Presentation by Christopher H. Lashley (TU Delft, IHE Delft) at the XBeach X (10th Year Anniversary) Conference, during Delft Software Days - Edition 2017. Thursday, 2 November 2017, Delft.

1. Nonhydrostatic and Surfbeat Model
Predictions for Extreme Wave Run-up
in Fringing Reef Environments
Christopher H. Lashley, IHE-Delft, Netherlands
Dano Roelvink, IHE-Delft, Netherlands
Ap van Dongeren, Deltares, Netherlands
Mark L. Buckley, USGS, USA
Ryan J. Lowe, University of Western Australia, Australia

2. “XBeach Surfbeat performs comparably well to
XBeach Nonhydrostatic.”
2/17

3. Background
Uprush of water above the SWL on a beach slope or structure:
1. Shoreline setup (<η>); and
2. Swash (SIG, SSS).
3/17

4. Research Objectives
A limited number of studies on run-up at reef-fronted coastlines.
Application of XBeach to:
1. Provide insight into the physical processes governing run-
up; and
2. Evaluate the performance of two model modes.
4/17

5. XBeach
1. Nonhydrostatic (XB-NH):
• Solves NLSW + nonhydrostatic pressure correction
• Short-wave resolving
• Calibration parameter: maxbrsteep (by default = 0.6)
2. Surfbeat (XB-SB):
• Wave action balance + Dissipation model + Roller model
• Short-wave (but not wave-group) averaged
• Calibration parameter: alpha (by default = 1)
5/17

6. Methods: Experiments
a) Case 1 - 29 tests: Hm0 (3.2 – 8.5cm), Tp (1 – 2.5s), hr (0 – 5.1cm)
b) Case 2 - 16 tests: Hm0 (4 – 24cm), Tp (1.3 – 3.2s), hr (0 – 9cm)
Calibration dataset
(Demirbilek et al., 2007)
Validation dataset
(Buckley et al., 2015)
6/17

7. Methods: Performance Metrics
Objective Functions:
• 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝛹𝛹 =
1
𝑛𝑛
∑ 𝛹𝛹𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋
𝑖𝑖
− 𝛹𝛹𝑜𝑜𝑜𝑜𝑜𝑜
𝑖𝑖 2𝑁𝑁
𝑖𝑖=1
• 𝑆𝑆𝑆𝑆𝑆𝑆𝛹𝛹 =
1
𝑛𝑛
∑ 𝛹𝛹𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋
𝑖𝑖
−𝛹𝛹𝑜𝑜𝑜𝑜𝑜𝑜
𝑖𝑖 2𝑁𝑁
𝑖𝑖=1
1
𝑛𝑛
∑ 𝛹𝛹𝑜𝑜𝑜𝑜𝑜𝑜
𝑖𝑖𝑁𝑁
𝑖𝑖=1
• 𝑅𝑅𝑅𝑅𝑅𝑅. 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝛹𝛹 =
∑ (𝛹𝛹𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋
𝑖𝑖
−𝛹𝛹𝑜𝑜𝑜𝑜𝑜𝑜
𝑖𝑖
)𝑁𝑁
𝑖𝑖=1
∑ 𝛹𝛹𝑜𝑜𝑜𝑜𝑜𝑜
𝑖𝑖𝑁𝑁
𝑖𝑖=1
Parameter Symbol
RMS wave height Hrms,TOT
Mean water level 𝜂𝜂̅
2% Exceedance
run-up
R2%
Maximum run-up Rmax
Shoreline setup <η>
Swash SSS and SIG
Calibration
Validation
7/17

8. Methods: Calibration
For each of the 29 tests in Case 1 (Demirbilek et al., 2007):
• maxbrsteep (XB-NH) varied from 0.3 to 0.8
• alpha (XB-SB) varied from 0.5 to 2
• Both in increments of 0.05
Optimal values by minimizing:
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑀𝑀𝑀𝑀𝑀𝑀 + 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻, 𝑇𝑇𝑇𝑇𝑇𝑇
Mean of optima selected for validation.
8/17

9. Calibration Results: Hrms,TOT & 𝜂𝜂̅
14 15 16 17 18 19 20 21 22 23 24 25
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
14 15 16 17 18 19 20 21 22 23 24 25
0.02
0.04
0.06
Observed
XB-NH Calibrated
XB-NH Default
XB-SB Calibrated
XB-SB Default
14 15 16 17 18 19 20 21 22 23 24 25
-0.01
-0.005
0
0.005
0.01
0.015
RMSE =0.1 (cm)
RMSE =0.3 (cm)
RMSE =0.13 (cm)
RMSE =0.17 (cm)
• XB-NH predicts Hrms
well.
• XB-SB overestimates
Hrms on reef flat.
• XB-NH predicts 𝜂𝜂̅
better than XB-SB.
9/17

10. 0.1 0.2 0.3
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Default XB-NH R
2%
Default XB-NH R
max
Calibrated XB-NH R
2%
Calibrated XB-NH R
max
Default XB-SB R
2%
Default XB-NH R
max
Calibrated XB-SB R
2%
Calibrated XB-SB R
max
Calibration Results: Run-up
Mode XB-NH XB-SB
Parameter maxbrsteep alpha
Default 0.6 1.0
Calibrated 0.5 1.4
Mean of optima
10/17

11. Validation Results: Hrms,TOT & 𝜂𝜂̅
10 15 20 25 30 35
-0.8
-0.6
-0.4
-0.2
0
10 15 20 25 30 35
0
0.05
0.1
0.15
0.2
Observed
XB-NH Calibrated
XB-NH Default
XB-SB Calibrated
XB-SB Default
10 15 20 25 30 35
0
0.05
0.1
RMSE =0.61 (cm)
RMSE =0.96 (cm)
RMSE =0.86 (cm)
RMSE =0.48 (cm)
• XB-NH predicts Hrms
accurately.
• XB-SB overestimates
Hrms on reef flat.
• XB-SB predicts 𝜂𝜂̅ well.
• XB-NH under-predicts
𝜂𝜂̅ on reef flat.
11/17

12. Validation Results: Wave Spectra
10
-2
10
-1
10
0
0
0.01
0.02
10
-2
10
-1
10
0
0
0.01
0.02
10
-2
10
-1
10
0
0
0.01
0.02
10
-2
10
-1
10
0
0
0.01
0.02
10
-2
10
-1
10
0
0
0.01
0.02
10
-2
10
-1
10
0
0
0.01
0.02
Observed
XB-NH
XB-SB
10 15 20 25 30 35 40
Cross-shore Location, x (m)
-0.8
-0.2
Depth(m)
1 4 7 11 13 16
12/17
Increasing dominance of infragravity motions shoreward of reef crest

13. Validation Results: Run-up
0.1 0.2 0.3
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Default XB-NH R
2%
Default XB-NH R
max
Calibrated XB-NH R
2%
Calibrated XB-NH R
max
Default XB-SB R
2%
Default XB-NH R
max
Calibrated XB-SB R
2%
Calibrated XB-SB R
max
13/17

14. Discussion: General
• XB-SB overestimated Hrms,TOT on the reef flat.
• XB-NH under-predicted 𝜂𝜂̅ on the reef flat.
• Similar to other short-wave resolving models applied to
fringing reefs (Skotner and Apelt, 1999; Yao et al., 2012; Fang
et al., 2014).
• XB-NH does not simulate overturning or plunging.
• Excludes formation and impact of wave rollers.
• Additional source of radiation stress → Higher 𝜂𝜂̅.
14/17

15. Discussion: (No) Roller
20 22 24 26 28 30 32 34 36
-0.05
0
0.05
0.1
Observed
XB-NH
XB-SB (Roller)
XB-SB (No roller)
20 22 24 26 28 30 32 34 36
-0.05
0
0.05
0.1
20 22 24 26 28 30 32 34 36
-0.05
0
0.05
0.1
RMSE
MWL
= 0.86
RMSE
MWL
= 0.85
RMSE
MWL
= 1.10.
• XB-SB (no roller)
underestimated 𝜂𝜂̅
on reef flat.
• Error increased with
wave non-linearity
(A0/h).
15/17

16. Discussion: Components of Run-up
• XB-NH:
• η under-predicted
but moderate scatter.
• SIG highly accurate.
• XB-SB:
• η over-predicted.
• SIG over-predicted.
• SSS under-predicted.
16/17

17. Conclusions
“In contrast to open sandy coasts, XB-SB performs comparably
well to XB-NH in fringing-reef environments.”
• Both modes predicted R2% and Rmax 20% deviation.
• Infragravity motions dominant at shoreline→ XB-SB.
• Limitations:
– 1D analysis;
– Focused on a single parameter for calibration; and
– Reef roughness not considered.
• The inclusion of wave rollers in the XB-NH?
17/17

18. Thank You
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19. References
• Buckley, M.L., Lowe, R.J., Hansen, J.E. and Van Dongeren, A.R., 2015.
Dynamics of wave setup over a steeply sloping fringing reef. Journal of
Physical Oceanography, 45(12): 3005-3023.
• Demirbilek, Z., Nwogu, O.G. and Ward, D.L., 2007. Laboratory study of
wind effect on runup over fringing reefs. Report 1. Data report, DTIC
Document.
• Fang, K.-z., Yin, J.-w., Liu, Z.-b., Sun, J.-w. and Zou, Z.-l., 2014. Revisiting
study on boussinesq modeling of wave transformation over various reef
profiles. Water Science and Engineering, 7(3): 306-318.
• Skotner, C. and Apelt, C.J., 1999. Application of a boussinesq model for the
computation of breaking waves: Part 2: Wave-induced setdown and setup
on a submerged coral reef. Ocean Engineering, 26(10): 927-947.
• Yao, Y., Huang, Z., Monismith, S.G. and Lo, E.Y., 2012. 1dh boussinesq
modeling of wave transformation over fringing reefs. Ocean Engineering,
47: 30-42.
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