entrainment neglected. Lee face deposition determined by a lee sorting function. Only bed load transport.Only bed load transport. Sediment fluxes through dune migration The sorting evolution model

10. Sediment fluxes through dune migration  variability in bedform dimensions The sorting evolution model (Leclair, 2002)  e.g. E(z) =  E stoss (z) p b dη b

11. Sediment fluxes through net aggradation / degradation The sorting evolution model distributed over depth according to exposure to flowdistributed over depth according to exposure to flow composition of fluxes uniform over bed elevationscomposition of fluxes uniform over bed elevations

12. Experiment E8-E9 by Ribberink (1987)Experiment E8-E9 by Ribberink (1987) 2 sand fractions (0.78 mm, 1.29 mm)2 sand fractions (0.78 mm, 1.29 mm) DunesDunes Start from exp E8Start from exp E8 Over 30h, feed of fines was decreased to 0Over 30h, feed of fines was decreased to 0 Total feed rate was maintained steadyTotal feed rate was maintained steady The Ribberink aggradation experiment

13. Active part of the bed Mean dune height and PDF troughs assumed steadyMean dune height and PDF troughs assumed steady Hydraulic roughness assumed steady (Ribberink, 1987)Hydraulic roughness assumed steady (Ribberink, 1987) Mean dune height  = 3cmMean dune height  = 3cm Active layer thickness  = 1/2 Active layer thickness  = 1/2 

14. Results: Net aggradation or degradation

15. Results: Composition of active part of bed

16. Results:Composition of bed load transport at downstream end of flume

20. Results: Vertical sorting

21. Note: no parameter tuningNote: no parameter tuning Taking into account the variability in dune dimensionsTaking into account the variability in dune dimensions allows sediment to be ‘stored’ at lower elevationsallows sediment to be ‘stored’ at lower elevations improves the predicted adaptation time scalesimproves the predicted adaptation time scales improves the predicted sorting profileimproves the predicted sorting profile Reduction to a simplified modelReduction to a simplified model Applicable to alternate bars? (data Lanzoni, Miwa)Applicable to alternate bars? (data Lanzoni, Miwa) Model PDF trough elevations (Van der Mark et al., 2005)Model PDF trough elevations (Van der Mark et al., 2005) New flume experiments at VTCHLNew flume experiments at VTCHL Discussion and conclusions

22. The research project is supported by: The Netherlands Organization for Scientific Research (NWO-STW) University of Twente (Civil Engineering) US National Center for Earth-surface Dynamics (NCED) The following persons have contributed to the work through discussion: Gary Parker, Jan Ribberink, Maarten Kleinhans, Suzanne Hulscher, Suzanne Leclair, Bert Jagers, Kees Sloff, Rolien van der Mark, and David Mohrig.

25. Case study 1: Results, composition active bed

26. lee q top stoss z x Apply the Einstein step length formulation (Einstein, 1950) to the stoss face:Apply the Einstein step length formulation (Einstein, 1950) to the stoss face: deterministic step lengths The sorting evolution model (Blom, 2003) At the lee face neglect entrainment. Lee face deposition determined by a newly-developed lee sorting function  i.At the lee face neglect entrainment. Lee face deposition determined by a newly-developed lee sorting function  i. Only bed load transport.Only bed load transport.

28. proportion of size fraction z little coarser than mean grain size coarse mean grain size Lee sorting function  i