Coupled wave and surge modelling for the eastern Irish Sea and implications for model wind-stress
Introduction
Surges in UK waters are generally caused by strong winds due to mid-latitude depressions passing over the UK from the Atlantic. Currents in the sea are accelerated due to variations in the atmospheric pressure gradient and also as a result of wind-stress (Gill, 1982). Lennon (1963) suggested that major west coast storm surges are caused by Atlantic secondary depressions passing from SW to NE over the northern part of the British Isles at a critical speed of about 40 knots. The wind-stress is most effective at producing a surface elevation gradient in shallow water. Depths in the eastern Irish Sea are only about 40 m on average and thus this area is prone to large surges which may cause flooding in low-lying coastal areas. Local surge generation in the eastern Irish Sea also results from a simple force balance due to the surge-generating winds being predominantly from the W and NW and the simple geometry of the coastline (see Figs. 1 and 5) but the external surge is also important, i.e. surge generation in the southern Irish Sea, Celtic Sea and SW Approaches (Jones and Davies, 1998).
Large surges at Liverpool can be up to 2.5 m (Wolf, 2008). During the night of the 12th November 1977 a severe storm (1.5 m surge) coinciding with tidal high water overtopped coastal defences throughout Lancashire and Cumbria. In the January 2007 event, the maximum surge in Liverpool reached 2.23 m. This is the second largest surge event in the last 10 years. The largest reached 2.26 m on the 27th October 2002, but no wave data were recorded and there are limited surge data. Liverpool Bay is sheltered from swell waves from the Atlantic and experiences locally wind-generated sea. Waves have been recorded in Liverpool Bay from November 2002 to the present (Wolf, 2008). The wave height typically exceeds 3 m during 5–10 events per year and exceeds 4 m during 1–5 events per year. The largest waves and surges in Liverpool Bay are generated by westerly and north-westerly winds which have the longest fetch.
Wave conditions may also be critical to coastal flooding, through overtopping of sea defences and low-lying areas. Wind waves are the mechanism through which the wind-stress interacts with the sea surface. Bulk parameterisations of the surface drag implicitly take account of the effect of waves (as drag increases with wind speed) but local conditions may mean that waves are not in equilibrium with the wind so it is of interest to model surge and waves simultaneously and examine their interactions.
Since the 1950s it has generally been accepted that the wind profile in the atmospheric boundary layer can be represented by a logarithmic law which appears very robust (Charnock, 1955). With the development of high frequency recording devices such as the sonic anemometer it has been possible to directly measure the surface wind-stress (Reynolds stress) by means of eddy correlation and/or dissipation methods from the turbulent velocity fluctuations, e.g. Smith and Banke (1975) and Taylor and Yelland (2001). These have led to various parameterisations of the stress in terms of the more readily available wind speed at 10 m above the sea surface, U10, giving the much-used empirical bulk formula such as Smith and Banke (hereafter S&B) and Wu (1982).
In surge models the S&B formula is frequently used to parameterise the wind-stress, but this formula has been found to under-predict the surge conditions in the southern North Sea (Mastenbroek et al., 1993; Williams and Flather, 2000). Williams and Flather (2000) found it necessary to enhance the wind by a factor of 1.1 (equivalent to replacing U10 by U25) to get good surge forecasts. This may be related to the spatial model resolution, in that the surge generation in shallow areas is poorly represented. The Charnock (1955) relationship is an alternative formula, which is used in the operational surge model at Proudman Oceanographic Laboratory. Janssen, 1989, Janssen, 1991, Janssen, 2004, Janssen et al. (2004) and Mastenbroek et al. (1993) have all investigated representing the surface stress in the presence of waves by a Charnock-like method in place of S&B. Using a constant Charnock value in the surge model allows the stress to be tuned to obtain the desired surge levels at a particular location. However, the optimum value may vary with location. It is thought the Charnock parameter is not constant but is related to wave-age (Drennan et al., 2005). Wave-age (cp/u*) is used to measure the stage of development of the wind sea, as waves grow they become longer and faster (Janssen, 2004). Here we aim to (i) use a consistent surface stress computation for wave and surge model and (ii) replace the constant value Charnock parameter with a wave-dependent parameter such that a global representation of the surface stress is obtained, without the need for tuning.
We use the Proudman Oceanographic Laboratory Coastal Modelling System (POLCOMS) as the surge model and the 3rd-generation spectral Wave Model (WAM). The November 1977 and January 2007 storm surge events have been used to study surge prediction in the eastern Irish Sea using both a coupled wave-tide-surge (POLCOMS-WAM) model and a tide-surge (POLCOMS) model. These two hindcast events have been simulated, to (i) investigate the effects of waves on the surge generation by modifying the surface drag and (ii) optimise the Charnock parameter without waves for the eastern Irish Sea. We modify POLCOMS so that a consistent formulation to WAM is applied for stress, which also facilitates coupling of the wave and surge models. A set of metrics for testing the models goodness of fit have been designed (Section 2.5). The model set up and hindcast events are presented in Section 2. The surge predictions are shown in Section 3. Different coupled and uncoupled methods were tried to represent the surface stress in POLCOMS to best simulate the surge residuals at coastal tide gauges. The findings are discussed in Section 4 with the focus mainly on Liverpool Bay. We conclude in Section 5 that it is important to retain the wave-age dependence of the wave model via the Charnock parameter to produce appropriate stress for storm surges in Liverpool Bay, when using POLCOMS-WAM.
Section snippets
Model set up
In order to accurately simulate the waves in the study area, we use the state-of-the-art 3rd-generation spectral Wave Model (WAM, Komen et al., 1994) modified for shallow water (Monbaliu et al., 2000). WAM does not include radiation stress, which may be important in shallow water. This will be investigated in future modelling work using a high resolution (∼180 m) model of Liverpool Bay. To allow investigation of the influence of externally generated waves propagating into the study area, a
Results
POLCOMS-WAM was used to hindcast the November 1977 storm surge event. The model was tuned to obtain the most accurate (regional) surge prediction across five coastal tide gauges in the eastern Irish Sea. To further validate the new model set up the January 2007 event was then simulated using a subset of the initial model configurations.
Discussion
The model was tested with different wind-stress using the S&B (uncoupled) and the Charnock (coupled and uncoupled) formulations. The model set up was calibrated using the November 1977 surge event and an extreme event in January 2007, for which good high resolution wind data, surge model boundary conditions, coastal tide gauge data and wave data are available. We concentrate our analysis on a deep (Douglas or Port Erin near to Douglas) and shallow (Hilbre) tide gauge location, to show the
Conclusions
The eastern Irish Sea provides simple wave and surge conditions. A consistent method to calculate the surface stress in the wave and surge models has been implemented. This paper presents metrics (Section 2.5) that are useful to assess the accuracy of surge prediction across a region. Using these metrics we have shown that a constant Charnock parameter can be tuned to give good surge results at a given location, but not necessarily optimum everywhere in time and space. The optimum value of the
Acknowledgements
This work was carried out as part of the NERC FREE CoFEE project, with the help and advice of Eric Jones regarding the 1977 surge event. His provision of wind data was gratefully received. Jane Williams is acknowledged for her assistance in providing model output and meteorological data for the 2007 surge event. Alejandro Souza is thanked for comments regarding the modelling results and presentation of data. Richard Pawlowicz is acknowledged for providing mapping tools to present the data. BODC
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