A number of complex, dynamic models are available for examining processes related to sediment transport, wave energy effects, beach profile changes, and so on.  While the rigour of such models is clearly an advantage for predicting physical changes and examining coastal processes, their application is severely limited for assessments in many countries, for two reasons.  First, such models often demand good quality, high resolution data for a range of variables and model parameters.  Good quality data is often very limited and therefore the range of methods for assessing the impacts of climate and sea-level changes is also restricted.  Second, the more complex coastal models are not well suited to addressing the issues of sea-level rise because very different time and space scales are involved.  In such circumstances, the detailed processes and predictive accuracy of the model may be less important than the capability to conduct simulations for the purpose of examining model sensitivities and uncertainties under sets of “what if” scenarios on coarse temporal and spatial scales.

Consequently, following the guidance given in the USCSP Handbook (Benioff et al., 1996, Chapter 5.5) and the UNEP Handbook (Feenstra et al., 1998), a variant of the ‘Bruun Rule’ (Bruun, 1962) was developed at the International Global Change Institute (IGCI) at the University of Waikato, New Zealand.  This method appears suitable for simulating shoreline changes on beach and dune systems.



The concept behind the 2-dimensional “Bruun Rule” model is explained in the USCSP Handbook (Benioff et al., 1996).  In effect, in the Bruun Rule the equilibrium profile of a beach-and-dune system is re-adjusted for a change in sea level (see Figure 1).  A rise in sea level will cause erosion and re-establishment of the equilibrium position of the shoreline further inland, as follows:

Ceq = z l / (h + d)     where:

Ceq is the equilibrium change in shoreline position (in metres)

z is the rise in sea level (in metres)

l  is the closure distance (the distance offshore to which materials are transported and “lost”, in metres)

h is the height in metres of the dune at the site

d is the water depth in metres at closure distance ( l/(d+h) thus gives slope)

Principles of the Bruun Rule as the basis for the coastal impact model

There are two important drawbacks to using this simple model to examine shoreline change under a trend of rising sea level.  First, it gives only the “equilibrium” (or steady-state) change.  In reality, coastal systems do not adjust instantaneously; rather, there is apt to be some time lag in the response.  Second, in reality shoreline retreat, as evidenced by historical data on beach profiles, is apt to occur in “fits and starts” over time, not as a steady, year-by-year incremental change.  This uneven response of the shoreline is partly a function of the chance occurrence of severe stormy seasons, which often cause erosion (in contrast, a season of very few, or mild, storms may allow the natural system to replenish the sediment supply and the shoreline to advance).

For these reasons, the Bruun Rule was modified slightly to add a response time and a stochastic “storminess” factor as follows:

dC/dt = (Ceq – C)/+  S     where:

is time (years)

C  is the shoreline position (metres) relative to that of t=0

Ceq  is the equilibrium value of C

is the shoreline response time (years)

S is a stochastically-generated storm erosion factor

In other words, the yearly change in shoreline is a function of the difference between where the shoreline should be (according to the Bruun Rule) in that year and where it actually is (as a consequence of what has occurred in previous years), as well as the effect of storms.  The greater the difference, the greater the potential erosion in that year, subject to the rapidity at which the system can respond.

The concept was incorporated into a costal impact model. The model is forced by changes in sea level (projections selected by the user from library files) and by the randomly selected “stormy seasons”, as defined by the user. The model runs on yearly time-steps and the results are displayed graphically.  


To launch the Coastal Impact Model you need to navigate to the Impact Model toolbar as depicted below and click first on 1] a study area from the far right part of the toolbar and then (global) and, 2] click on the coastal impact model icon on the left:

After clicking on the impact model icon the interface for the model will be displayed.  As this is the only impact model loaded in your current purchased version of SimCLIM only the option of choosing the coastal impact model will be available to you as shown below.

Click on coastal erosion.

The primary interface for the coast erosion impact model as depicted below will be displayed.

In order to use the modified version of this Bruun, the user must select values for each of the following: site-related model parameters; sea-level rise scenario; and storm characteristics.

Site-related parameter values:  

For application at a given site, it is necessary to select the values for the model parameters:

To create a new site you click on Manage Sites from the main coastal model dialogue box. Enter the name of the site and its location and other data derived from the literature.

  • The shoreline response time () governs the responsiveness of the system to sea level rise in a given year.  For example, if  is set to 6, the annual change in shoreline will be one-sixth of the “potential” change indicated by the equilibrium situation (if sea level is constantly rising, the system is continually in dis-equilibrium).

  • The closure distance (l) is the distance offshore at which sediments are effectively “lost”.  This value is not very easy to ascertain and expert advice should be sought.

  • The depth of material exchange (d) is the water depth at closure distance at which the sediments are lost.  It is assumed that the depth is greater at high wave energy sites.

  • The dune height (h) is the frontal dune height from mean sea level.

  • The model parameter called residual movement is the very long term change (on the order of centuries) in shoreline position. This factor largely relates to long-term trends in sediment supply and transport as they affect erosion and accretion.

SLR Scenario: The input to the model is sea level rise, selected through the user choice of sea-level scenarios.  First, the user can set the value for the residual sea-level rise (which is the historical trend, in metres per year), assumed to be due to a combination of vertical land movement, global sea-level trends and regional trends.  The value chosen will be applied up to the year 1990 and added to the scenario of future sea level rise for 1990-2100.  

Second, there is a large library of future scenarios (for 1995-2100) from which the user can choose. The latest IPCC scenarios are the four labelled RCP (the Representative Concentration Pathways values here are the projections from the Fifth Assessment Report).  The choice of “baseline” scenario (the last selection in the library) sets the future component of sea-level rise to zero and instead provides a simple extrapolation of the past rate of sea level rise into the future.

Third, there is a choice of climate sensitivity.  The choice reflects the range of scientific uncertainty in climate and sea level modelling.  Here, the user selects a low, medium or high projection to be associated with the choice of scenario.

Storm Parameters: Choose the Strom Parameters tab circled in the dialogue box depicted below. The model assumes that particularly stormy seasons provide the energy required to potentially erode the shoreline.  The “storminess”, and thus the erosion potential, in any given year is selected randomly from a normal distribution with a user-defined mean and standard deviation.  These values can be selected by the user on an ad hoc basis to give a reasonable interannual variability in shoreline change, as compared to observational data on shoreline variation. During simulation, values are selected randomly from the distribution. For randomly-selected values that are zero or negative, the erosive potential is set to zero, which usually allows accretion to occur and the shoreline to advance toward its equilibrium position.  Positive values are scaled according to the state of dis-equilibrium and applied to the shoreline erosion.  The user is encouraged to change the mean and standard deviation in order to examine the effects on shoreline change on yearly, decadal and longer time-scales.

Each simulation of the model can provide a unique sequence of past and future storm seasons.  This is useful for looking at short-term variability and extremes in relation to long-term trends in average sea level change as they can potentially affect the coastline.  

For more sophisticated analyses in which the user is interested in the statistical properties of such storm effects, the user can tick the Monte Carlo Simulation option (see dialogue box above). With this option, the model is run repeatedly in order to obtain a sample from which the mean and distribution for each year can be described.  The user selects the number of simulations (i.e. the sample size) and the confidence interval to be displayed graphically.  This analysis can provide information on the average conditions as well as an assessment of risks arising from the natural variability in the system.


Adding your own study area is very easy to do. Simply clear the ‘select a site text from the name box and type in an identifier for your new study area. Assign an ID number and input the latitude and longitude (see below). Click on and you are ready to enter the Information for the site and begin to run different scenarios.

Results:  To run the model, click on Run Simulation at the bottom of the dialogue box. The model begins running in 1940 (in order to “warm up” the model) and ends in 2100. The results of the analysis immediately appear in tabular form. To view the results graphically, click on a column heading, which will give you the choice of outputs to view. Choose the outputs to view and click OK, which will bring up a graph. In most cases, the key output variable to examine is the current shoreline.

Example of model results showing changes in

shoreline position

An example of the model results is shown in Figure 2.  Although the model begins in 1940, at least the first decade of results should be ignored as the model is “winding up”.  The vertical axis shows the change in shoreline position from the “equilibrium” position in 1940 (i.e. zero).  The negative values indicate shoreline retreat in metres.  In order to estimate the result of the chosen scenario of sea level rise, one should take the difference between the average shoreline positions around 1990 and the future date of interest (e.g. 2050).  This difference can be estimated visually.  For example, in the Figure above, the retreat of the shoreline between 1990 and 2100 is about 22 metres.

There are a host of other outputs that can be produced as depicted in the dialogue box below. Simply click on the boxes for the ones you want and click to have them displayed graphically.


It is very important to bear in mind that the coastal impact model is not a “predictive” model, in the same sense that more sophisticated dynamic coastal models based on physical processes are able to predict coastal responses from first principles.  Rather, it is a “simulation” tool.  While it produces realistic shoreline behaviour (i.e. shoreline retreats when sea level rises; decadal and interannual scale variations in shoreline position are generated that match observations; etc), such responses are not “determined” from actual physical processes.  

Thus, in terms of application, the coastal impact model is not a scientific tool for predictive modelling.  Rather, it is a tool that can produce scientifically reasonable shoreline behaviour in response to sea-level changes and is useful for asking “what if” questions about coastal changes as a basis for impact assessments, coastal planning and management.

References cited:

Bruun, P. 1962:  Sea level rise as a cause of shore erosion.  Journal of the Waterways and Harbours Division, Proceedings of the American Society of Civil Engineers, Vol. 88, pp. 117-130.

Benioff, R., S. Guill and J. Lee (eds), 1996:  Vulnerability and Adaptation Assessments:  An International Handbook.  Kluwer Academic Publishers, Dordrecht

Feenstra, J.F., I Burton, J.B. Smith and R.S.J. Tol (eds), 1998:  Handbook on Methods for Climate Change Impact Assessment and Adaptation Strategies.  United Nations Environment Programme (UNEP), Nairobi, Kenya, and the Institute for Environmental Studies, Amsterdam, The Netherlands.