This review of modelling approaches to long-term coastal morphodynamics starts with the briefest introduction to coastal morphodynamics and its effects on society. Different tools are needed to predict the response of the coastline at different scales, but they can all be ascribed to a limited number of model types. The traditional approach is to use a model to make a deterministic prediction of future morphology (or the position of a morphological feature). However, an increasing awareness of the importance of probability and risk has led to an increase in the use of models for making stochastic predictions.
Introduction to model types
In order for coastal managers to address the issues raised by changes to coastal morphology, it is necessary to have data and models that will allow the morphodynamic behaviour to be simulated over the different time and space scales illustrated.
Different modelling methods are needed to predict the response of the coastline at different scales. These methods come with different levels of reliability, accuracy, skill and required expertise and may be allocated to one of the following basic types:
- Process-based numerical models;
- Behaviour-based numerical models
- Statistical analysis;
- Geomorphological analysis;
- Parametric equilibrium models; and
- Emerging techniques
Behavioural versus process-based modelling
‘Behavioural’ or ‘behaviour-oriented’ algorithms are developed to simulate known behaviours, such as the tendency for a beach to develop towards an equilibrium form, rather than the physics from which this behaviour emerges. In practice all models straddle the boundary between behavioural and process-based representation as no model includes all the physics involved. For example, even a detailed sediment transport model goes from knowledge of input conditions (waves, currents, sediment characteristic, bedforms, etc.) to sediment concentration and flux without calculating the full details of the turbulence or force balance on each grain.
There is therefore an element of abstraction and an attempt to represent the behaviour of (parts of) systems in all models. However, there is clearly a spectrum from the most detailed process-based models (which are based on physical laws and hope that by integrating through space and time the final bathymetry will be reproduced) to those that are wholly behavioural (such as use of the Bruun rule to model coastal retreat). The former apply behavioural modelling to small-scale processes, while the latter apply behavioural modelling to the entire beach.
One important question to be addressed is therefore at what time and space scale do we start to model behaviour (with effectively all processes at smaller scale being included in the behaviour)? This depends on the time and space scale to be modelled. One attempted classification has been produced within the EU project Prediction of Aggregate-Scale Coastal Evolution, PACE (Cowell et al., 2003a and 2003b). Their approach is summarised in Figure 3 and is based on a cascade of complexity where coastal behaviour at one scale comes from the residual effects of higher order (smaller scale) processes yet is also constrained by the effects of lower order (larger scale) processes.
Examples of the use of behavioural modelling in long-term simulations include:
- One-line beach models describe sediment transport due to a longshore component of wave energy (process based, though abstract) whilst it also assumes an unchanging long term averaged surface slope (behavioural).
- The cross-shore exchange of sand in a N-line model is based on answering the question “how much should the beach steepen or flatten towards its equilibrium profile?” The volumes of sand transferred cross-shore are calculated from the rate of change in morphology, rather than the change in morphology being calculated from the net sediment transport budget.
- SCAPE describes the process of soft rock erosion, but it employs a behavioural description of shore platform erosion (using a shape function) and landward sediment transport following a storm.
The key advantages of behavioural models over more process-based sediment transport models for large-scale, long-term simulations are stability and robustness. In this context, the crudeness and the simplicity of the longshore and cross-shore transport modules in a N-line model have contributed to the model’s success as they have contributed to its stability. The more behavioural models have a limited ability to represent the effects of coastal structures on the beach, for example, but can model open beach evolution up space and time scales of about 100km and 100years. The sections on process-based modelling and behavioural modelling are therefore separated by the time and space scales at which behavioural modelling is applied, but the position of the boundary is somewhat arbitrary.
- Cowell, P.J., Stive, M.J.F., Niederoda, A.W., de Vriend, H.J., Swift, D.J.P., Kaminsky, G.M. and Capobianco, M., 2003, ‘The coastal-tract (part 1): a conceptual approach to aggregated modelling of low-order coastal change’, Journal of Coastal Research, 19(4): 812 – 827.
- Cowell, P.J., Stive, M.J.F., Niederoda, A.W., Swift, D.J.P., de Vriend, H.J., Buijsman, M.C., Nicholls, R.J., Roy, P.S., Kaminsky, G.M., Cleveringa, J., Reed, C.W. and de Boer, P.L., 2003, ‘The coastal-tract (part 2): Applications of aggregated modelling of lower-order coastal change’, Journal of Coastal Research, 19(4): 828 – 848.
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