Coastal Process Models

In this thesis coastal process models are defined as those models that investigate the mechanisms of transferring wind generated energy from an offshore region, across the bathymetry towards the shoreline, i.e. coastal wave propagation. There is a wide range of oceanic and tidal models, (Abbott (1997); Jones and Xing (1997); Bode and Hardy (1997); Prandle (1997); Li (2001)), which can also be applied to the investigation of coastal processes. However these models generally consider phenomena at larger scales than wave propagation models which are the focus of the remainder of this thesis.

Carrying out any form of intervention along a coastline, whether it is the construction of new defences, a harbour or marina, or the establishment of a nature conservation area, will affect the way that coastal processes cause waves to interact with the shoreline. It is important that the magnitude of any changes to the natural balance are studied and fully understood before work is allowed to proceed.

There are many natural processes that interact in the coastal zone. It is a highly dynamic environment that is shaped by the wind, waves, tides and currents, and by the way that energy from these sources is then re-distributed through the beach sediments and other structures in the inshore area. If accurate predictions can be made about the local coastal response to proposed developments, then successful shoreline management decisions can be made.

Soulsby (1993), identifies three main ways of predicting coastal response to the action of waves upon it:

• Observational experience • Physical models

• Numerical models.

2.3.1 Observational Experience

This is based on the expectation that by visually monitoring the actual response of a coastline over time, predictions can be made about what may happen to it in the future. (Eveland (1999); Livingstone (1999); Alves (1999); Guillen (1999)). Although this may be useful information to use in conjunction with other methods, it is dangerous to rely on this approach in isolation especially for long term predictions. A detailed study of a coastline over 10 years for example may be expected to give a fair indication of what might happen in the next 10 years, but it would be unwise to extrapolate this over longer time scales such as the 100 years required for the SMP. Another problem with this type of approach is the difficulty in predicting the effects of future change. Climate change or a new seawall will both have an effect on the way the sea interacts with the coastline, but there is no way of predicting what this might be with any certainty by using this approach.

2.3.2 Physical Models

Physical models involve the construction of a scaled down version of a particular coastal area (Armer, 1981; Carvahlo, 1989; Brampton et al. 1991). They are especially useful for modelling processes that are not sufficiently well understood to allow numerical description, and have the major advantage of allowing the modeller to see exactly what is going on (Soulsby, 1993). They are mostly used for models of complex energy interactions such as wave disturbance in harbours. Obviously there is a great deal of work involved in the accurate construction of such models, which have to take account not only of the size of the elements being modelled, but also their behaviour within fluid flows which may be difficult to reproduce at small scales. Another major disadvantage of physical models is the time and expense needed to create them.

Soulsby (1993) reflects that, “Twenty years ago it was widely predicted that by now physical modelling would have been completely superseded by numerical modelling” and then goes on to describe the many situations in which physical models still provide the best solution. His assumption that they would still have an “...important role in another twenty years time” is still open to debate, but most modellers would probably agree that in 20 years from now a real requirement for physical models is unlikely to be considered

‘important’ in standard modelling practice.

2.3.3 Numerical Models

Numerical models are the most popular option for investigations into coastal processes. Recent increases in the processing speed and storage capacity of the desktop PC, combined with continual algorithm development have widened the choice of models available so that recourse to the physical model is becoming quite rare.

There are numerical models for all aspects of interaction in the coastal zone, which, within the scope of coastal process models in this thesis, can be loosely split into three areas:

• Offshore Wave Prediction • Wave Transformation • Sediment Transport

Often a single suite of software will include an example of all three of these main model types. Offshore wave prediction models take offshore wind and fetch conditions to predict the amount of energy in the offshore sea area. Once defined, this offshore condition is transformed into an inshore wave condition by predicting its passage across the inshore bathymetry, modelling the effects of phenomena such as wave refraction, wave diffraction and wave reflection. This is done with a wave transformation model. Once the size of the inshore wave is known at a point on the coast, the energy it contains can be simulated through the breaker zone by a sediment transport model which will then predict the direction and amount of sediment transport caused by the energy moving onshore.

This section looks in detail at the structure and range of wave transformation models available. It is the key type of model used in this research and as such is most relevant to the rest of the thesis. There are several full review documents in existence, the most comprehensive being Dodd and Brampton (1995) and Fleming (1992) which deal with developments up to the early-mid 1990s. More recent modelling developments are considered by Dingemans (2000) and more specific examples can be found in Oliviera et al. (1997); Oliveira and Anastasiou, (1998); Sanders et al, (1998); Booij et al. (1999); Bayram and Larson, (2000) and Panchang et al., (2000). What follows is a summary of the key features, and readers are referred to the above documents for more details if required.

2.3.3.1 Wave Transformation Models

Wave transformation models are designed to simulate the transmission of wave energy from deep-water offshore conditions across a section of bathymetry, to predict the resulting inshore wave condition. All existing wave models include wave shoaling and wave refraction (Dodd and Brampton, 1995). With increasing levels of complexity, some models also incorporate additional processes such as wave diffraction, seabed friction, wave reflection, energy loss due to wave breaking, wave-current interactions and wind- wave interactions. Some models are monochromatic, which means they work with a single wave definition (i.e. a single wave direction and frequency). More sophisticated models can incorporate a wave spectrum which defines waves of all frequencies and directions. In general the more sophisticated the model, the more expensive in terms of money, processing time and computing power it will be to run. Unfortunately “...a more expensive model does not guarantee better results” (Dodd and Brampton, 1995).

The first wave models were developed at the University of California in 1939. These were very simple and modelled wave refraction of the predictable long crested waves seen off the Californian coast. In 1943, numerical models of wave refraction were used to predict inshore wave heights for the D-Day landings, and by 1960 the use of hand calculations to predict wave refraction based on the laws of optical physics was well established. Early methods were based on the tracing of wave rays. A wave ray is a line

that tracks the path of an incoming wave defined orthogonal to the wave crest. Wave rays are tracked from offshore, inwards across the bathymetry. All are initially defined with an equal spacing. Refraction calculations assume that energy is conserved within the system, therefore if the bathymetry causes wave rays to converge, wave height must increase to accommodate the same amount of energy, and conversely as they diverge, wave heights must decrease. This is shown in Figure 2.2. Full details can be found in Sorenson, (1978); Chadwick, (1993) or Bearman, (1989). W ave Crest W ave Ray Bottom Contour Shoreline

Figure 2.2 Wave Refraction (adapted from Sorenson 1978)

As the wave rays move inshore and enter shallow water, at depths of less than half the wavelength the wave will begin to ‘feel’ the bottom. Once in this zone the water depth determines the speed of the wave. In Figure 2.2, the two wave rays approach the shore at an oblique angle with a spacing of jy. As the wave ray at B] hits the shallower water at di

the w ave starts to retract or bend and align itse lf more parallel to the shore. W hen the w ave rays cross into water depth d: which is even shallow er, this process is repeated. This is w ave refraction. If bathymetric shape results in a convergence o f the w ave rays as show n in Figure 2.2, {si > s'2), this means that to accom m odate the same amount o f energy within this distance the w ave height must increase.

The sim plest m od els are forward tracking w ave ray m odels. The w ave rays are set at regular intervals offshore and the w ave energy is m odelled forwards across the bathymetry. A m onochrom atic w ave field is assum ed (i.e. one w ave direction and one w ave frequency) and the inshore w ave condition is generated from the w ave ray pattern. (Figure 2.3)

Bathym etry

W ave Rays

Dry Land

Figure 2.3 Schem atic diagram to show Forward Tracking W ave Refraction

The assum ptions in these m odels are generally held to be too sim plistic for them to be used ex ten siv e ly in practice. Certainly around the UK coastline, w aves are usually short crested w hich indicates that the w ave field com prises m any different w ave periods and directions. T his is due to the com plex coastline offering a very variable fetch w hich leads to a highly changeable offshore wind clim ate. In these sorts o f conditions a w ave spectrum needs to be m odelled (Dodd & Brampton 1995).

Backtracking w ave refraction m od els work using the same general theory as forward tracking, but their design allow s the incorporation o f a w ave spectrum. M ultiple w ave rays defined at incremental directions are transformed from an inshore location back out to sea for a range o f selected w ave frequencies. T his defines a set o f transfer functions that map the m ovem ent o f energy from the inshore point to the offshore boundary. The inverse o f this set o f functions can then be applied to a matching offshore frequency spectrum to generate the inshore w ave clim ate from the relationship b etw een the offshore w ave condition and the energy m ovem ents in the inshore bathymetry. This is a very efficient to m i o f m odel as w ave rays that do not reach the offshore boundary are excluded from any subsequent calculations. (Figure 2.4)

Bathym etry

Inshore Point

W ave Rays

Dry Land

Figure 2.4 Schem atic diagram to show Backward Tracking W ave Refraction

A s their nam es suggest, these tw o types o f m odel predict only w ave refraction and shoaling - w ave shoaling describes a direct effect on w ave height in sh allow water and is included in virtually all m odels.

It w as the inability o f these m odels to sim ulate w ave diffraction that led to new d evelopm ents. W ave diffraction is an important effect that can alter the energy balance in a w ave field. It is m od elled using a developm ent o f the m ild-slope equation proposed by B erk h off (1 9 7 2 ). W ave diffraction is the m ovem ent o f energy sidew ays along the w ave crest w hen energy gradients are unsustainable. This occurs when w aves pass an im perm eable structure, for exam ple when approaching a breakwater as is show n in Figure 2.5. It is a m ovem en t o f energy orthogonal to the forward w ave ray m ovem ent m odelled in w a ve refraction and therefore it needs a different approach in m odelling tenns. If energy is m o vin g sidew ays along the w ave crest in this w ay, then the w ave height along this part o f the w a ve crest w ill decrease.

D iffracted W aves

Breakw ater In com in g

w a v e crests

Figure 2.5 W ave D iffraction (adapted from C hadw ick e / 1993)

W ave diffraction is norm ally m odelled on a finite difference grid. This is a rectangular cell based grid in w h ich a solution to the w ave equations is generated for every grid cell in each row as it is reached. It is often described as ‘forward m arching’ as it works in this w ay one row at a tim e. T his allow s energy to be m odelled both forwards and sidew ays across the bathymetry and can therefore include both w ave refraction and w ave diffraction. (Figure 2.6)

t / f / / / / ‘ " v

f '

/ L

Figure 2.6 Energy m ovem ents required to m odel diffraction and refraction on a finite

difference grid

In Figure 2.6, the shaded area depicts the row s on the grid for w hich a solution has already been calculated by the m odel. The bold arrows show h ow energy from the outlined yellow cell can be m odelled both sidew ays along the w ave crest to sim ulate w ave diffraction and also forwards to sim ulate w ave refraction. The w ay in w hich this type o f m odel works means that a solution for the w av e field is generated for one com plete row at each step. T his is w hy grid-based réfraction-diffraction m odels are far more time consum ing to run than the ray tracing types.

M odels o f this type can also be modi f e d to sim ulate the m ovem ent o f backscattered energy, i.e. w ave reflection. Instead o f the option o f energy m ovem ents in 3 directions, (forwards, and left or right), a fourth consideration o f energy m oving backwards in the grid is also included, w hich w ill clearly take even longer to run. This situation is com m on ly found in harbours and marinas for exam ple where a constricted space en closed by w alls provides reflective surfaces to create the energy m ovem ents.

More m odem m odels, the so called ‘3'^'* G eneration’ are based on further develop m en ts o f the m ild-slope equations. T hey include som e or all o f the above large scale energy

movements but also include processes that alter the total wave energy in the model, e.g. wave breaking over offshore banks, energy dissipation by seabed friction, or wave growth due to wind effects in the area of study. Some examples can be found in Oliveira

et al. (1998); Booij et al. (1999) and Bayram et al. (2000). These more modem

algorithms are found in newer software packages such as SWAN, for example, which was developed by the University of Delft, and is distributed over the internet (http://swan.ct.tudelft.nl; Booij (1996); Holthuijsen (1998)).

2.3.3.2 Model Validity

All coastal process models attempt to predict energy movements as waves travel onshore. Regardless of the sophistication of the model and the type of process that is being modelled, the complexity of the situation in reality demands that some assumptions have to be built into them. This is the only way the algorithms will work because there is no numerical solution to adequately model all the processes present in such a dynamic environment. This has led to criticisms of the process from some quarters. Thieler et al.

(2000) question the underlying assumptions on which coastal modelling is built. In particular they ask why the results of models are used to make engineering decisions when it is openly acknowledged that there are processes that exist in reality that are not reflected in the algorithms. “Concern about the validity of these assumptions in producing a model’s answer is often expressed, but rarely do model users analyse or quantify the uncertainties”. Although this paper is mainly concerned with sediment transport models, the comments it contains are more widely applicable as these models are often driven by output from wave transformation models.

In their defence numerical models are backed up by the use of field validation. Regardless of the deficiencies of the models, if their results are compared with field studies and internal parameters are adjusted to ensure that the model is producing comparable results, then the shortcomings of the assumptions in the model can be overcome. Conference proceedings from Sogreah Grenoble (deOraauw, 1988) detail many attempts to use field measurements to validate numerical models. The emphasis of this document is on the difficulty of carrying out such studies. Bakker (1998) concludes

that matching field data collection conditions to the output of coastal models is very difficult, and Birkemeier (1998) stresses the importance of collecting field data expressly for the purpose of field validation as any other field data will not be suitable. This point is also made by Seymour (1998) who lists 14 separate guidance notes for field data collection for validation studies. Of the 10 papers in this conference report only one, de Vriend (1998) actually discusses how measurements taken in the field were used in the verification of models, but then goes on to say that the bulk of the data collected was of no use at all. Several papers set out clear guidelines for model validation field studies, emphasising the need for very clear objectives regarding the type of model to be validated and the likely processes that need to be measured. Overall, the conclusion of the papers is, that although difficult, field validation is not an impossible task. In the absence of a better alternative, it is one that will have to be relied on in the future.

2.3.3.3 Model Selection

The key decision for wave modellers is the choice of model type. The model choice should be made based on knowledge of the physical processes that are found in the study