Swell wave progression in the English Channel: implications for coastal monitoring

: Energetic swell waves, particularly when they coincide with high water levels, can present significant coastal hazards. To better understand and predict these risks, analysis of the sea levels and waves that generate these events and the resulting coastal impacts is essential. Two energetic swell events, neither of which were predicted by modelled flood forecasts, occurred in quick succession in the English Channel. The first event, on 30 January 2021, produced moderate significant wave heights at or just below the 0.25 year return period along the southwest English coast, but combined with significant swell caused overtopping at East Beach in West Bay and at Chesil Beach. The second event, on 1 February 2021, generated the highest wave energy periods measured at many locations along the southern English coastline and, at high water, caused waves to run up over the promenades at Poole Bay and Christchurch Bay and caused overtopping at Hayling Island. Both events are described in detail, and their spatial footprints are mapped through a joint return period analysis using a copula function. It is found that typical joint return period analysis of water level and significant wave height underestimates potential impacts, while a joint consideration of water level and wave power ( P ) describes the 31 January event better and a joint consideration of water level and energy period ( T e ) best describes the 1 February event. Therefore, it is recommended that T e and P are adopted for coastal monitoring purposes, and that future studies further explore the use of both parameters for swell monitoring.


Introduction
Energetic swell waves in the English Channel, particularly when they coincide with high water levels, can present a significant coastal hazard, causing beach erosion and damage to coastal structures and defences (e.g., Draper and Bownass 1983;Palmer et al. 2014;Sibley and Cox 2014). Swell is defined as waves that have been generated in another region of the ocean and have propagated out of the area of generation. Typically, longer-period waves generated by a low-pressure system travel faster than storms and therefore move out of the storm area (Draper and Bownass 1983). Waves that are not generated by local wind conditions may arrive without warning and without wind; therefore, taking coastal users and managers by surprise, making swell waves a danger to public safety.
From time to time, the UK is subject to long-period swell waves originating from storms developing in the western Atlantic, southeast of Newfoundland. Typically, energy dissipates over distance. However, in certain cases, trapped fetch conditions occur when a depression moves roughly in the same direction and at the same speed as the main wave group, maintaining an input of energy into the longer-period waves (Sibley and Cox 2014). The English Channel is a narrow tidal strait adjacent to a large fetch, the Atlantic Ocean, in which trapped fetch conditions can occur (Fig. 1). Once swell waves pass through the relatively small window of the Western Approaches, Sibley and Cox (2014) suggest that they are refracted towards the coast by Hurd Deep, which lies west to east in the middle of the English Channel, but are also refracted as they come into shallow water near the coast.
This study uses data from a dense network of wave buoys in the English Channel to describe two swell events that occurred in quick succession in the English Channel. The first was on the 30 January 2021 and the second on 1 February 2021. Neither event was predicted by modelled flood forecasts, but both caused overtopping of defences along the Fig. 1. Locations of the wave buoys and tide gauges used in this study. All wave buoys are owned and operated by the NNRCMP, except those indicated with an asterisk, which are owned and operated by CEFAS. All tide gauges are owned and operated by the UK National Tide Gauge Network. Map created in ESRI ArcGIS, boundary layer from EuroGeographics (Eurostat), and bathymetry base layer from GEBCO Grid.
English south coast, and surprised coastal engineers and managers. This analysis will evaluate non-traditional wave parameters as predictors of swell hazard and suggest ways to improve the monitoring of the latter phenomenon with the aim of better supporting decision making with regard to flood and coastal risk management and further assist modelling and prediction efforts.
The wave parameters typically used for the design of coastal structures are significant wave height (H s ) (in this study, H s refers to the spectrally derived H m0 ) and the zero up-crossing period (T z ). Nonetheless, swell waves have long been appreciated as contributors to the overtopping of beaches (Carr 1983;Draper and Bownass 1983;Bradbury et al. 2007), gravel beach recharge design (Bradbury et al. 2011), and the design of defence structures (Hawkes 1999). Indeed, swell conditions are now an integral part of run-up and overtopping formulas for beaches (e.g., Poate et al. 2016) and a key consideration in the design of coastal defences (EurOtop 2018). Nonetheless, even in recent years, overtopping of defences due to swell events occasionally occurs and has been documented by Palmer et al. (2014) and Sibley and Cox (2014). It is important to remember that, although new tools have been developed to assess swell in the design of new assets, many ageing assets around England were not designed for extreme long-period swell events. Documenting and analysing the metocean conditions, sea levels, and waves that continue to cause overtopping of beaches and defences is a useful exercise to better understand the threats presented by swell events and develop methods to better monitor and predict them.
The wave parameters typically used for operational beach monitoring are significant wave height (H s ) and peak period (T p ). In England, these parameters are provided in real time by the National Network of Regional Coastal Monitoring Programmes of England (NNRCMP 2021), where a "storm alert threshold" is provided for H s for each wave buoy deployed by the programme as a monitoring tool for coastal engineers and managers (Dhoop and Thompson 2018). T p values provided on the website are used by coastal engineers on the southern coast of England to monitor swell waves (pers. comm. S. Cope, Coastal Partners Havant Borough Council). The wave data captured by the NNRCMP is also displayed on the CEFAS WaveNet website (2021), which provides a five-day prediction, supplied by the Met Office, for most wave buoys. These data are fed into the Met Office wave and tide surge models and the National Flood Forecasting Service, which aims to provide sufficient time for coastal managers to prepare for flooding. The SWEEP Operational Wave and Water Level model is also available on the NNRCMP website (2021). The model was developed by the University of Plymouth Coastal Processes Research Group and provides a three-day forecast of waves, water levels, and wave overtopping for the southwest coast of the UK. Both events described in this study were under-predicted by modelled forecasts, and although T p functioned as a good monitoring tool to notify engineers of when the swell arrived at a particular buoy, it did not provide a full appreciation of the energy contained in the swell.
In summary, certain swell events continue to prove difficult to predict and monitor. This study describes the meteorological conditions of two such events, and the waves and water levels that they produced. In addition to the standard engineering parameters (H s , T p , T z , and Direction), two additional parameters were calculated. First, the energy period (T e ) is a useful complement to T p because it is less subject to rapid changes. As the ratio of the first negative and zeroth moments of the wave spectrum T e = m −1 m 0 , the parameter represents more of the lower frequency energy in the spectrum while avoiding marked jumps in the time series, typical of T p . Second, wave power (P) is used to account for both the wave height and wave period in a single parameter. The timing of the swell as it propagated through the Channel, and the energy of the swell was then mapped along the English coastline.
However, phenomena such as overtopping, beach erosion, and coastal flooding are often the result of the combined actions of two or more physical processes, most importantly water level and wave action. Therefore, the wave data were combined with water level data to assess the joint return periods achieved at each wave buoy site. The spatial extent of the swell events was evaluated by mapping the joint return periods of the water level and one of the three wave parameters, H s , T e , or P, at each wave buoy. This is followed by a description of the overtopping that occurred in East Beach and Chesil on 30 January and at Poole Bay, Christchurch Bay, and Hayling Island on 1 February 2021.
Finally, recommendations for coastal monitoring and operational beach-management purposes are discussed. It is suggested that it would be beneficial to add T e to the suite of standard wave parameters currently used in coastal monitoring. Real-time provision of both T p and T e could provide a more holistic appreciation of a swell event. In addition, P, as a measure of both wave height and period, could be a valuable addition for events where swell is combined with a significant amount of wind-generated waves, although, in theory, these could be monitored by observing both H s and T e .

Data sources
In total, data from 20 wave buoys and seven tide gauges were analysed, allowing for a high-resolution description and analysis of the swell waves and water levels during the 30 January and 1 February events. Three datasets were used to accomplish this study.
The first and primary dataset is the wave data from the fleet of coastal wave buoys deployed around the English coastline by the NNRCMP. The network consists of 37 Datawell Directional Waverider (DWR) MkIII buoys and is funded by the Department for Environment, Food and Rural Affairs (DEFRA) through the Environment Agency. Raw Datawell (2020) 64-bin spectral files and quality-controlled archived data from 18 wave buoys deployed along the English south coast were used (Fig. 1). Spectrally derived and archived parameters are quality controlled according to the procedures published by Mason and Dhoop (2017). The Rye Bay wave buoy was not used as it was (re)deployed on 26 February 2021 and therefore missed both events described in this study. All buoys used in the analysis were at water depths of ∼10 m Chart Datum (CD). The longest dataset is Milford-on-Sea (Hampshire), which started in 1996, and the shortest was Porthleven (Cornwall), which started in 2011. The mean data length for the wave buoys used was 15 years.
The second dataset of wave data were retrieved from CEFAS WaveNet, funded by DEFRA through the Environment Agency. From the 15 wave buoys deployed around the British Isles, two Datawell DWR MkIII wave buoys deployed in the English Channel at Poole Bay and Hastings were used (Fig. 1). Where available, the full 64-bin spectral data are used to derive the processed parameters. When not (yet) available, iridium telemetry data were used (less than 1% of all wave data used). The iridium spectra have 27 frequency bins that can vary from spectrum to spectrum as they are calculated to best represent the specific dataset. All post-recovery and telemetry spectra were quality controlled according to the procedures outlined on the CEFAS website (CEFAS 2021). The Poole buoy (Dorset) is located at a water depth of 28 m CD and the Hastings buoy (East Sussex) at a water depth of 43 m CD. The dataset from Hastings spans 19 years, while the dataset from Poole comprises 18 years' worth of measurements.
Water levels were retrieved from the UK National Tide Gauge Network, which is available from the British Oceanography Data Centre (BODC) archive. The network comprises 43 operational tide gauges owned by the Environment Agency. Quality-controlled data from seven tide gauges located along the English south coast were used (Fig. 1). The longest record is at Newlyn (Cornwall), which started in 1915, and the shortest at Bournemouth (Dorset), which started in 1996. The mean data length for the tide gauges used was 51 years. Prior to 1993, the data frequency was hourly, and from January 1993, it increased to 15 min.

Wave power and energy period calculations
The wave power represents the rate of transfer of energy through each metre of the wavefront. In this study, wave power is used to account for wave height and wave period, both of which have distinct and joint influences on coastal events, in a single parameter. Wave power is defined as follows (Folley 2016): where ρ is the density of seawater (1025 kg/m 3 ), g is the acceleration due to gravity at 9.81 m/s 2 , H m0 (H m0 = 4 ffiffiffiffiffiffi m 0 p ) is the significant wave height based on m 0 , the zero moment of the power spectrum, and T e is the wave energy period. The wave power is proportional to the significant wave height squared and wave energy period. However, most historical and ongoing wave measurement data typically only provide the spectral peak period (T p ) and mean zero up-crossing period (T z ) as processed parameters and not the energy period (T e ), which is needed to calculate wave power. This holds true for the wave data provided by both the NNRCMP and CEFAS WaveNet used in this study.
Although T e has not been reported as a standard output parameter of a Datawell DWR MkIII, it can be derived from the raw spectral files from the buoy by calculating the first negative moment and the zeroth moment, where the frequency moment m n of the spectrum is defined as where E( f ) is the variance density spectrum (m 2 ·Hz −1 ), f is the frequency, and df is the frequency bandwidth (Hz).
The energy period (T e ) can then be defined as the ratio of the first negative moment of the spectrum to the zero moment, as given by Eq. 3.
Because T e is proportional to the first negative moment of the wave spectrum, the parameter gives more weight to the lower frequencies and therefore the longer periods in the spectrum than wave period parameters such as T p or T z .

Univariate extremes analysis
To gauge the likelihood of the swell events discussed in this study, the energy period (T e ) return periods were calculated for each wave buoy site. To do this, a peaks-over-threshold approach with the threshold defined as the 99.5th percentile is used, with a 48 h storm separation window, to create a sample of independent and identically distributed observations. A generalised Pareto distribution was fitted to the sample, and parameter estimates were derived using the maximum likelihood method (Coles 2001). Both the threshold and storm separation window are rules-of-thumb to make the analysis more efficient while still providing reasonable parameters for the analysis. The same parameters are used in the analyses performed by the NNRCMP and are discussed in detail in Dhoop and Thompson (2018).

Joint probability analysis
The spatial extent of the swell events was examined by producing maps of the spatial footprint of the events based on the joint return period of the water level combined with one of three different wave parameters: significant wave height (H s ), energy period (T e ), or wave power (P), at each wave buoy.
Joint return periods between the two time series were calculated using a bivariate copula function. Over the last 15 or so years, copula functions have been widely used in coastal engineering to examine a combination of wave heights and periods (De Waal and Van Gelder 2005), storm surges, and wind waves (Wahl et al. 2012;Di Bernardino et al. 2013), and sea level and wave height (Mazas and Hamm 2017). It should be noted that, as mentioned above, this study uses a number of heuristics to make the analysis easier to apply to all wave buoy sites while providing the most reasonable spatial footprint and does not attempt to provide any design characteristics for any particular location.
The following four-step methodology is implemented in MATLAB and is typical of UK coastal engineering, as the same steps are used in the JOIN-SEA software (Hawkes et al. 2002): (i) Data selection of the joint time series (ii) Modelling of the marginal distributions (iii) Analysis of the dependence structure (iv) Estimation of joint return periods

Data selection of the joint time series
Samples for dependence modelling were extracted from concurrent time series of water levels and wave parameters using a multivariate threshold similar to that of Li et al. (2014). It is assumed that, in order for high and (or) energetic swell waves to cause significant beach erosion, overtopping, or coastal flooding at all wave buoy sites, they must occur at or around the high water level. Therefore, a subsample of the 5% highest tides and their concurrent wave parameters were extracted. From this subsample, the sample for dependence modelling was extracted by applying a high threshold for the wave parameter (Fig. 2). This threshold varies site by site and is determined by the desired sample size. It can be argued that a sufficiently large sample is needed to capture the dependence between variables. Therefore, we follow Mazas and Hamm (2017) and strive for 20 events per year (i.e., the shortest time series of 10 years has a desired sample size of 200 events). Independent events were assured by applying a storm separation window of 48 h. This window was adopted as a rule of thumb for all sites as a compromise between assuring independent observations and losing valid observations due to tightly clustered, but independent storms (e.g., the unusual 2013-2014 storm season; see Malagon Santos et al. 2017).

Marginal distributions
The joint probability approach used in this study uses a mixture distribution: an extreme value analysis is carried out to model the tail of the distributions of water level and the wave parameter, while the dependence (Section 2.4.3) is modelled from the sample of joint high water levels and the wave parameter derived in Section 2.4.1.
Similar to the univariate extreme analysis described in Section 2.3, for the water level and each wave parameter, a threshold is set above which the exceedances are modelled by a generalised Pareto distribution. The threshold value was again determined by the desired sample size. Following Bernardara et al. (2014) and Mazas and Hamm (2017), 10 events per year are strived for (i.e., the shortest time series of 10 years has a desired sample size of 100 events). Independence was again assured by applying a storm separation window of 48 h.

Dependence structure
The dependence between the water level and the wave parameter is measured using Kendall's rank correlation coefficient (τ), a well-known nonparametric measure of dependence (e.g., Wahl et al. 2012).
Following Sklar's theorem (1959), the joint cumulative distribution function H X,Y = P½X ≤ x,Y ≤ y can be described by the univariate marginal distributions of X and Y, F X and F Y , via a copula C: The copula function used in this study needs to be applicable to a large number of wave buoy sites with different wave climates and with potentially different levels of dependence between water level and wave parameter. Because the calculated joint return periods need to be comparable to one another, a bivariate normal copula or Gaussian copula was used for all sites (as is used in the JOIN-SEA software, Hawkes et al. 2002). The Gaussian copula is described by the dependence parameter θ (or correlation parameter), which is derived using the copulaparam function in MATLAB.

Estimation of joint return periods
The joint return periods for each swell event were evaluated by plotting two peaks on a joint return period plot: (i) the peak of the wave parameter with the associated water level and (ii) the highest water level during the event with its associated wave parameter (Fig. 3). The plot is constructed by extracting the contours from the copula at nine intervals (2,5,10,15,20,25,50,75, and 100 years joint return periods), shaped by the dependence parameter θ, while the marginal distributions calculated in Section 2.4.2 inform the x-and y-axes. The highest joint return period achieved between the two peaks was considered as the joint return period of the event.
The concept of return periods can be ambiguous, particularly in a bivariate context. Despite work by Serinaldi (2015) outlining the misinterpretations of return periods in a multivariate setting, return periods are still a staple when discussing probabilities in coastal engineering and are therefore still used in this study. For the sake of clarity, because Sample of high water levels extracted via a peaks-over-threshold approach from the concurrent sample of water levels at Newhaven and waves from the Seaford DWR (left). From the sample of high water levels from Newhaven (quadrants 1 + 2), a subsample is extracted for dependence modelling by applying a high threshold for energy period (T e ) from the Seaford DWR (blue line, 20% exceedance in this example), resulting in the sample represented by the blue markers in quadrant 2 (right). the sampling strategy described in Section 2.4.1 extracted the exceedances of both the water level and wave parameter, the joint return periods in this work are to be understood as the return periods associated with the joint exceedances of both variables.

Swell-generating mechanism
To find the generating area for the swell measured on 30 January 2021, the UK Met Office synoptic analysis charts for the previous few days were examined. The chart for 12:00 UTC on 28 January 2021 shows a new depression southeast of Newfoundland (low 973 mb) ( Fig. 4; Table 1). This low quickly moved in a northeast direction and at 00:00 UTC on 29 January it can be seen as a low that had deepened to 967 mb. Twelve hours later, the depression continued its northeasterly movement at a slightly slower pace and persisted at a low rate of 968 mb. At this point, the westerly winds generating waves on the southern flank are conservatively estimated from the synoptic chart by the authors to be ∼55-60 knots. Such wind speeds are not uncommon in Atlantic storms. The low continued its northeasterly movement, filling to 975 mb by 00:00 UTC on 30 January. Twelve hours later, the low was positioned west of Land's End and filled to 981 mb. Finally, at 00:00 UTC on 31 January the remains of the depression centered over Nantes in France.

Swell propagation through the channel
To track the swell waves as they travel through the English Channel, their first manifestation in the peak period (T p ) is plotted on a timeline (x-axis in Fig. 5). The first instances of T p were site-specific and in the range of 15.4-22.2 s. The energy contained in the swell manifested at each wave buoy site is shown as the peak energy period that was achieved at the site during the event (y-axis in Fig. 5). To investigate how common the swell measured at each wave buoy location is, and to make the swell comparable between sites, the T e return period achieved at each site was calculated (circle size in Fig. 5). Fig. 3. Joint return period plot of water level and energy period (T e ). In red, peak T e is indicated with the associated water level. In blue, the highest water level during the event is indicated with the associated T e . The values are from the 1 February 2021 swell event.
On 30 January, the swell first manifested at Porthleven at 14:00 UTC. Between 15:00 UTC and 15:30 UTC, the waves reached Looe Bay and western Lyme Bay. By 16:30 UTC, West Bay and Chesil recorded the swell. By 18:00 UTC, the swell manifested in Christchurch Bay and Poole Bay. One hour later, the waves refracted around the Isle of Wight and reached Hayling Island. The most easterly location where swell was visible in T p was Seaford at 20:30 UTC. From its first measurement at Porthleven to the eastern most measurement at Beachy Head, the swell travelled ∼430 km in ∼6.5 h, moving at an average speed of 66 km/h or 36 knots. The highest return periods were achieved at the Looe Bay, West Bay, and Chesil wave buoys. Figure 5 shows that, at some buoys, the swell waves manifested in T p later than one would expect based on their location and the timing of their detection at neighbouring  buoys. This is the case at Penzance, Dawlish, and Pevensey Bay. The primary reason for this is the prevalence of locally generated wind waves in the spectra of those sites, which hid the swell component until the swell manifested strongly enough in the spectrum. A second reason may be that the buoys are all east-facing, and it may therefore take some time for the swell to refract around to reach them.

Spatial footprint
The spatial footprint of this event is mapped by calculating joint return periods at each wave buoy site using a copula function, focussing on the time of primary concern when they occur at or around high water. Joint return periods are calculated for the water level . The x-axis denotes when swell first manifested in peak period (T p ), the y-axis shows the peak energy period (T e ) achieved during the event. The size of the markers gives an indication of the T e return period achieved at the site. On the map, the size of the marker is relative to the T e return period achieved at each wave buoy site. Map created in ESRI ArcGIS, boundary layer from EuroGeographics (Eurostat), and bathymetry base layer from GEBCO Grid. and one of the three wave parameters: significant wave height (H s ), energy period (T e ), or wave power (P).
Because the swell passed through the channel around high water, the high water levels pushed the joint return periods above 1 in 2 years at all sites where the swell was observed (Fig. 6). Looking closer at the joint water level and H s footprint, higher joint return periods were achieved between Porthleven in Cornwall and Tor Bay in West Lyme Bay (numbers 2 and 5 in Fig. 1) with joint water levels and wave heights at Penzance, Looe Bay, Start Bay, and Tor Bay (numbers 1, 3, 4, and 5 in Fig. 1) exceeding the 1 in 5 year joint return period.
Investigating the joint water levels and T e achieved at the buoys, a 1 in 5 year joint return period was achieved at almost all instruments where the swell was measured, ranging from Porthleven in Cornwall to Seaford in East Sussex (numbers 2 and 17 in Fig. 1).
Finally, by examining the map of joint water level and P, the latter itself being a function of T e and H s squared, high joint return periods were achieved at Porthleven (1 in 25 years) and Looe Bay (1 in 20 years) (numbers 2 and 3 in Fig. 1). One in 5 year joint return periods were also exceeded at Start Bay, West Bay, and Chesil (numbers 4, 7, and 8 in Fig. 1). Further east, in Christchurch Bay and Poole Bay, the 1 in 5 year joint return period was exceeded at Poole Bay (number 11 in Fig. 1), but not at the two buoys located closer to the shore.

Impact at East Beach and Chesil
At East Beach in West Bay, small-scale overtopping occurred during the 30 January swell event. The event came as a surprise and caused significant erosion, resulting in some "cliffing" of the beach (Fig. 7). However, it should also be noted that the crest width of the beach was significantly reduced before the event. The cliffing is believed to have been caused by the high content of fine material present in the shingle at the time. This was likely disturbed during the construction of a new rock revetment in 2019. Prior to this, the clean shingle had no cohesive properties. With time, it is expected that the fine material will wash from the shingle (pers. comm. M. Worley, Environment Agency).
Chesil Beach suffered notable overtopping with flooding around Chiswell and Brandy Row. Several cars were damaged, and a significant amount of shingle was swept onto the promenade and street. The lower beach foreshore suffered from erosion, while the upper beach experienced accretion, with material deposited just below the crest of the open beach and level with the top of the sea wall at Chesil Cove. It is possible that this exacerbated the overtopping in places by providing a shingle ramp for wave run-up, allowing water to overtop the sea wall (pers. comm. D. Picksley, Environment Agency). The erosion at Chiswell can clearly be seen in the two photos taken before and after the event as part of the Southwest Regional Coastal Monitoring Programme's CoastSnap project (Fig. 8).

Swell-generating mechanism
To find the generating area for the swell measured on 1 February 2021, the UK Met Office synoptic analysis charts for the previous few days were again consulted. The chart for 00:00 UTC on 30 January 2021 shows a new depression southeast of Newfoundland (low 957 mb) ( Fig. 9; Table 2). This low moved in a northeast direction, and by 12:00 UTC on 30 January, it can be seen as a low that had filled to 962 mb. Twelve hours later, the depression continued its northeasterly movement at a slightly more rapid pace and continued to fill at 969 mb. At this point, the westerly winds on its southern flank are conservatively estimated from the synoptic chart to be ∼55 knots, similar to the 30 January event and not uncommon for an Atlantic storm. The low continued its northeasterly movement, filling to 978 mb by 12:00 UTC on 31 January. By 00:00 UTC on 1 February, the depression had weakened and lost Fig. 6. Spatial footprints of the 30 January 2021 swell event. The size of the markers is congruent with the joint return period achieved at the site. The spatial extent of the swell events is shown by mapping the joint return periods of water level and one of three wave parameters: (a) significant wave height (H s ), (b) energy period (T e ), or (c) wave power (P). Map created in ESRI ArcGIS, boundary layer from EuroGeographics (Eurostat), and bathymetry base layer from GEBCO Grid.  its identity and was incorporated in a complex low-pressure system, having filled to 987 mb. The final remains of the depression appear to be centered between Bremen and Dortmund in Germany.

Swell propagation through the channel
The first manifestation of the waves in T p (values were site-specific and ranged between 18.2 and 25 s) is plotted against swell intensity (peak energy of the event) and T e return period (Fig. 10).
On 1 February, the swell was first measured by the Porthleven buoy at 03:30 UTC and reached Looe Bay at 05:30 UTC. West Bay and Chesil were confronted with the swell around    (T p ), the y-axis shows the peak energy period (T e ) achieved during the event. The size of the markers gives an indication of the T e return period achieved at the site. On the map, the size of the marker is relative to the T e return period achieved at each wave buoy site. Map created in ESRI ArcGIS, boundary layer from EuroGeographics (Eurostat), and bathymetry base layer from GEBCO Grid.
speed of 60 km/h or 32 knots. The highest return periods were achieved at Boscombe, Poole Bay, and Hayling Island. Figure 10 shows that again, at some buoys, the swell waves manifested in T p later than one would expect based on their location and when the neighbouring buoys registered the swell. This is the case at Penzance, Start Bay, Tor Bay, Dawlish, Chesil, Sandown Bay, Pevensey Bay, and Hastings. A possible explanation is that the majority of these are east-facing sites where it would take some time for the swell to refract around to reach the particular wave buoy.

Spatial footprint
Because waves are the most dangerous during high water levels, at each wave buoy, the joint return period of the water level and one of three wave parameters is calculated: significant wave height (H s ), energy period (T e ), or wave power (P).
As was the case during the 30 January event, because the swell passed through the channel around high water at most wave buoy sites, the 1 in 2 year joint return period was exceeded at all locations (Fig. 11). Examining the joint water level and H s footprint, at no location was the 1 in 2 year joint return period exceeded, making it clear that wave heights did not contribute significantly to the event. The same pattern holds true for the joint return periods of water level and wave power; at no location was the 1 in 2 year return period exceeded.
In contrast, looking at the map showing joint water level and T e , the 1 in 2 year return period was exceeded at all sites, with the exception of Tor Bay (number 5 in Fig. 1) on the southeast coast of Devon. At all other sites, at least the 1 in 5 year return period was exceeded, with the 1 in 100 year return period exceeded at Boscombe in Poole Bay and at Hayling Island in the Solent (numbers 10 and 14 in Fig. 1).

Impact at Christchurch Bay, Poole Bay, and Hayling Island
At Hayling Island, significant and dangerous overtopping occurred during the 1 February 2021 swell event. This was unexpected and caused flooding in the gardens along Southwood Road, although the flood defences managed to retain the majority of the overtopping within the promenade. In places, the waves flattened the crest of the beach which required emergency repairs and deployment of construction plant to reinstate the standard of protection (pers. comm. A. Pearce, Coastal Partner Havant Borough Council) (Figs. 12 and 13).
The 1 February swell event also caused a surprising amount of water to run up over the promenades at Poole Bay and Christchurch Bay, which likely cannot be simply attributed to antecedent beach levels (pers. comm. M. Wadey, Bournemouth, Christchurch and Poole (BCP) Council).
It is also worth mentioning that on 26 February 2021, part of the east wing of Hurst Castle, located on the Hurst Spit shingle bank, collapsed. Although the collapse is not a direct result of the two swell events described in this studythe foundations of the east wing were already severely underminedthe two swell events may have expedited the collapse.

The 30 January 2021 swell event
The reported significant impacts of the 30 January event are focussed along the coastline of western Dorset. At East Beach in West Bay small-scale overtopping and erosion occurred resulting in the cliffing of the beach, although it should be noted that the beach was already depleted. In addition, notable overtopping occurred at Chesil Beach, damaging cars and Fig. 11. Spatial footprints of the 1 February 2021 swell event. The size of the markers is congruent with the joint return period achieved at the site. The spatial extent of the swell events is shown by mapping the joint return periods of water level and one of three wave parameters: (a) significant wave height (H s ), (b) energy period (T e ), or (c) wave power (P). Map created in ESRI ArcGIS, boundary layer from EuroGeographics (Eurostat), and bathymetry base layer from GEBCO Grid. moving significant amounts of shingle from the lower foreshore to the upper beach, onto the promenade, and into the street.
The storm that generated the swell originated on 28 January as a new Atlantic depression southeast of Newfoundland that tracked due east, with forcing winds moving in a relatively straight line relative to the curvature of the earth that directed long-period swell waves directly towards the UK. During the strongest storm development period, when the low travelled across the Atlantic, trapped fetch conditions as described by Sibley and Cox (2014) may have occurred as the center travelled at a speed between 28 and 36 knots  with a gradient wind speed on the southern flank estimated at ∼55-60 knots ( Table 1), suggesting that the speed of movement of the low center kept track with the group wave speed. However, the center did not enter the English Channel, as around midday on 30 January, the storm changed direction bending south past Land's End towards Brittany in France.
When the swell first arrived at West Bay and Chesil between 16:30 UTC and 17:00 UTC, a surge of ∼27.9 cm was measured at the Weymouth NTSLF tide gauge. At the peak of the event, defined as when H s peaked at 3.49 m at West Bay and 4.04 m at Chesil, between 20:30 UTC and 21:30 UTC, the surge had dropped to ∼14.65 cm. High water occurred close to the peak at 20:00 UTC with a maximum water level of 1.32 m OD on a spring tide. In West Bay, T p peaked at 20 s, T e at 15 s, P at 86 kW/m 2 , and peak wave direction was 210°( southwest by south). At Chesil, T p peaked at 22.2 s, T e at 12.1 s, P at 120 kW/m 2 , and peak wave direction was 220°(southwest).
The 30 January event was driven by a combination of swell entering the English Channel and low pressure centered west of Land's End, generating high wave heights for the southwest regions of the English coastline. These conditions resulted in high wave powers generated at the Porthleven and Looe Bay wave buoys, exceeding 1 in 20 and 1 in 15 years of joint return periods for water level and wave power, respectively. Due to the nature of the event, the spatial footprint that best captures the impact of the event is the combined consideration of the water level and wave power.
Two observations regarding the impact of wave height during the event are worth pointing out. First, neither in West Bay nor Chesil, the two sites where overtopping was recorded, did H s exceed the storm alert threshold on the NNRCMP website, again emphasising the well-established point that energetic long-period waves are an important component of overtopping and beach erosion and are therefore important to monitor. Nonetheless, the second observation is that no overtopping was reported at either site during the even more energetic 1 February event, likely because significant wave heights were quite low (Section 4.2.1). Other factors that likely influenced the different impacts of both swell events at West Bay and Chesil are the storm tracks and wave directions, but detailed analyses of these are outside the scope of this study.
A final observation worth considering is that, when monitoring swell by tracking T p , the wind waves generated by the depression off Land's End managed to hide the swell in this parameter for a considerable amount of time at locations such as Penzance and Dawlish before the swell peak became dominant in the wave spectrum.

The 1 February 2021 swell event
The reported impacts of the 1 February event are centered on the coastline of east Dorset and the Solent in Hampshire. At Poole Bay and Christchurch Bay, water ran up over the promenades, and at Hayling Island, a significant amount of overtopping occurred, flattening the crest of the beach and requiring emergency repairs and deployment of construction plant on the beach.
The storm that generated the swell originated on 30 January as a new Atlantic depression southeast of Newfoundland. This storm also tracked northeast with forcing winds travelling in a relatively straight line, pushing long-period swell waves directly towards the British Isles. Again, trapped fetch conditions may have occurred as the storm crossed the Atlantic with the center travelling at speeds between 33 and 39 knots with a gradient wind speed on the southern flank estimated at ∼55-60 knots, suggesting the movement of the low kept track with the group wave speed. However, by 1 February, the depression had weakened and became incorporated into a complex low-pressure system that moved across the English Channel, potentially continuing to feed the wave group passing through.
When the swell waves arrived at the buoys deployed in Poole Bay and at Hayling Island, at 07:30 UTC and 08:30 UTC, respectively, a surge of ∼32.7 cm was measured at the Portsmouth NTSLF tide gauge. At the peak of the event, defined as when T e peaked at 18.7 s at Boscombe and 20.6 s at Hayling Island, between 12:30 UTC and 13:30 UTC, the surge dropped slightly to 27.1 cm. High water occurred 1 h after the peak of the event at Boscombe and during the peak at Hayling Island with a maximum water level of 2.16 m OD on a spring tide. At Boscombe, H s peaked at 1.42 m, T p at 25 s, P at 11 kW/m 2 , and peak wave direction was 186°(south by west). At Hayling Island, H s peaked at 1.92 m, T p at 25 s, P at 29 kW/m 2 , and peak wave direction was 180°(south).
The 1 February event and its related impacts were entirely driven by the swell waves travelling through the English Channel. The complex low travelling across the channel did not generate any significant wind speeds or wind waves. These conditions resulted in a calm weather day during which an exceptionally energetic swell passed through the channel, generating some of the highest energy period measurements on record at the buoys in the channel, but relatively low H s measurements. Owing to these conditions, the spatial footprint that best captures the impact of this event is the combined consideration of the water level and T e .
The 1 February event is close to a schoolbook example of the dangers swell events pose, especially during a calm day. At Poole Bay and Christchurch Bay, waves unexpectedly running up the promenades are a danger to the public, while at Hayling Island the swell significantly flattened the beach crest. Furthermore, the swell entered at an angle in the channel and was energetic enough to travel all the way through, still being distinctly visible in the data from the Folkestone buoy in Kent.

Implications for coastal monitoring
The two consecutive, but quite different, swell events documented in this study present an opportunity for coastal monitoring programmes to reflect on how waves, and in particular swell waves, are measured and reported.
Currently, long-period swell monitoring through measurements is primarily performed by observing (or setting an alert for) peak period (T p ). Because T p is defined by the period at the wave spectrum peak, it is subject to rapid changes. Moreover, if there are more than two distinct frequency components with similar peak energies, the time series of T p can appear to fluctuate markedly. These properties of the parameter can be advantageous and will typically result in swell being first picked up in this parameter. However, as was the case at some locations during the 30 January event, swell can also remain hidden in T p if sufficient wind waves are generated for the wind wave peak on the spectrum to dominate the swell peak. A solution to this is to partition the wave spectrum into its wind and swell components and focus on the peak period for the swell component only, thereby excluding any contamination of wind-wave energy. However, because the lower frequencies in a standard (Datawell) wave spectrum are not as finely resolved, relatively large step changes in a time series of T p swell will remain. Such a bimodal wave spectrum is typically referred to as a bimodal sea state and is monitored post hoc by the NNRCMP by calculating the occurrence of bimodal seas as a monthly percentage (Mason and Dhoop 2018) and is available as a regularly updated spreadsheet (NNRCMP 2021).
A well-established tool for wave monitoring is the definition of a threshold condition, such as the storm alert threshold defined on the real-time data pages of the NNRCMP website. A similar threshold condition could prove useful for swell monitoring. However, the rapidly changing nature of T p makes this parameter unsuitable for such use. In an attempt to quantify the energy contained in the swell events discussed in this study, T e was found to provide a much smoother time series. As the ratio of the first negative and zero moments of the wave spectrum, the parameter represents more of the lower frequency energy in the spectrum while avoiding marked jumps in the time series. Figure 14 shows a time series of peak period (T p ) and energy period (T e ) as measured by the wave buoys at West Bay, Chesil, Boscombe, and Hayling Island, covering both swell events discussed above. In red, a horizontal line was added as an indicative "swell alert threshold" at the 0.25 year return period for the energy period. The threshold was chosen to mimic the 0.25 year return period threshold used for H s by the NNRCMP. The reasoning is that, on average, four times per year conditions occur that have the potential to move a significant quantity of beach material. The threshold condition applied in Fig. 14 appears to function relatively well; the threshold is exceeded at West Bay and Chesil during both events, while at Boscombe and Hayling Island, the threshold is exceeded only during the 1 February event, matching the findings of this study.
As Mason et al. (2008) suggested, the addition of T e to the current set of wave parameters provided as an industry standard in coastal monitoring could prove beneficial for monitoring swells in the future. An additional benefit of T e is that it is the standard wave period used for wave run-up and overtopping formulae (EurOtop 2018) and may therefore be of particular use to calibrate and provide a check on overtopping models. A complication to this end is that T e is typically not a standard output of most wave measuring instruments. Nonetheless, it can be derived from the wave spectrum, a dataset already provided by most providers of wave data (e.g., CEFAS, NNRCMP) in England, in a straightforward manner. Alternatively, the parameter can be derived from additional instrument-specific parameters (for example, using Datawell DWR MkIII parameter outputs, see Appendix 1).
Fig. 14. Time series of peak period (T p ; black) and energy period (T e ; red) at those sites with reported impacts from the 30 January and 1 February swell events. The red horizontal line represents the 0.25 year return period for T e as an indicative swell alert threshold.
It is also worth noting that, despite the irregularities noted in Sections 3.1.2 and 3.2.2, swell propagates through the English Channel from west to east in a progressive manner. Up to a point, it is therefore possible to receive a couple of hours early warning of incoming swell at those locations further east up the Channel by monitoring T p and T e at more westerly located wave buoys. Furthermore, by partitioning the wave spectrum in its wind and swell components and by monitoring the peak period of the swell component only, it is possible to avoid swell remaining hidden owing to a wind-wave peak dominating the spectrum. A closer examination of the time dependencies between T p , T p swell, and T e at different locations along the southern English coastline could prove useful for coastal monitoring purposes.
Finally, while it is perfectly reasonable to be well-informed about both swell events by monitoring H s in tandem with T e , once the latter is provided as a parameter for monitoring purposes, it is a relatively small effort to provide wave power as a parameter that incorporates both wave height and period. Wave power (P) is particularly useful when a swell event is combined with locally generated waves, such as the 30 January event.

Conclusions
Energetic swell waves, particularly when they coincide with high water levels, can present a significant coastal hazard. Two such events occurred in quick succession in the English Channel. The first, on 30 January 2021, was driven by a combination of swell entering the English Channel and a depression centered west of Land's End, generating moderate wave heights for the southwest regions of the English coastline. The event caused overtopping at East Beach in West Bay and at Chesil Beach.
The second event, on 1 February 2021, was entirely driven by the swell waves travelling through the English Channel. A complex low travelled across the channel but did not generate any significant wind speeds or wave heights. The event generated some of the highest energy period (T e ) measurements on record at the buoys deployed in the channel and caused waves to run up over the promenades at Poole Bay and Christchurch Bay and caused overtopping and flattening of the beach crest at Hayling Island.
Spatial footprints of both events were generated through joint return period analysis of water level combined with one of three different wave parameters: significant wave height (H s ), energy period (T e ), or wave power (P). The water level at which a swell event occurs will significantly contribute to the severity of the impact of that event in terms of overtopping or beach erosion. T e was calculated to provide a smoother time series for swell monitoring, compared to T p . As the ratio of the first negative and zero moments of the wave spectrum, T e represents more of the lower frequency energy in the spectrum while avoiding marked jumps in the time series. Wave power (P) was calculated in an attempt to account for both wave height and wave period in a single parameter.
The 31 January swell event, with its significant contribution of moderate wave heights due to the low centered off Land's End, was best described by the joint return periods of water level and wave power. The 1 February event is almost entirely driven by swell and is therefore best captured by the joint return periods of the water level and T e .
Finally, T e was found to be a valuable addition to the standard wave parameters used to describe the two swell events under discussion. T e , providing a smoother time series than the rapidly changing T p , allowed for improved quantification of the swell energy and has the potential for threshold setting for "swell alerts". The parameter could also prove useful in supporting modelling efforts, particularly overtopping models, by providing a check on predictions. Therefore, T e should be considered for inclusion in the arsenal of wave parameters currently used for coastal monitoring and beach-management purposes. In addition, P, as a measure of both wave height and period, could be a valuable addition for events where swell is combined with a significant amount of wind-generated waves, although, in theory, these could be monitored by observing both H s and T e . Inclusion of these parameters will ensure that swell events with the potential to impact coastal flooding and erosion, but which are not currently captured in standard flood warning models, can be more closely monitored.

Declarations
Contributor's statement Thomas Dhoop conceptualised the study, performed the analysis, and wrote the original draft of the paper. Charlie Thompson supervised the work and reviewed and edited the original draft.

Funding statement
The Channel Coastal Observatory, as part of the National Network of Regional Coastal Monitoring Programmes (NNRCMP), is funded by the Department for Environment, Food and Rural Affairs (DEFRA) through the Environment Agency.