Tuesday, 27 September 2011
Example MIKE 21 Coupled Model to investigate swell wave propagation in the English Channel

Introduction

In February this year (2011) a large storm in the North Atlantic caused swell waves with periods of 20-25 seconds to propagate into the English Channel. Whilst this is not unusual in itself (beaches along the south coast have historically been subject to similar storms), the combination with high water of these small wave height, long period waves led to a series of flooding “near misses” along the South Coast as swell waves led to damage and overtopping of some defences including natural barrier beaches.

It is important to note that many of the beaches along the south coast are gravel/shingle dominated barriers which are typically considered reflective in morphological classifications (Short 1979). Greenwood (1984) noted that reflective beaches, which are already prone to sub-harmonic edge waves, can interact with longer period swell waves leading to an amplification of wave run up, a mechanism which leads to higher than anticipated overtopping and overwashing of the crest with consequent implications for barrier stability and hinterland flooding. With increasing emphasis from operating authorities being placed on beach management of such natural defences, it is important to understand the driving conditions in an event such as this to plan effective management.

With this in mind, DHI have developed a demonstration model of this event to show how the Flexible Mesh series of models allows you to take large scale North East Atlantic basin driving forces to understand the impact at a local scale. The coupled model developed makes use of the Spectral Wave and Hydrodynamic modules of the MIKE by DHI software and uses freely available data sources as inputs.

For this regionally focused modeling study, bathymetry data has been sourced from the GEBCO 08 Grid bathymetry data set which provides a 30 arc-second grid of the entire globe. Tidal data was obtained from the MIKE 21 toolbox to allow the flow model to be adequately resolved.

In addition the driving forces of the storm in the North East Atlantic needed to be represented. For this the NOAA/NCEP reanalysis data was used. This data set can provide driving wind fields and pressures for the entire globe and a temporal and spatial subset was utilized for this demonstration. The NOAA/NCEP reanalysis data is 6 hourly at a spatial resolution of 2.5 degrees. Available pressure charts from the UK Met Office provide a validation of the data set used as seen in Figure 1 below.


Figure 1 – Met office and NOAA/NCEP reanalysis data used as forcing conditions for the model.

The mesh used for the modelling was optimized to provide a suitable representation of the features of interest in the storm and whilst starting out as a mesh of the entire North Atlantic for the entire duration of the storm system, this was reduced to a smaller North-East Atlantic model for a period including 3 days prior to the storm striking the South coast of the UK. This was to enable the wave model to be run in fully spectral mode, the most suitable for allowing the wind/wave generation and transport process to take place and at a computational speed that would be achievable for operational forecasting models (~1-2 hour model run times for combined wave and flow conditions).

Validation

To assess the validity of the model, wave, wind and water level data have been downloaded from the Channel Coastal Observatory. These data (Figure 2) showed the progression of the swell event up the English channel over a period of approximately 3 hours. Further investigation (Figure 3) of the data also showed the peak in the relatively small wave heights had a periodicity that was synchronous with the peak of high water suggesting a higher harmonic effect or a ‘tide push’ similar to that observed by surfers and recently measured off the coast of Cornwall (Davidson 2009).

Figure 2 - Wave height and peak period from Channel Coastal Observatory measurements in the English Channel.

The role of the high water and in particular the tide was highlighted during the validation process when the wave model was run alone. The results (Figure 3) suggested that the wave heights were similar whilst the conditions were dominated by wind waves but once the longer swell period was established the model was failing to reproduce the measured conditions. The timing of the peak wave periods was also in error. Once the model was run with the tidal hydrodynamics included, the results began to be more representative of the conditions observed and the importance of the tide on the size of the waves that were encountered became evident. This suggests that care should be taken when applying the Spectral Wave model alone in areas dominated by swell events with tidal currents and consideration should be given to the use of the coupled wave/flow model.

Figure 3 – Comparison of measured wave data (black), coupled wave/flow model data (red) and wave only model data (green).

Results

The outputs of the model can be seen in more detail in Figures 4, 5 and 6 below. In the Atlantic, it can be seen that the storm stalls for a period as the pressure field becomes more egg shaped around midnight on the 15th February. Whilst not the strongest winds, it is apparent from the resulting wave conditions that the compression of the low pressure by higher pressure to the south leads to the formation of a front of longer period swell waves which propagate to the North East but also a significant portion is directed towards the English Channel where it gets progressively constrained.


Figure 4 – Animation of the storm generation and propagation from the North East Atlantic into the English Channel


Figure 5 – Area plots of wave height and period for the North East Atlantic and the English Channel area.

The detailed plots from Figure 6 show that the spatial and temporal resolution of the NOAA/NCEP data are not perfect for the job of representing the local detail in the wind field. Two things are apparent from the top panel. Firstly that there is locally an increase in wind speed in the first 12 hours up to midday on the 15th with model winds approximately 5% lower than the measured winds and the winds are from the South and South East that lead to the largest waves at approximately 2m. The spectral outputs from the wave gauge suggest that the wave periods at this point are up to a peak of 6 seconds, consistent with wind sea.

Secondly the coarse temporal step of 6 hours is unlikely to capture the variation in wind speeds necessary to reproduce the directionally varying winds as the storm evolves. Notwithstanding both of these limitations in the input data, the model provides a valid representation of the key storm parameters.

The second panel highlights the difference local winds generated across the channel make with respect to wave height in the first 12 hours, and also shows the influence of the tide on the peak wave heights, something picked out in both the measured and the modeled data.

The peak and mean wave periods in panel 3 generally show a good timing of the storm along the channel, once allowance had been made for the effect of the tides as noted in Figure 3 above. Differences in the maximum value of peak wave periods is considered to be due to the spectral analysis methods used for deriving the Tp values from the Rustington wave gauge versus that used in the model.

The spectral outputs from the model shown in the bottom panel highlight the evolution of the event from a single peaked wind sea from the south/south east (150-180⁰N) to a double peaked spectrum dominated by energy from the south west (200⁰N). Of note is that the spectrum still retains a proportion of energy from 150-180⁰N during the peak of the storm from 19:00 on the 15th till 02:00 on the 16th. At shingle barrier beaches this could have led to an amplification of any naturally reflective properties or edge wave harmonics, leading to additional overtopping impacts.


Figure 6 – Outputs from the model at the approximate position of the Rustington Channel Coastal Observatory Wave gauge

Conclusions

It is apparent that the February 2011 storm was significant with respect to the propagation of swell waves into the English Channel. The fact that there wasn’t more damage inflicted during the storm is testament to the fact that the swell event struck 1-2 days after neaps on relatively low tides. It is possible that if the storm had arrived 3-4 days later the impact could have been much greater.

This data analysis and demonstration model has achieved several goals: -
  • Shown the value of the flexible mesh models to take large scale processes and assess their impact at the local scale
  • Use of a range of freely available data sets to get an initial stage assessment of the physical conditions
  • Highlighted the need for use of coupled models to adequately represent the complex wave and tidal combinations in the English Channel
  • Provided possible further evidence of the existence of “tidal push” with respect to swell events
  • Highlighted that the damaging effects of swell wave events on shingle barrier beaches is potentially not only due to large “height” waves
  • Tested the initial feasibility of implementing effective warning systems of swell events on the south coast barrier beaches

References

Greenwood, B., 1984. Hydrodynamics and sedimentation in wave-dominated coastal environments.. Elsevier 1984 pp. 387

Davidson M.A. O’Hare T.J. and George K.J 2009. Tidal modulation of incident wave heights: Fact or Fiction? The Reef Journal, Volume No. 1 2009 Editor: D.J Phillips Sub-Editors and Convenors: K. Black and J. Borrero. http://thereefjournal.com/Publications.html

Short, A.D., 1979. Wave power and beach stages: A global model. Proc. 16th Int. Conf.
Coastal Eng., Hamburg, 1978, pp. 1145-1162

Many thanks to Nick Elderfield for preparing the above paper, and the MIKE 21 Coupled FM demonstration model (MIKE 21 FMHD and MIKE 21 SW). For more information, please e-mail mikebydhi.uk@dhigroup.com
.

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DHI is an independent, international consulting and research organisation with the global objective of advancing technological development and competence with respect to water, in all of its environments.

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