SWAN's underestimation of long wave penetration into coastal systems

1. IAHR 2015, The Hague, The Netherlands, 2 July 2015
Joint IAHR-COPRI Symposium on Long Waves and Relevant Extremes
SWAN’s Underestimation of Long Wave
Penetration into Coastal Systems
Jacco Groeneweg and Joana van Nieuwkoop
Deltares, The Netherlands

2. Context
1. Primary motivation
2. Conclusions from previous studies
3. Goal of present study
4. Reanalysis of hindcast studies
5. Conclusions and recommendations
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3. Safety assessment of primary sea and flood defenses
Hydraulic Boundary Conditions (HBC)
Numerical modelling (SWAN)
Motivation (1)
• Various improvements in SWAN (journal publications, conference presentations)
• Penetrated North Sea wave energy underestimated by SWAN
Bed Level
[m NAP]
UHW1
Measured
SWAN
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4. Motivation (2)
Primary goal: Provide an explanation for SWAN’s underestimation
of swell wave penetration in tidal inlet systems and, if possible,
improve SWAN.
No conclusive explanation for underestimation from several studies
in the past, until
• Groeneweg et al. (JWPCE, 2015): hypothesis that 2D nonlinear
interactions play an important role
• Groeneweg et al. (ICCE2014): theoretical explanation and
further verification
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5. TRITONSWANObserved
Numerical analysis (1) – JWPCE 2015
Case 2 (Hm0 = 0.082m; T = 1.87s;
short-crested)
TRITON
SWAN
Hm0 [m]1. Waves refract on channel edge.
2. Under oblique angles SWAN is not sufficiently able to transport
the energy into and across the channel.

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D
B
TRITON SWAN
BB
D
NONLINEAR
Hm0 = 0.082 m
LINEAR
Hm0 = 0.00082 m
B
D
Simplified geometry
depth [m]
Hypothesis:
(2D) Nonlinear interactions
play an important role in the
transmission of energy from
flats into navigation channels.
Case 3 (T = 1.45 s; long-crested)
Numerical analysis (2)

7. Through nonlinear shoaling
energy is transferred to
larger incident angles!
φ2,-2 φ2,2
φ1,3φ1,1φ1,-1φ1,-3
φ2,0
φ3,3φ3,1φ3,-1φ3,-3
f[Hz]
ky [rad/m]
Theoretical explanation – ICCE 2014
White arrows: super-harmonic interactions
Red / purple arrows: sub-harmonic interactions
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[]
Courtesy: Toledo (JFM, 2013)
deep
d = 0.4 m

8. Further verification – ICCE2014
• Overestimation of second harmonic
with SWAN over transitional slope.
TRITON SWAN SWAN, no LTA
BB
D
• Spectrum TRITON in deep part
broader at primary frequency D
• 2D nonlinear interactions broaden the
spectra in directional space, so
components are generated that can
enter the channel.
• Mechanism not in SWAN (only 1D) !!!
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9. Goal of the present study
• Determine under which conditions SWAN underestimates the
low frequency wave energy when propagating into complex
tidal inlet systems.
• Special attention is paid to the role of nonlinear interactions and
refraction.
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10. Method
• Re-analysis of existing wave hindcasts of
storm periods in three regions (buoys; radar)
• SWAN with atmospheric and hydrodynamic
forcing from the same sources
• Numerical and physical settings similar
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Eastern Wadden Sea
19 cases
Western Scheldt
30 cases
Ameland tidal inlet
29 cases
radar

11. H10[m]
Depth[m]
Peak wave dir [degN]
Results – Ameland tidal inlet (1)
Strong correlation between l-f energy
underestimation and geometry, and thus
channel orientation, location of tidal flats,
water depth, wind/wave direction.
AZB21
AZB21
Depth [m]

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Results – Ameland tidal inlet (2)
observed
SWAN
Observed waves enter or cross the channel,
whereas the computed waves are refractively
trapped to the channel edges.
White arrow:
dominant wave direction (radar)
Purple arrow:
peak wave direction (SWAN)

13. Conclusions and discussion
• For many instances a mismatch between measured and computed
l-f energy is observed in the tidal inlet gorge, to a large extent
determined by the local geometry relative to water depth, incident
wave direction (wind direction).
• For all three areas, cases were found where differences could be
explained by the hypothesis of Groeneweg et al. (2014, 2015):
• The observed waves could enter or cross the channel,
whereas the computed waves were refractively trapped to the
channel edges.
• L-f part of observed spectra directionally broader than the
computed spectra, due to 2D nonlinear interactions.
• But not for all cases: differences already at offshore boundary,
strong currents may be effective, other inaccuracies in SWAN may
play a role.
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14. • Since there are many factors that determine the reliability of SWAN
results in the considered complex areas, do not derive a generic
concept to correct SWAN results for the observed underestimation
of low-frequency wave energy.
• Develop a 2D alternative for the presently implemented 1D three-
wave interaction formulation (LTA) in SWAN.
• Make use of simultaneously measured 2D wave spectra and radar
data.
• While storms are rare, the information they provide is very
valuable. Continuation of the measurement programs in the
Wadden Sea and Zeeland estuaries is recommended.
Recommendations
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15. Acknowledgements
The presented work is part of the WTI 2017 project (“Research
and development of safety assessment tools of Dutch flood
defences”), commissioned by the department WVL of
Rijkswaterstaat in the Netherlands.
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