Simulation of Coastal Inundation by Waves

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Simulation of Coastal Inundation by Waves
Inundation by storm surges and tsunamis, as well as smaller storm waves, is a considerable risk faced
by coastal communities. Over the past few years, flood events on the eastern coast of the USA, as
well as in Japan and the Indian Ocean, for example, have highlighted the need for an understanding of
potential impacts.
A wide range of natural processes can result in waves in aquatic environments. Water waves can be
caused by, for example:
 surface forcings (such as wind and atmospheric pressure) leading to wind waves, swell and storm
surges
 tidal potential leading to tides
 subsea bathymetry changes leading to tsunamis
This wide variety of causes leads to a large range of wave periods. Wind-generated waves tend to
have periods in the order of seconds to minutes, tsunami range from minutes to hours and tides are
typically from hours to days.
Wavelength is a product of wave period and wave speed and shallow water (or long) waves are
defined as waves which have a wavelength that is at least 20 times the local water depth. This means
that waves with wavelengths in the order of several tens of kilometres can still technically be defined
to be shallow water waves when travelling through relatively deep waters. For example, a wave with a
wavelength of 100km could be defined to be a long wave in up to 5000m of water, depending on the
wave period.
The MIKE by DHI software suite contains a number of modules that are suitable for investigating
coastal flooding resulting from the incidence of both large and smaller waves. Two principal
approaches are outlined in this document, which have previously been used by DHI to study wave
inundation, together with a third standard approach. Between them, the three methods cover the
majority of the wide range of combinations of wave conditions and water depths which can occur.
This document is for information only and, if used to guide future studies, the most appropriate
approach for each event considered must be determined based on proposed model domain and wave
characteristics.
Method 1: Storm Surges and Tsunamis over Large Areas
The MIKE 21 HD (‘classic’ rectilinear or FM flexible mesh formulation) module solves the shallow
water wave equations and can therefore be used to investigate shallow water waves over large
domains, as long as the resolution of the grid/mesh is sufficiently small. A minimum of 100
cells/elements per wavelength is required to ensure the wave is accurately represented and, when
considering long waves, this means that the cell/element size must be directly related to the water
depth and the incident wave period. Therefore, for small wave periods in relatively shallow water, this
can lead to very small cell/element sizes which can limit the suitability of this approach.
With a variable resolution available across the domain, a single MIKE 21 FM HD model can be used to
simulate both the nearshore development of the incident wave field and the overland flow of the
resulting overtopping volume of water. The resolution of buildings within a model mesh can generate
small elements in places and this generally restricts the maximum time step within the adaptive time
step process. If buildings are to be resolved within the onshore section of the model domain, care
should therefore be taken that element sizes do not restrict the overall model run time significantly.
When planning such studies, appropriate understanding of the initial forcing conditions is required to
ensure that the resulting model is suitably representative. For storm surges, this means adequate

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resolution in time and space of the approaching depression and wind field, and for tsunamis, an
adequate representation of the initial disturbance that causes the long wave progression.
Links to relevant examples:
http://www.dhigroup.com/News/2012/04/24/ModellingOf11AprilEarthquakeOffSumatraAndMiniTsunam
i.aspx
http://www.dhigroup.com/News/2004/12/26/SumatraTsunami26thDecember2004.aspx
http://www.dhigroup.com/News/2005/04/26/TsunamiModeling.aspx
http://www.dhigroup.com/upload/mikebydhi2010abstracts/A017_MODELLING_EARTHQUAKE_AND_
SUBMARINE_SLUMP_INDUCED_TSUNAMIS_USING_MIKE_21.pdf
http://www.dhigroup.com/News/2011/03/18/ModellingTheCatastrophe%E2%80%93TheWaveOnLand.
aspx
Method 2: Low Probability Events in a Small Nearshore Area
For shorter period waves in shallower water depths that would result in prohibitively small element
sizes in a MIKE 21 FM HD model, the MIKE 21 Boussinesq Wave (BW) model can usually be applied.
This module is based on the numerical solution of an extended form of the two-dimensional
Boussinesq equations, a form of the shallow water wave equations. The Boussinesq equations
include non-linearity as well as frequency dispersion, which is introduced in the flow equations by
taking into account the effect that vertical accelerations have on the pressure distribution.
The major restriction of the classical Boussinesq equations is their water depth limitation. The
extended form of the Boussinesq equations incorporates a significant improvement of the dispersion
characteristics and the maximum depth to deep-water wavelength ratio, d/L, is increased from 0.22 to
0.5. With these extended equations, the MIKE 21 BW module is suitable for simulation of the
propagation of wave trains travelling from deeper water to shallow nearshore environments.
MIKE 21 BW uses the ‘classic’ rectilinear grid as its basis and requires careful consideration of
incident wave characteristics to determine appropriate resolution and time step. In general, for a given
wavelength and water depth, the resolution required by a BW model is typically in the order of 1-5m
with a time step of significantly less than 1s. These characteristics tend to limit the spatial extent of a
BW model and also the duration of the event considered. For example, a BW model would not
realistically be used to investigate an area larger than a few square kilometres or an event lasting
longer than an hour or so.
Links to relevant examples:
http://www.dhigroup.com/upload/MIKEbyDHISuccessStory-M21BW-MoffatNichol.pdf
Method 3: Combined Approach
It is expected that most large wave events will be suitable for simulation using Methods 1 or 2.
However, some wave and water depth combinations will still fall into the ‘in-between’ category that
precludes either method. In these cases, a combined approach can be adopted. This three-step
approach is summarised as follows:
Step 1: MIKE 21 Spectral Wave (SW) model is used to transform the wave climate from offshore to
nearshore
Step 2: MIKE 21 BW 1D is used to create a look-up table of overtopping volumes for the local flood
defences using the calculated wave conditions for a varying water level

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Step 3: MIKE 21 FM HD (or ‘classic’) is used to simulate the overland flow resulting from overtopping
of the local defences, represented by a line structure which references the look up table
created in Step 2
General Comments
1. As with all modelling studies, good quality bathymetry and topography data is required to ensure an
accurate representation of ground and bed levels. These are one of the main boundary conditions
of a hydrodynamic model and should be subject to rigorous checking.
2. Validation of any model developed under any of the methods outlined above is essential if the
outputs are to be used to influence any planning or design decisions.