# Model help:CEM

## CEM

The CEM model, the Coastline Evolution Model, simulates the evolution of a shoreline due to gradients in breaking-wave-driven alongshore sediment transport. The original CEM has been componentized to consist of the longshore transport module (CEM) and a wave input module (WAVES).

## Extended model introduction

The CEM model assumes that the coast consists of a high percentage of mobile sediment and its other assumptions are more applicable at shoreline lengths of km’s and larger. The model was initially designed to investigate an instability in the shape of the coast caused by waves approaching with ‘high’ angles (with the angle between offshore wave crests--i.e. before transformation over approximately shore-parallel contours--and the coast > 45 degrees).

Although a number of wave (and geometry) parameters can be entered, the most vital input control for CEM is the wave climate. The current version of the CEM is driven by simplified directional wave climate controlled by two main input parameters: the asymmetry of the incoming waves angle and the proportion of high-angle waves. This model is not designed to accurately simulate a specific geographic location in detail but rather to more generally represent how a shoreline with highly mobile sediment may respond to varying wave angles. The value in this model is in the breadth it offers in representing how different wave climates can result in different potentially interesting shoreline configurations. Ashton and Murray (2006b) present a more thorough description of the model parameters and theoretical underpinning.

## Model parameters

CEM does not need input files from the user, its input is entirely specified in the CMT graphical user interface. To obtain output from this component make sure you toggle on the output files; as a default they are OFF.

## Coupling parameters

### Uses ports

CEM requires wave parameters as supplied by the WAVES component.(Model Help of WAVES).

CEM requires a sediment flux (bedload) originating from one or more river distributary channels. This is provided by the AVULSION component.

### Provides ports

CEM provides an elevation grid of offshore geometry after erosion and deposition is done in every timestep.

The elevation is required for the AVULSION component.

## Main equations

- Alongshore sediment transport

[math]\displaystyle{ Q_{s} = K_{2} H_{0} ^ \left ( {\frac{12}{5}} \right ) T ^ \left ( {\frac{12}{5}} \right ) cos ^ \left ( {\frac{6}{5}}\right ) \left ( \Phi _{0} - \theta \right ) sin \left ( \Psi _{0} - \theta \right ) }[/math] (1)

[math]\displaystyle{ K_{2} = \left ( {\frac{\sqrt{g \gamma}}{2 \pi}}\right ) ^ \left ({\frac{1}{5}} \right ) K_{1} }[/math] (2)

- Predictions of shoreline evolution

[math]\displaystyle{ {\frac{d \eta}{d t}} = - {\frac{K_{1}}{D_{sf}}} H_{b} ^ \left ({\frac{5}{2}} \right ) {\frac{d^2 \eta}{d x^2}} }[/math] (3)

[math]\displaystyle{ cos^ \left ( {\frac{1}{3}}\right ) \left ( \Phi_{b} - \theta \right ) \approx 1 }[/math] (4)

- Alongshore component of the radiation stress

[math]\displaystyle{ S_{xy} = H^2 sin \left ( \Phi - \theta \right ) cos \left ( \Phi - \theta \right ) }[/math] (5)

- Shoreline instability

[math]\displaystyle{ {\frac{d \eta}{d t}} = - {\frac{K_{2}}{D}} H_{0} ^ \left ({\frac{12}{5}} \right ) T^ \left ( {\frac{1}{5}} \right ) \{cos^\left ( {\frac{1}{5}} \right ) \left ( \Phi_{0} - \theta \right ) [ cos^2 \left ( \Phi _{0} - \theta \right ) - \left ( {\frac{6}{5}} \right ) sin^2 \left ( \Phi_{0} - \theta \right )] \} {\frac{d^2 \eta}{d x^2}} }[/math] (6)

- Shoreline adjustment

[math]\displaystyle{ \Delta F = {\frac{\left ( Q_{in} - Q_{out} \right )}{\left ( D_{sf} + B \right ) \Delta W^2}} }[/math] (7)

[math]\displaystyle{ \Delta t \propto \left ( {\frac{K_{1}}{D_{sf}}} H_{0} ^ \left ({\frac{12}{5}} \right ) T^\left ( {\frac{1}{5}}\right ) \right ) \Delta x^2 }[/math] (8)

[math]\displaystyle{ \Delta Y_{bb} = {\frac{\left ( D_{sf} + B \right ) }{\left ( D_{bb} + B \right )}}\Delta Y_{sl} }[/math] (9)

[math]\displaystyle{ W_{c} = W_{0} + \Delta Y_{bb} - \Delta Y_{sl} }[/math] (10)

[math]\displaystyle{ \Delta Y_{bb} = {\frac{\left ( W_{c} - W_{0} \right )}{\left ( 1 - {\frac{\left ( D_{bb} + B \right ) }{\left (D_{sf} + B \right )}} \right )}} }[/math] (11)

[math]\displaystyle{ \Delta Y_{sl} = {\frac{\left ( W_{c} - W_{0}\right )}{\left ({\frac{\left ( D_{sf} + B \right ) }{\left ( D_{bb} + B \right ) } - 1} \right )}} }[/math] (12)

## Notes

The parameters: **Shoreface Slope**, **Shoreface Depth** and **Shelf Slope** set the initial geometry of the shoreface domain and the shelf domain. Simulations will use the shoreface depth as an effective erosion depth, but deposition can take place to deeper depths if the shoreface is accreting on a deeper shelf.

## Examples

*An example run with input parameters as well as a figure / movie of the output*

*Follow the next steps to include images / movies of simulations:*

*Upload file: https://csdms.colorado.edu/wiki/Special:Upload**Create link to the file on your page: [[Image:<file name>]]*.

*See also: Help:Images or Help:Movies*

## Developer(s)

## References

- Ashton A., Murray B.A. Arnault O. Formation of Coastline Features by Large-Scale Instabilities Induced by High-Angle Waves. Nature Magazine. Volume 414. 15 November 2001
- Ashton A.D., Murray A.B. High-Angle Wave Instability and Emergent Shoreline Shapes: 1. Wave Climate Analysis and Comparisons to Nature. Journal of Geophysical Research. Volume 111. 15 December 2006.
- Ashton A.D., Murray A.B. High-Angle Wave Instability and Emergent Shoreline Shapes: 2. Wave Climate Analysis and Comparisons to Nature. Journal of Geophysical Research. Volume 111. 15 December 2006.

## Links

Movies generated with the stand-alone CEM model are documented in the CSDMS movie gallery. https://csdms.colorado.edu/wiki/Coastal_animations