The document summarizes work to develop a phase-resolving morphodynamic model in XBeach's non-hydrostatic mode. While the non-hydrostatic model better represents dune erosion and runup on steeper beaches compared to the surf-beat approach, the standard sediment transport equations do not fully apply. The model shows promise but needs improvements to turbulence modeling and splitting of velocities to better simulate morphodynamics on various beach types. Resolving short waves also allows improved hydrodynamics near structures through diffraction effects. Overall, the non-hydrostatic model provides a more detailed representation of coastal response but requires further development and testing of sediment transport.

1. XBeach morphodynamics in
non-hydrostatic mode
Towards the development of a phase-
resolving morphodynamic model
8 november 2017
Robert McCall, Dano Roelvink, Tim van der Biezen, Willem
Bodde, Nathanaël Geleynse, Ad Reniers, Matthijs Gawehn,
Kees Nederhoff, Cleo Jongedijk, plus many others

2. 8 november 2017
Contents
• Background
• Sediment transport in XBeach
• What works, what doesn’t?
• Moving forward

3. November 8, 20173
Background
• XBeach development started 10 years ago to help in the
prediction of impacts of hurricanes
• Important to be able to solve all types of coastal / barrier
island response to hurricane forcing in one model
Swash regime Collision regime Overwash regime Inundation regime
[Sallenger, 2000]

4. November 8, 20174
Background
• XBeach development started 10 years ago to help in the
prediction of impacts of hurricanes
• Important to be able to solve all types of coastal / barrier
island response to hurricane forcing in one model
• To do so required resolving infragravity waves: dominant on
dissipative sandy coasts during storms
Swash regime Collision regime Overwash regime Inundation regime
[Sallenger, 2000]

5. Background
• XBeach applied surf-beat approach
• Wave groups and IG waves resolved: better than stationary wave
models like Delft3D / ADCIRC
• Individual incident-band waves not resolved: lower computational
demand
8 november 2017

6. Background
• XBeach surf-beat approach extensively tested and validated
• Works well for dissipative beaches
8 november 2017
Hurricane-induced overwash at
Santa Rosa Island
(for those who somehow missed this, animation by Dave Thompson)

7. Background
• Disadvantage of surf-beat approach is that incident-band (short)
waves parameterized
• Intra-wave surface elevation and flow from linear wave theory
(extended to include Stokes drift)
• Wave shape and effect on sediment transport
• Wave breaking
• Assumption of single representative wave frequency, as well as
celerity and group velocity
• No shoreline run-up and reflection
8 november 2017

8. Background
8 november 2017
Coastalzones
Swash zone
Breaker zone
Shoaling zone
Deep water
Coastal type
Dissipative
(sandy)
Highly reflective
(gravely/structures)
Infragravity
dominated
Short wave
dominated
Mixed energy
Waves during storm conditions
• Where surf-beat approach should work well

9. Background
8 november 2017
• Where surf-beat approach should work well
• Beaches where IG waves dominant forcing
Coastalzones
Swash zone
Breaker zone
Shoaling zone
Deep water
Coastal type
Dissipative
(sandy)
Highly reflective
(gravely/structures)
Infragravity
dominated
Short wave
dominated
Mixed energy
Waves during storm conditions

10. Background
8 november 2017
• Where surf-beat approach should work well
• Beaches where IG waves dominant forcing
• Relatively deep, nearshore zone where short wave
parameterization holds
Coastalzones
Swash zone
Breaker zone
Shoaling zone
Deep water
Coastal type
Dissipative
(sandy)
Highly reflective
(gravely/structures)
Infragravity
dominated
Short wave
dominated
Mixed energy
Waves during storm conditions

11. Background
8 november 2017
• Surf-beat approach does not work well on steeper beaches
• As also shown by De Beer in the previous session
Coastalzones
Swash zone
Breaker zone
Shoaling zone
Deep water
Coastal type
Dissipative
(sandy)
Highly reflective
(gravely/structures)
Infragravity
dominated
Short wave
dominated
Mixed energy
Waves during storm conditions

12. Background
• For steeper beaches perhaps non-hydrostatic approach better?
• Again, as pointed out by De Beer in the previous session
8 november 2017

13. Background
• In XBeach-G we use non-hydrostatic wave model to simulate storm
impacts on gravel beaches
• Good representation of run-up in non-hydrostatic (bias ~ 1.5%)
• Surf-beat underestimates by ~30–40%
8 november 2017
Observed run-up
Modelledrun-upXBeach(-G)
Non-hydrostatic
Surf-beat

14. Background
• Good representation of overtopping in non-hydrostatic mode
• Surf-beat fails to predict overtopping except with low freeboard
Front barrier
Back barrier
Schematic overtopping
data collection
Overtopping swashes
Dry bed
Observed
non-hydrostatic
Surf-beat

15. Background
• In XBeach-G we couple non-hydrostatic model to gravel sediment
transport equations
• Morphological response of beaches to varying storm conditions
predicted well
8 november 2017
Measured pre
Measured post
Modelled post
Maximum SWL

16. Background
• Can we model sandy beach morphodynamics using the non-
hydrostatic wave model?
• How does it compare to the surf-beat model?
• What does it do better?
• What worse?
• What improvements needed?
8 november 2017

17. Sediment transport in XBeach
• Bed load and suspended load depend on critical velocity and
equilibrium transport equation derived for steady currents + waves
8 november 2017
𝑐 𝑒𝑞 =
𝐴
ℎ
𝑢2 + 0.64𝑢 𝑟𝑚𝑠
2 − 𝑢 𝑐𝑟
𝑛
𝑢 𝑐𝑟 = 𝑓
𝑢
𝑢 + 𝑢 𝑟𝑚𝑠
Mean (steady) current
(Steady) RMS wave orbital velocity

18. Sediment transport in XBeach
• Bed load and suspended load depend on critical velocity and
equilibrium transport equation derived for steady currents + waves
• In surf-beat approach mean currents and IG waves (from
NLSWE) are included in umean, intra-wave velocities (from wave
action balance) included in urms
8 november 2017
𝑐 𝑒𝑞 =
𝐴
ℎ
𝑢2 + 0.64𝑢 𝑟𝑚𝑠
2 − 𝑢 𝑐𝑟
𝑛
𝑢 𝑐𝑟 = 𝑓
𝑢
𝑢 + 𝑢 𝑟𝑚𝑠
uE from NLSWE:
Mean flow + IG waves
Parameterized orbital velocity
(plus parameterized turbulence)

19. Sediment transport in XBeach
• Bed load and suspended load depend on critical velocity and
equilibrium transport equation derived for steady currents + waves
• In surf-beat approach mean currents and IG waves (from
NLSWE) are included in umean, intra-wave velocities (from wave
action balance) included in urms
• As all waves resolved in extended NLSWE, in non-hydrostatic
model all intra-wave velocities currently included in “umean” term!
8 november 2017
𝑐 𝑒𝑞 =
𝐴
ℎ
𝑢2 + 0.64𝑢 𝑟𝑚𝑠
2 − 𝑢 𝑐𝑟
𝑛
𝑢 𝑐𝑟 = 𝑓
𝑢
𝑢 + 𝑢 𝑟𝑚𝑠
u from extended
NLSWE: mean flow +
IG waves + intra-wave
velocities
Null

20. What works, what doesn’t?
• Compare to dune erosion flume experiment (Van Gent et al., 2008)
• Dissipative beach
• Experimental data fundamental to development of XBeach surf-beat
model (Van Thiel de Vries, 2009; Roelvink et al., 2009)
8 november 2017

21. What works, what doesn’t?
• Profile evolution: okay, about as good as surf-beat model
8 november 2017

22. What works, what doesn’t?
• Wave height transformation reasonable: forcing okay
8 november 2017

23. What works, what doesn’t?
• Suspended concentration: reasonable, but underestimating
concentration near dune foot
8 november 2017

24. What works, what doesn’t?
• Dune erosion experiment with dune foot revetment (Deltaflume;
Steetzel, 1987)
• Dune foot revetment protects dune from erosion at base, but waves
can run up the revetment and attack higher in the profile
8 november 2017

25. What works, what doesn’t?
• Surf-beat approach under estimates erosion due to limited IG run-up
to unprotected dune (can be improved with parameterization of HF
wave run-up; Van Thiel de Vries et al., 2012)
• Non-hydrostatic model provides better estimates of dune erosion
above the revetment
• Neither model captures scour hole near revetment toe
8 november 2017

26. What works, what doesn’t?
8 november 2017
• Simulating hurricane-induced dune erosion and overwash
• Santa Rosa Island, FL during Hurricane Ivan 2004
• Used in the development of XBeach surf-beat

27. What works, what doesn’t?
8 november 2017
• Measured bed level change and
XBeach surf-beat (with smax
parameter) show foredune erosion
and deposition on back barrier

28. What works, what doesn’t?
8 november 2017
• Measured bed level change and
XBeach surf-beat (with smax
parameter) show foredune erosion
and deposition on back barrier
• In non-hydrostatic model bed level
change is overestimated (also with
smax parameter)

29. What works, what doesn’t?
8 november 2017
• Morphological response on steeper beach
Coastalzones
Swash zone
Breaker zone
Shoaling zone
Deep water
Coastal type
Dissipative
(sandy)
Highly reflective
(gravely/structures)
Infragravity
dominated
Short wave
dominated
Mixed energy
Waves during storm conditions

30. What works, what doesn’t?
8 november 2017
• Morphological response on steeper beach
• Bardex II experiment (Masselink et al., 2013)
• Beach face slope ~ 1:8, D50 ~ 0.4 mm

31. What works, what doesn’t?
8 november 2017
• Morphological response on steeper beach
• Despite resolving incident-band swash, XBeach non-hydrostatic
does not simulate morphological response of steeper beach well
MSc Cleo Jongedijk

32. What works, what doesn’t?
8 november 2017
• Morphological response on steeper beach
• Sediment concentration in uprush too low, in backwash too high
• Additional physical processes (swash zone turbulence, boundary
layer effect, infiltration) needed to simulate well
MSc Cleo Jongedijk
Uprush too low
Backwash too high

33. Moving forward
• Turbulence model for non-hydrostatic
• Continued development and validation of long-wave turbulence
model in XBeach for short waves, based on critical surface
elevation slope
• Potential development of turbulence model with source term based
on energy loss
8 november 2017
Under prediction

34. Moving forward
• Splitting velocity components in to mean and wave-driven parts to be
used in transport equations
8 november 2017
𝑐 𝑒𝑞 =
𝐴
ℎ
𝑢2 + 0.64𝑢 𝑟𝑚𝑠
2 − 𝑢 𝑐𝑟
𝑛
Time-average velocity 𝑢(𝑡)
Approximate intra-wave velocity u t − 𝑢(𝑡)

35. Moving forward
• Splitting velocity components in to mean and wave-driven parts to be
used in transport equations
• Reduces barrier island lowering and washover, but (much) more
testing required
8 november 2017

36. Moving forward
• Redevelopment of entire transport module using transport equation
based on instantaneous bed shear stress (as done in XBeach-G for
bed load)
• Addition of parameterizations of swash zone processes (turbulence,
boundary layer dynamics, infiltration) to better represent
morphodynamics of steeper beaches
• Coupling with quasi-two-layer non-hydrostatic model nh+ for better
representation of undertow in surf zone
8 november 2017

37. Moving forward
• Start investigating other areas where non-hydrostatic may be better
• Additional result of resolving incident-band waves is that non-
hydrostatic solves for diffraction (surf-beat does not)
• Expect differences in morphodynamic response near structures
8 november 2017
waves

38. Moving forward
• Models show differences in wave propagation around structures due
to diffration
8 november 2017
Instantaneous Time-average

39. Moving forward
• Morphological response broadly similar, but increased erosion near
structure in non-hydrostatic relative to surf-beat
8 november 2017

40. Conclusions
• Standard sediment transport relations not truly valid for XBeach non-
hydrostatic and therefore not everything works properly
• However, non-hydrostatic morphodynamic model shows promise:
• Dune erosion appears to be well represented in non-hydrostatic
model
• Resolving short waves allows better approximation of
hydrodynamics and morphodynamics around structures:
• Better estimate of wave run-up and erosion above (and
overtopping over) steep revetments
• Inclusion of wave diffraction leads to different estimates of local
erosion
• Runtime is doable, even for large models
• Still plenty of challenges still to work on
8 november 2017

41. Thank you

42. What works, what doesn’t?
8 november 2017
• Start of overwash