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This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, non-linear interactions in deep water; 4, white-capping dissipation; 5, non-linear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. Keywords

Currents effects on waves have lead to many developments in numerical wave modeling over 5 the past two decades, from numerical choices to parameterizations. The performance of 6 numerical models in conditions with strong currents is reviewed here, and observed strong

Although the tendency for surge peaks in the Thames to occur on rising tide has been recognized for some time, no satisfactory physical explanation has been presented. The phenomenon almost certainly results from non-linear interaction between tide and surge and it is the mechanism of this interaction which is examined in the present study.A statistical analysis o f surges recorded at 10 ports located along the east coast of Britain demonstrated the development of interaction as surges propagate southwards. This analysis showed that surges tend to develop a peak on the rising tide in the Thames irrespective of the phase relationship between tide and surge in the northern North Sea.A one-dimensional model of the River Thames was used to examine how surge-tide interaction varied for surges of differing types. In order to identify the mechanics of interaction, a new modelling technique was developed involving two models, one of tidal propagation and one of surge propagation, operated simultaneously with cross-linkages in the form of perturbation terms providing the effects of interaction. By this means it was shown that quadratic friction is the dominant interaction mechanism in the Thames.

Wind waves and elevated water levels together can cause flooding in low-lying coastal areas, where the water level may be a combination of mean sea level, tides and surges generated by storm events. In areas with a wide continental shelf a travelling external surge may combine with the locally generated surge and waves and there can be significant interaction between the propagation of the tide and surge. Wave height at the coast is controlled largely by water depth so the effect of tides and surges on waves must be also be considered, while waves contribute to the total water level by means of wave setup through radiation stress. These processes are well understood and accurately predicted by models, assuming good bathymetry and wind forcing is available. Other interactions between surges and waves include the processes of surface wind-stress and bottom friction as well as depth and current refraction of waves by surge water levels and currents, and some of the details of these processes are still not well understood. The recent coastal flooding in Myanmar (May 2008) in the Irrawaddy River Delta is an example of the severity of such events, with a surge of over 3m exacerbated by heavy precipitation. Here we review the existing capability for combined modelling of tides, surges and waves, their interactions and the development of coupled models.Keywords: tides, storm surges, wind waves, coastal flooding, wave-current interaction, numerical modelling 1 Coastal Flooding -Impacts of coupled wave-surge-tide models Judith Wolf AbstractWind waves and elevated water levels together can cause flooding in low-lying coastal areas, where the water level may be a combination of mean sea level, tides and surges with storm surges and waves often being generated by the same storm event. In areas with a wide continental shelf a travelling external surge may combine with the locally generated surge and waves and there can be significant interaction between the propagation of the tide and surge. Wave height at the coast is controlled largely by water depth so the effect of tides and surges on waves must be also be considered, while waves contribute to the total water level by means of wave setup through radiation stress. These processes are well understood and accurately predicted by models, assuming good bathymetry and wind forcing is available. Other interactions between surges and waves include the processes of surface wind-stress and bottom friction as well as depth and current refraction of waves by surge water levels and currents, and some of the details of these processes are still not well understood. The recent coastal flooding in Myanmar (May 2008) in the Irrawaddy River Delta is an example of the severity of such events, with a surge of over 3m exacerbated by heavy precipitation. Here we review the existing capability for combined modelling of tides, surges and waves, their interactions and the development of coupled models.

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We revisit the surge of November 1977, a storm event which caused damage on the Sefton coast in NW England. A hindcast has been made with a coupled surge-tidewave model, to investigate the effects of waves on the surge generation by modifying the surface drag. The POLCOMS-WAM modelling system has been used to model combined tides, surges, waves and wave-current interaction in the Irish Sea on a 1.85km grid. This period has been previously thoroughly studied e.g. Jones and Davies (1998) and has been chosen here to validate the POLCOMS-WAM model to test the accuracy of surge elevation predictions in the study area. A one-way nested approach has been set up. It was demonstrated that (as expected) swell from the North Atlantic does not have a significant impact in the eastern Irish Sea. To capture the external surge generated outside of the Irish Sea a (1/9º by 1/6º) model extending beyond the continental shelf edge was run using the POLCOMS model for tide and surge.The model results were compared with tide gauge observations around the eastern Irish Sea. The model was tested with different wind-stress formulations including Smith and Banke (1975) and Charnock (1955). It has been demonstrated that Smith and Banke can be well-approximated by a constant Charnock parameter, but this varies with location. In order to get a single parameterisation that works with wavecoupling the wave-derived surface roughness length has been imposed in the surge model. One of the largest surge events that occurred at Liverpool in the last 10 years, in January 2007, has also been simulated to validate this model set up to demonstrate its robust application in the Liverpool Bay area.

Within the framework of a Tyndall Centre research project, sea level and wave changes around the UK and in the North Sea have been analysed. This paper integrates the results of this project. Many aspects of the contribution of the North Atlantic Oscillation (NAO) to sea level and wave height have been resolved. The NAO is a major forcing parameter for sea-level variability. Strong positive response to increasing NAO was observed in the shallow parts of the North Sea, while slightly negative response was found in the southwest part of the UK. The cause of the strong positive response is mainly the increased westerly winds. The NAO increase during the last decades has affected both the mean sea level and the extreme sea levels in the North Sea. The derived spatial distribution of the NAO-related variability of sea level allows the development of scenarios for future sea level and wave height in the region. Because the response of sea level to the NAO is found to be variable in time across all frequency bands, there is some inherent uncertainty in the use of the empirical relationships to develop scenarios of future sea level. Nevertheless, as it remains uncertain whether the multi-decadal NAO variability is related to climate change, the use of the empirical relationships in developing scenarios is justified. The resulting scenarios demonstrate: (i) that the use of regional estimates of sea level increase the projected range of sea-level change by 50% and (ii) that the contribution of the NAO to winter sea-level variability increases the range of uncertainty by a further 10-20cm. On the assumption that the general circulation models have some skill in simulating the future NAO change, then the NAO contribution to sea-level change around the UK is expected to be very small (<4cm) by 2080. Wave heights are also sensitive to the NAO changes, especially in the western coasts of the UK. Under the same scenarios for future NAO changes, the projected significant wave-height changes in the northeast Atlantic will exceed 0.4m. In addition, wave-direction changes of around 20 degrees per unit NAO index have been documented for one location. Such changes raise the possibility of consequential alteration of coastal erosion.