A considerable amount of research has been carried out over the last 20 years to develop predictive numerical models of coastal evolution covering periods of up to 20 years or more. These models are based on representations of physical processes and typically include forcing by waves and/or currents, a response in terms of sediment transport and a morphology-updating module. However, there are still major gaps in our understanding of long-term morphological behaviour (de Vriend et al., 1993; Southgate and Brampton, 2001; de Vriend, 2003; Hanson et al., 2003) which mean that modelling results are subject to a considerable degree of uncertainty. Their use requires a high level of specialised knowledge of science, engineering and management.
Southgate and Brampton (2001) provide a guide to model usage, which considers the engineering and management options and the strategies that can be adopted, while working within the limitations of a shortfall in our scientific knowledge and data. The main types of models are:
- Coastal profile models
- Coastal area models
- One-line models (and the related N-line models)
Coastal Profile Models
Coastal profile models simplify the coastal system to a 2D system (with elevation and cross-shore distance being the two dimensions) which assumes longshore uniformity. These models commonly include wave shoaling, energy loss due to depth-limited wave breaking and bottom friction, cross-shore undertow, tidal currents and sediment transport. All such models predict beach profile changes due to cross-shore sediment transport. Alternatively they can be used to model the cross-shore distribution of longshore sediment transport, although this does not update the bathymetry. Cross-shore and longshore transport are generally calculated separately.
Van Rijn et al. (2003) compared the results from coastal profile models with hydrodynamic and morphodynamic data on the time scale of storms and seasons. Profile models were shown to predict the cross-shore variation in significant wave height to within 10% if properly calibrated. They were also shown to predict offshore and longshore current speeds in the laboratory and in the field within 40%. Profile models can also reasonably represent the movement of outer and inner sand bars on the time-scale of storms. They cannot simulate the beach recovery process on the post-storm scale, as the 3D processes involved are not sufficiently well understood to be parameterised. Profile models cannot be used to simulate the behaviour of sand bars or the beach on a seasonal scale unless they have been tuned using beach profile data.
Recent advances in the understanding of skewness and asymmetry in the surf zone, the development of phase resolving nearshore numerical wave models and the improvement of coastal sediment transport models all hold out the possibility of improving coastal profile models to be able to model beach recovery. If this can be done then profile models may be able to model periods between a tide and a few weeks where there is presently a shortage of understanding of beach behaviour due to a shortage of data and model skill.
In these models, the sand beach morphology is represented by a single contour, and such models are therefore often referred to as “one-line” models. Usually the x-axis is established approximately parallel to the coastline, and the y-axis directed offshore. The changes in the position of this contour, together with other parameters such as wave conditions, currents, and sediment transport rates, are functions of only longshore position (x) and time (t) and so the model is referred to as “one-dimensional”.
Predictions of changes in the beach and nearshore seabed plan-shape are produced. The beach profile is usually assumed to be constant, i.e. unchanging with time. A good starting point for those interested in the theory and application of beach plan-shape models is the paper by Bakker, Klein Breteler and Roos (1970) . This not only discusses the simplest “one-line” approach to such modelling but also takes the first step in the development of a model that allows some variation in profile along the shoreline.
One-line numerical models originated from analytical solutions to the diffusion equation for the small amplitude departures from a rectilinear coastline (Pelnard-Considère, 1956, Falqués, 2003 ). There has been revived academic interest in the use of analytical solutions in recent years (Falqués, 2003; Murray and Ashton, 2003; Reeve, 2006) but most one-line modelling for coastal management is likely to be performed using numerical models (e.g. Hanson and Kraus, 1989; Ozasa and Brampton, 1980) due to their flexibility in modelling realistic, non-idealised coastlines.
1-line numerical models can include seawalls and groynes by including simple parameterisations of their effects on the beach. They have been extensively used to model the evolution of sandy coastlines with studies ranging from one to two kilometres and a few years up to tens of kilometres and decades (Hanson and Kraus, 1989). [link to Hans Hanson’s paper]
Sometimes the one-line model is extended to model a number of different contours. These models are known as N-line models.
N-line models (or multi-layer models) are a generalisation of the more common 1-line model type to include the representation of more than 1 contour line. The first N-line model was that of Bakker (1968) and subsequent models have included Perlin and Dean (1979), Hanson and Larson (1999) and Steetzel and Wang (2004). The cross-shore profile is schematised as a number of mutually-interacting layers. The cross-shore profile evolves because of the interactions between the layers. The long-shore profile of each contour evolves in the same way as a 1-line model, only with potential contributions to the sediment budget in a cell coming from offshore and inshore cells as well as the up-drift and down-drift cells. The coastal evolution is therefore a function of cross-shore and long-shore transport. The spatial extent varies from 1 – 100km while the timescale ranges from seasons to 100 years.
In Steetzel’s model the cross-shore transport is based on differences from an equilibrium profile. Formulae have been derived for equilibrium slope and transport rates based on empirical formulae and the output from process-based models. If the profile is too steep, offshore sediment transport will occur in the model. However, despite their additional detail N-line models have not been used often, mainly because the cross-shore behaviour is not realistically represented. Such models therefore have normally needed much more calibration than 1-line models and have not always provided much more information than was needed to calibrate them. Recent advances (Hanson and Larson, 1999 and Steetzel and Wang, 2004) have improved the description of cross-shore and long-shore behaviour.
Coastal area models
Process-based coastal area models have been used for years to study short term (generally depth-averaged) hydrodynamic and sediment transport problems, and given their ability to simulate fields that are both identifiable and (potentially) verifiable, there is appeal in the potential for applying such models to longer term problems. However, the issues associated with application of process based models are long-established (see for example, de Vriend et al., 1993), and include problems associated with the requirement to model large areas, with relatively fine meshes (in order to resolve the relevant processes) and the need to simulate relatively long timescales. There are also the associated problems of supplying the model with the correct set of input conditions (and sometimes the sequence of these conditions) that will determine the morphology.
In order to drive the model for long-term simulations it is necessary to perform simplifying or filtering techniques [link to Ida’s paper].
One of the limitations of coastal area models for considering beach evolution in front of coastal structures are that surf-zone processes, such as undertow, are not represented in the model. Wave reflection and diffraction are only rarely included in coastal area models.
- Southgate, H.N. and Brampton, A.H., 2001. ‘Coastal Morphology Modelling: a guide to model selection and usage’, HR Wallingford Report SR 570.
- De Vriend, H.J., 2003. On the prediction of aggregated-scale coastal evolution. Journal of Coastal Research, 19(4) 757 – 759.
- Hanson., H., Aarninkhof, S., Capobianco, M., Jiménez, J.A., Larsom, M., Nicholls, R.J., Plant, N.G., Southgate, H.N., Steetzel, H.J., Stive, M.J.F. and de Vriend, H.J., 2003. Modelling coastal evolution on yearly to decadal timescales. Journal of Coastal Research, 19(4) 790 – 811.
- Van Rijn, L.C., Walstra, D.J.R., Grasmeijer, B., Sutherland, J., Pan, S. and Sierra, J.P., 2003. The predictability of cross-shore bed evolution of sandy beaches at the time scale of storms and seasons using process-based Profile models. Coastal Engineering 47: 295 – 327.
- Bakker, W.T., Klein Breteler, E.H.J. and Roos, A., 1970, ‘The Dynamics of a coast with a groyne system’, Proceedings of the 12th International Conference on Coastal Engineering, ASCE, 1001-1020.
- Falqués, A., 2003, ‘On the diffusivity in coastline dynamics’, Geophys. Res. Lett., 30(21), 2119, doi:10.1029/2003GL017760.
- Murray, A.B. and Ashton, A., 2003. Sandy-coastline evolution as an example of pattern formation involving emergent structures and interactions. Proceedings of the International Conference on Coastal Sediments 2003. CD-ROM published by World Scientific Publishing Corp. and East Meets West Productions, Corpus Christi, Texas, USA. ISBN 981-238-422-7.
- Reeve, D., 2006, ‘Explicit expression for beach response to non-stationary forcing near a groyne’, Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, 132(2), 125 – 132.
- Ozasa, H. and Brampton, A.H., 1980. Mathematical modelling of beaches backed by seawalls. Coastal Engineering, Volume 4, pp 47 – 63. doi:10.1016/0378-3839(80)90005-8
- Hanson, K. and Kraus, N.C., 1989. GENESIS – generalized model for simulating shoreline change, Volume 1: reference manual and users guide. Tech Rep CERC-89-19, USAE-WES, Coastal Eng Research Centre, Vicksburg, Miss.
- Bakker, W.T., 1968, ‘A mathematical theory about sand waves and its application on the Dutch Wadden isle of Vlieland’, Shore and Beach 36(2): 4-14.
- Perlin, M. and Dean, R.G., 1979. Prediction of beach planforms with littoral controls. Proc 16th Int Conf Coastal Engineering, ASCE, 1818-1838.
- Hanson, H. and Larson, M., 1999, ‘Extension of Genesis into the cross-shore dimension – from 1-line to N-line’, In Proc. 5th Conf on Coastal and Port Engng in Developing Countries, pp. 312-323.
- Steetzel, H.J. and Wang, Z.B., 2004. ‘A long-term morphological model for the whole Dutch Coast. Part 1: Model formulation’, Alkyon Hydraulic Consultancy and Research and WL | Delft Hydraulics, report Z3334/A1000 for RIKZ Rijkswaterstaat.
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