All simulations have been conducted using the AMM15 configuration of the NEMO ocean model (Madec et al., 2016). Full details on the operational implementation of the AMM15 configuration for CMEMS are provided by Tonani et al. (2019, this issue). The science settings and further background on model performance are detailed by Graham et al. (2018a, b). Through use of a 1.5 km grid spacing, sufficient to resolve the internal Rossby radius on the NWS, it has been demonstrated that AMM15 can represent local-scale processes such as eddies, fronts, internal tides, and exchanges across the shelf break.

Meteorological forcing is provided by interpolation from the operational European Centre for Medium-Range Weather Forecasts (ECMWF) global forecast data at around 14 km horizontal resolution and applied at 3-hourly temporal frequency. Surface forcing is implemented using the CORE bulk parameterisations (Large and Yeager, 2004). All simulations are initialised from the same initial condition, based on a 30-year non-assimilative AMM15 run detailed by Graham et al. (2018a). Lateral boundary conditions for the Atlantic are provided every 3 h from the uncoupled Met Office operational 1/12∘ North Atlantic ocean system (Blockley et al., 2014) and for the Baltic Sea every hour using the operational Baltic Sea products from CMEMS (Berg and Weismann Poulsen, 2012). All simulations are run with a 60 s integration time step. Details of the meteorological forcing, ocean initial condition, and boundary conditions are identical to those described by Tonani et al. (2019, this issue) and are therefore consistent with the current operational implementation of AMM15.

Ocean data assimilation in the DA and CPL_DA runs use the NEMOVAR 3D-variational assimilation scheme (Waters et al., 2015) which employs a multi-variate balance to account for correlations between ocean variables as defined in Weaver et al. (2005). Increments are applied to the 3-D temperature, salinity, u and v velocities, and the sea surface height (SSH). As detailed by King et al. (2018), assimilated observations include in situ and satellite observations of SST and subsurface profile observations of temperature and salinity from Argo floats, XBTs (expendable bathythermographs), CTDs (conductivity, temperature, and depth), gliders, and marine mammals. Sea level anomaly (SLA) observations from satellite altimeters are assimilated in the deep parts of the domain (where the ocean is deeper than 700 m).

Wave simulations are produced for the NWS using a configuration of the WAVEWATCH III (Tolman et al., 2014) spectral wave model (Saulter et al., 2017). The wave model is defined to cover the same domain extent as AMM15, but using a spherical multiple cell grid refinement approach (Li, 2012), which has variable horizontal resolution nesting from 3 km across much of the domain down to 1.5 km spacing for all cells adjacent to the coast and/or where the depth of a 3 km grid cell would be shallower than 40 m. A wave model global time step of 600 s is used. The wave model is forced by winds from the same ECMWF global atmospheric model as used for ocean forcing at 3-hourly temporal frequency. The influence of the ocean state on wave evolution is already captured in the current operational NWS wave forecasting system through use of previously forecast ocean currents as an additional external forcing (Palmer and Saulter, 2016).

For brevity, the following discussion therefore focuses on the impact of wave effects on the ocean model results only. The case study results presented by Lewis et al. (2018a), for example, suggest that the impact of two-way ocean–wave feedbacks on wave results is limited compared with including ocean processes through external forcing without feedbacks, as currently applied in the Met Office operational wave forecast system.

The implementation of wave–ocean coupling in the AMM15 system follows that described by Lewis et al. (2018b). Coupling between the ocean and wave model components is achieved by exchanging information between NEMO and WAVEWATCH III using the OASIS3-MCT libraries (vn3.0; Valcke et al., 2015). All variables are averaged and exchanged at hourly frequency. Limited-period case study experiments using more frequent exchanges have previously suggested that hourly coupling is sufficient to assess the first-order impact of wave coupling on the ocean state.

The scientific basis for representing wave–ocean interactions in AMM15 is described in Sect. 3 of Lewis et al. (2018b), with technical details of the NEMO ocean model wave coupling code used in this study provided in Appendix B of Lewis et al. (2018b). This implementation closely follows the work of Breivik et al. (2015) and Staneva et al. (2017), and for brevity these details are not repeated here. The associated code is now supported for wider use by the ocean modelling community from NEMO version 4. In brief, the main interactions introduced in the CPL and CPL_DA experiments are a.

modification of water-side surface stress on the ocean by wave growth and dissipation (Eq. 3; Lewis et al., 2018b);

Note that the wave coupling by Lewis et al. (2018b) was applied using the direct flux surface forcing scheme of NEMO, rather than the CORE bulk forcing used here, and using meteorological forcing from the Met Office Unified Model simulations.

As a further improvement from Lewis et al. (2018b), the zonal and meridional components of the wave-modified surface stress (i.e. τocn components) are exchanged directly from WAVEWATCH III to NEMO, rather than defining a fraction of the total atmospheric stress acting on the ocean as in Breivik et al. (2015). This avoids the need for NEMO to recalculate the surface stress using a wave-modified drag coefficient, thereby removing a source of potential inconsistency between the wave and ocean models. However, note that the WAVEWATCH III surface scheme assumes a neutral atmospheric boundary layer, and use of the wave-modified momentum flux may no longer be in equilibrium with heat and humidity fluxes. While initial testing (not shown) indicated a relatively small effect from the change in representation of the surface stress, further work is required to more fully review the representation of the surface momentum across atmosphere, ocean, and wave model codes.

Only wave effects acting on the ocean momentum budget are considered in this study. Wave impacts on the calculation of turbulent heat and moisture fluxes and accounting for the wave energy flux transferred to the ocean are omitted. Instead, the treatment of wave breaking on the surface boundary for TKE (turbulent kinetic energy) is parameterised using the Craig and Banner (1994) scheme, with the default value of the Craig and Banner coefficient of 100 used in all simulations. There is also no explicit treatment of Langmuir turbulence, such as through use of a vortex-force formulation (e.g. Uchiyama et al., 2010), or of ocean bed stress (e.g. Soulsby et al., 1995), both of which may be important in the regional ocean context. These simplifications are appropriate for an initial implementation of wave coupling within the NWS forecast system, given known sensitivities of the vertical mixing and radiation schemes to parameter choices. Future work will need to reassess model tuning when including these additional coupled processes. For example, while several studies have introduced a wave dependence in the TKE parameterisation, the values of this coefficient can be highly variable, and further testing will be required to assess a suitable choice for the range of this parameter in the ocean–wave coupled system.

As highlighted by a number of studies discussed in the introduction, a key driver of ocean dynamics by waves has been found to be the modification of surface stress. In equilibrium, for a fully developed wind-sea state, the input of momentum to surface waves from the wind is matched by its dissipation into the ocean, and the water-side stress acting at the top of the ocean, τocn, is equal to the total atmospheric stress, τatm. For younger, growing waves, there is a net input of momentum from the atmosphere to waves (τocn<τatm). Where waves break, the input of momentum from waves to the ocean exceeds the local input atmospheric stress (τocn>τatm). The distribution of τocn/τatm simulated by WAVEWATCH III is shown in Fig. 1b and e for summer and winter, respectively. The magnitude of changes due to waves is shown to be larger in winter than summer, although common features can be identified in both seasons. Regions of wave breaking are identifiable by darker red shading immediately along western coastlines of the UK, France, and Denmark. Waves tend to enhance the momentum transferred to the ocean in regions of prevailing wave activity – to the north-west of the NWS in winter and more directly west of the NWS in summer. Momentum transfer is also enhanced on average across the Celtic Sea (south-western approaches to the UK) and through the central North Sea, particularly in summer. In contrast, regions to the lee of land such as through the Irish Sea and to the east of the UK are characterised as regions of growing waves where momentum is stored in waves rather than transferred from the atmosphere to the ocean (blue areas in Fig. 1b and e).

Also shown are seasonal mean distributions of simulated significant wave height (Fig. 1a, d) and Stokes drift speed (Fig. 1c, f). The Stokes drift speed generally increases with wave height (and forcing wind speed), with highest seasonal mean values of up to 16 cm s-1 in regions of greatest wave activity across north-western approaches to the UK. There is also a dependency on water depth, leading to lower values (approximately 5 cm s-1) in near-coastal regions.

The impact of wave coupling on simulated SST, in the absence of data assimilation, is shown in Fig. 3 as seasonal mean differences between FR and CPL_FR through the 2016–2017 trial period. Figure 3 shows substantial spatial and temporal variability in mean differences due to wave effects in the eddy-dominated deeper ocean off the NWS to the west of the model domain. In contrast, results on the shallow NWS show relatively little inter-annual variation in the impact of coupling, with a consistent spatial distribution of differences for a given season in both 2016 and 2017. Figure 3b also highlights that the impact of wave coupling takes relatively little time to spin up from common initial conditions in January 2016. For brevity, the subsequent analysis therefore focuses on results from winter 2016/2017 and spring, summer, and autumn 2017 only as being representative, and results on the NWS as being of primary interest to users of operational forecast data in this region.

Away from the immediate vicinity of coastlines, an annual cycle in the influence of wave coupling on simulated SST can be seen on the NWS, with a mean reduction of up to 0.5 K during summer (Fig. 3c, g). In winter, the impact is a lot more mixed, with much of the NWS having slightly increased SST in the CPL_FR simulation by approximately 0.2 K (Fig. 3e) around frontal systems (Ushant front, Celtic Sea front) and the Norwegian trench, but some areas still show slight warming. On average, the regions most impacted have increased momentum transfer into the ocean in coupled relative to uncoupled simulations (Fig. 1), in both winter and summer, which drives enhanced mixing. These results are consistent with shorter-duration case study experiments presented by Lewis et al. (2018b) and will be discussed in further detail in Sect. 4.3.

The influence of wave coupling is relatively smaller through the Irish Sea, English Channel, and southern North Sea. This is likely to be due to a combination of these areas being well mixed throughout the year (e.g. Huthnance et al., 2009; van Leeuwen et al., 2015), and also coincident with areas of net storage of momentum within growing waves (Fig. 1). The influence of waves in the English Channel and southern North Sea appears to be increased during spring, where the mean SST is slightly increased in CPL_FR relative to FR (Fig. 3b, f).

While the main sensitivity of SST to wave coupling on the NWS can be characterised as a net warming in the winter and cooling in the summer, closer examination shows this pattern can be reversed in the immediate vicinity of some coasts. Most notable differences occur along the south-eastern coast of England.

In contrast to Fig. 3, the mean impact of wave coupling on SST in the simulations with ocean data assimilation is relatively small across all seasons (e.g. Fig. 4 shows summer 2017 results for reference). This was reflected in the consistency of the summary statistics for DA and CPL_DA discussed in Sect. 3. Also shown in Fig. 4 are maps of the largest instantaneous differences in simulated SST between CPL_DA and DA at each model grid cell during the season. This highlights that while the seasonal mean SST differences are small, the instantaneous impact of wave coupling can be non-negligible even for the assimilative systems and of the order of 1 to 2 K. Highest variability in SST due to wave feedbacks is found in off-shelf regions and in the near-coastal regions, particularly where wave breaking is prevalent such as along the eastern Bay of Biscay. There is also notable sensitivity around coasts and seasonal mixing fronts, presumably due to their highly dynamic nature. However, regions with increased sensitivity to wave processes are not necessarily reflected in the distribution of mean SST changes (Fig. 3).

The relative cooling due to waves in summer is reflected in an increase in a mean cool bias of AMM15 between FR and CPL_FR simulations in the summary metrics discussed in Sect. 3. This is also highlighted in Fig. 5, which compares the spatial distribution of RMSD computed between the model and all observations for CPL_DA during 2017, binned in latitude and longitude areas of 0.25∘ spacing across the region where data were assimilated. Differences are negligible with data assimilation active (Fig. 5b), but comparing RMSD for CPL_FR and FR suggests that the regions of greatest cooling coincide with a relative degradation in RMSD, by of approximately 10 %–20 % in the central North Sea and by up to a maximum of 50 % in the Celtic Sea (south-west approaches to the UK, Fig. 5c).

The comparison against in situ observations on the NWS for each season (not shown) is more variable than Fig. 5, noting that most available sites are located near the coast (e.g. Lewis et al., 2018b). Results are improved for CPL_FR relative to FR at several locations, most notably around southern and eastern UK coasts, although the general pattern is of wave coupling leading to poorer verification scores at many locations.

Example comparisons between model and observations from two locations are highlighted in Fig. 6. Given the high resolution of the ocean model data, and to compensate for potential co-location errors, mean model values in a 5×5 grid cell region around each location point are compared with observations, unless otherwise stated. This may lead to some smoothing of features but is considered to be more representative.

The Celtic Sea observation (buoy 62094; marked as “CS” in Fig. 3a) is located to the south of Ireland where the influence of waves on SST was shown to be seasonally varying. The summer cooling results in greater scatter of CPL_FR results relative to observations for warmest temperatures (Fig. 6a). Results from a nearby coastal site on the south-west English peninsula at Perranporth (marked “PP” in Fig. 3a) show relatively warmer simulated SST in summer (warmest temperatures) with wave coupling in improved agreement with observations.

RMSD and MD are relatively crude summary indicators of model performance, in particular for assessing systems which are highly variable in space and time, and when making comparisons to a control system with relatively high skill, as in this study. To gain further insight into model variability, time series of coincident observed and simulated SST were compared spectrally. To support spectral comparison across a wide range of frequencies, the time series were initially “pre-whitened” (i.e. converted to rates of change) by computing the differences of successive values. A linear trend was also removed and a split cosine taper was added to the ends of the detrended series in order to minimise “periodogram leakage” (Weedon et al., 2015). The irregular spacing of the data in time required use of the Lomb–Scargle discrete Fourier transform (Press et al., 1992) and the output periodogram (with 2 degrees of freedom) was smoothed using three applications of a discrete Hanning spectral window thereby increasing the degrees of freedom to 8.

Figure 6 shows that the power spectra of the rates of change of SST at the CS and PP locations are in good agreement with observed spectra for both the DA and CPL_DA simulations (Fig. 6b, d). In particular spectral peaks at the diurnal and semi-diurnal (M2 tide) frequencies are well represented. To formally compare the time series, cross-spectral analysis was used (Weedon et al., 2015). For example, for the SST variability at the diurnal scale, the amplitude ratio of the rate of change of the DA simulation compared to the rate of change of the observations at the CS site is 0.87±0.04 K (±95 % confidence interval). The phase difference at this frequency is 9.3±5.0∘, indicating that at the diurnal scale the DA simulation is approximately in phase with (i.e. not leading or lagging) the observations. Similarly, at the diurnal scale the CPL_DA simulation has an amplitude ratio of 0.77±0.05 K and a phase difference of 8.0±4.9∘.

At periods shorter than the semi-diurnal scale (i.e. at higher frequencies), the average power for both DA and CPL_DA drop relative to observed at the CS and PP buoys. Additionally, a simulated quarter-daily (M4 tide) spectral peak is not detected in the observations. This initial assessment demonstrates the utility of cross-spectral analysis as a tool for assessing model performance and for highlighting areas for required improved representation of high-frequency variability.

A collection of observing sites in the German Bight provide a rare source of in situ subsurface temperature observations (Fig. 3a). Figure 7 compares observed seabed temperature (SBT) at the UFSDB (UFS Deutsche Bucht) buoy location with simulations during 2017. Summary statistics for all sites in the region are listed in Table 4 for comparison. In general, results for CPL_DA and DA are very similar, with wave coupling leading to a small degradation in RMSD and MD metrics at all sites other than UFSDB. Given that the German Bight is a well-mixed region of the NWS, the consistency between SST and SBT impacts should be expected. For much of the year, SBT simulations at UFSDB for DA and CPL_DA are in good agreement with observations (correlation coefficient 0.98 for 2017). However, both clearly warm too quickly relative to observed from mid-May, perhaps due to stronger mixing than observed in NEMO, and remain biased warm until early August (noting observations are unavailable from this time until mid-September). In contrast, SST results at this location (not shown) are much more consistent with observations throughout the year (MD of -0.03 K; Table 4). It is notable that the rate of springtime seabed warming is slightly reduced in CPL_DA compared to CPL, and an observed sharp increase in SBT in mid-June is also much better captured with wave coupling.

Power spectra of SBT at UFSDB (Fig. 7b) highlight the overall consistency between CPL_DA and DA, although the spectral peak at semi-diurnal frequency is slightly more pronounced for CPL_DA. Both simulations generally underestimate the amplitude of variability relative to observations at most frequencies.

To better characterise and understand the impact of wave coupling in the NWS, the evolution of model temperature profiles during 2017 is considered. Figure 8 shows an example of temperature differences due to wave coupling through the shallow NWS depth at a location in the central North Sea (labelled “NS” in Fig. 3a). Results are compared both with and without ocean assimilation, and temperature profiles are averaged daily and across a 5×5 collection of nearby grid cells. Also plotted in Fig. 8 are time series of the ocean-model-diagnosed mixed layer depth (MLD), using the density-based definition of Kara et al. (2000). The annual variation in MLD illustrates that the selected location is seasonally stratified – well mixed during winter and transitioning to being stratified below a shallow mixed layer during summer (e.g. Huthnance et al., 2009).

In summer there is a clear dipole in the structure of temperature differences with relative cooling due to waves through the shallow mixed layer and warming at depth (Fig. 8b, c). The intervening layer within 10 m below the MLD shows large temperature differences (> 1 K). This structure is consistent with a mechanism of enhanced mixing due to a net input of momentum from surface waves (Fig. 1b, e), deepening the MLD, thickening the pycnocline, and encouraging mixing of warmer near-surface water further from the surface. A deepening MLD in summer also implies that surface heating is warming a larger volume of water with wave coupling, thereby leading to a relatively cooler mixed layer and SST (Fig. 3). The model-diagnosed MLD is typically deepened by a few metres between simulations with and without wave coupling in summer. However, differences of up to 10 m (for a MLD which is typically of the order of 20–30 m deep in summer) can be seen for isolated periods of time and specifically during the autumn transition back to a well-mixed state.

Although the AMM15 ocean assimilation scheme has introduced assimilation of temperature profiles, very few are located in the seasonally stratified regions of the NWS (e.g. Fig. 3 of King et al., 2018) and none were available during the 2016–2017 experiment period. It is therefore not surprising that assimilation of SST limits the region of temperature differences due to wave coupling to the mixed layers in Fig. 8b. The impact of wave coupling on the temperature structure at and below the MLD is therefore consistent between the experiments with and without assimilation.

The spatial patterns of seasonal MLD differences due to wave coupling across the NWS (Fig. 9) are most consistent with the pattern of SST differences between CPL_FR and FR (Fig. 3e–h). This result also highlights that the MLD variability on the NWS is mostly temperature driven. The relative deepening by approximately 10 m due to wave coupling through the autumn transition in Fig. 8 is particularly pronounced and widespread throughout the Celtic Sea and along the full extent of the shelf break between Bay of Biscay to the south to Shetland Islands in the north.

The MASSMO4 glider campaign (e.g. Palmer et al., 2018) during spring and summer 2017 provides an independent source of high vertical resolution data against which to assess the simulated MLD results. A glider followed a westward trajectory in the North Atlantic as plotted in Fig. 10a between 21 May and 6 June 2017, crossing the shelf break on 31 May 2017. This time of year coincides with a shallowing mixed layer in seasonally stratified areas of the NWS (e.g. Fig. 8). Figure 10a shows the simulated MLD in the region on 1 June 2016 of about 40 m on the shelf. Figure 10b compares the MLD recalculated from model and observation temperature and salinity data, based on Kara et al. (2000) from vertical profiles measured by the glider. There is considerable variability in MLD during the observed period, which is captured relatively well by all simulations (RMSD of about 9 m). On average, the uncoupled FR and DA results are biased too shallow (by 2.9 m for FR and 2.2 m for DA) while the deepening due to wave coupling results in a smaller MLD difference, although now biased deep (by 0.9 m for CPL_FR and 1.7 m for CPL_DA). Periods when coupled MLD values were deeper than observations occur during late May, when the glider was located on the NWS. In June, when the glider was off-shelf and simulation errors are increased, the impact of wave coupling leads to clearer improvement relative to uncoupled simulations.

This analysis has demonstrated an annually varying cycle in the impact of wave coupling on ocean temperatures on the NWS, associated with a deepening of the mixed layer through enhanced mixing. It is encouraging that the quantitative agreement between model results and observations is not degraded considerably, and improves in some respects. In practice, the ocean model physics (e.g. turbulence and radiation schemes) and assimilation options are developed to provide forecast systems which best match the available observations. To date, these have been developed in a forced-mode ocean-only context. Having established an effective baseline wave-coupled configuration for the NWS, it is clear that further improvements can be realised through revisiting parameter choices within these schemes.

The impact of wave coupling on the NWS sea surface salinity (SSS) during 2017 is summarised by the mean differences between CPL_DA and DA in Fig. 11a. To first-order approximation these results are independent of whether ocean data assimilation was active, so CPL_FR and FR results are omitted. There is also no clear variation in the impact of waves across the different seasons.

As expected, the greatest sensitivity of salinity to wave coupling is focused on areas where river freshwater mixes into the ocean. The net tendency is for increased SSS across NWS in all seasons of up to 1 psu along the Bay of Biscay and German Bight coasts, but more typically less than 0.3 psu across the North Sea, English Channel, and some western UK coastal areas. This suggests that the effect of river freshening is diminished, perhaps through a combination of enhanced vertical mixing or lateral advection. By contrast, wave coupling leads to reduced SSS at the outflow from the Bristol Channel and northward through the Irish Sea.

Schloen et al. (2017) studied the impact of wave coupling on salinity in the southern North Sea in detail using ocean and wave models with unstructured grids based on a month-long simulation, and described how wave-induced transport of salt led to changes in the horizontal salinity distribution in the vicinity of the German Wadden Sea islands. There is remarkably strong agreement between Fig. 11b and the results of Schloen et al. (2017; Fig. 10a) in the distribution of fresher and saltier surface water due to wave coupling over a broader area along the Dutch and German coasts. Both this study and their results show saltier water north and southward of the Wadden Sea islands (fed from the river Ems), and larger increases in salinity along the Danish coast focused near the outflow of the Elbe. Immediately to the west, a dipole of salinity differences occurs at the outflow from the Weser, which leads to relatively fresher water propagating further off-shore into the North Sea. Finally, the impact of wave coupling in a relatively constrained area near the Rhine outflow towards the south in Fig. 11b is characterised by a relative freshening, again in good agreement with Schloen et al. (2017). Apart from some near-coastal differences along eastern England, the distribution of mean seabed salinity (SBS) differences (Fig. 11c) in the region is highly consistent with the SSS results. This implies that wave-induced changes to horizontal rather than vertical mixing processes are dominant. Summary statistics comparing model simulations during 2017 with observed SSS and SBS are listed in Table 5.

Results in Table 5 reflect the larger sensitivity to wave effects for the three locations closer to the coast, for which summary metrics for both SSS and SBS are markedly improved with wave coupling at FINO1 (yellow star) and TWEMS (dark blue), both located in the area of increased SSS, while results are degraded at UFSDB in the region of freshening salinity (light blue; Fig. 11).

Figure 12 shows a comparison between CPL_DA and DA simulations with observed SSS and SBS through 2017 at UFSDB. Both CPL_DA and DA are clearly too fresh with substantial biases in SSS and SBS. This can be partly attributed to the use of a climatological freshwater boundary condition in the operational AMM15 configuration considered in this study. However, there is also a clear impact of wave coupling on the salinity variability throughout 2017. CPL_DA results show greater variability across the year at both levels, with good correspondence to the observed variability which is not reflected in the summary MD and RMSD metrics. This is demonstrated further by the agreement between power spectra for the observed and simulated time series in Fig. 12b and d. Both simulations reproduce the observed peak at the semi-diurnal M2 tidal frequency (12.42 h) well, with limited impact of wave coupling evident. The results are also consistent at this site for higher frequencies, with further spectral peaks in surface salinity corresponding to the M4 and M6 tidal components. While these spectral peaks are maintained in the salinity simulations at the seabed, they are not observed. This might suggest that accounting for the effects of seabed–wave coupling in shallow seas could lead to further improvement (e.g. Soulsby et al., 1995). Alternatively, this difference in observations could be related to how freshwater flux boundary conditions are distributed vertically in NEMO. There is also a clear difference in the variance in CPL_DA and DA at periods longer than daily, especially for SBS (Fig. 12d). CPL_DA shows improved results compared to DA relative to the observed spectrum. This is consistent with the more qualitative assessment of longer-term variability in Fig. 12c.

Results from the nearby TWEMS buoy, located on the edge of the region of increased salinity in Fig. 11b (dark blue marker in Figs. 3a and 11), are shown in Fig. 13. The increased salinity at TWEMS reduces the negative bias against observations. Power spectra from the 2017 results in Fig. 13b and d highlight a much greater amplitude of the salinity semi-diurnal cycle at both the surface and seabed in the DA simulation than in observations, which is improved for CPL_DA results. Focusing on the time series of SSS and SBS during January 2017 only (Fig. 13a and c) demonstrates a remarkable improvement of the agreement between observed and simulated salinity at both the surface and seabed with the inclusion of wave processes. This change of amplitude suggests the influence of wave coupling in modulating wave–tide interactions in the region (e.g. Lewis et al., 2019), but a more systematic study is beyond the scope of the current work.

The summary statistics presented in Sect. 3 indicate that the net impact of wave processes on sea surface height (SSH) is negligible in terms of long-term statistics for the simulated sea level anomaly (SLA) in comparison with satellite altimeter observations. The spatial distribution of RMSD for each experiment (not shown) indicates generally neutral changes across much of the NWS but improvements of approximately 10 % across the North Sea with wave coupling.

Of more relevance for natural hazard prediction are the extremes of simulated SSH, given the requirement of accurate SSH simulation for warnings of coastal storm surge and inundation. Figure 14 therefore shows the distribution of the largest positive and negative SSH differences between CPL_DA and DA during winter 2016/2017, noting these differences are independent of whether ocean data assimilation was active or not. Greatest variability occurs during winter and autumn seasons, focused around coastlines as might be expected. Instantaneous SSH reductions of up to 10 cm can be found due to wave coupling on the NWS. However, on the western and eastern UK and southern North Sea coastlines, known to be susceptible to storm surges and coastal flooding (e.g. Wolf, 2008), more substantial increases in SSH of over 25 cm are simulated with wave coupling. This result is consistent with the conclusions of Staneva et al. (2017). Impacts along the Bay of Biscay coastline are constrained to areas very close to the coast, in agreement with Bertin et al. (2015).

SSH is a combination of the long-term mean sea level, diurnally varying tide, and additional residuals, mostly driven by meteorological variability as illustrated through storm surges. In order to provide a more quantitative assessment of forecast skill against in situ tide gauge observations around the UK coast, a Doodson X0 low-pass filter is applied to co-located observed and simulated SSH (e.g. Pugh, 1987; Consoli et al., 2004) within each 3-month season. The mean sea level for each simulation or observation site is first removed by computing a long-term mean for each time series. This is beneficial in that any offset errors or drifts between observed and model chart datums and variations across different gauge locations are implicitly removed from the analysis. The low-pass filter then attempts to remove the main tidal variations. The filtered value at each output time, XFt, is computed separately for each observation and simulated time series from hourly values, Xt, based on Eq. (1) with M=19 samples as 1XFt=F0Xt+∑m=1MFmXt+m+X(t-m). The filter, Fm, provides a weighted average with 30 weights as listed by Consoli et al. (2004).

Figure 15a shows a typical example of filtered SSH observed and simulated at Sheerness on the south-east coast of England (marked “Sh” in Fig. 3a) during winter 2016/2017. Similar results are found for other coastal tide gauge comparisons and times of year. Unlike when considering the total SSH, for which the variability is dominated by tidal energy, there is a clear difference between CPL_DA and DA results for the subtidal (or low-pass filtered) part of the signals (Fig. 15a). In particular, the CPL_DA (and CPL, not shown) simulations give improved agreement with the filtered tide gauge observations when they exceeded 0.4 m on several occasions between late December and mid-January 2018. The peak observed and CPL_DA simulated values above 0.6 m occurred during a period when storm surge warnings were issued for south-eastern England due to coincidence with high tides. In addition to better capturing periods of maximum positive filtered SSH, Fig. 15a shows improved agreement with largest negative SSH during early February 2017. All observed and simulated filtered SSH at Sheerness during 2017 are compared in Fig. 15b, applying separate Doodson filter calculations for each 3-month season. Due to the filtering methodology, the summary RMSD statistics are small (and bias zero by definition), but the CPL_DA results indicate a reduced RMSD and increased correlation coefficients relative to DA results. Most critical, it is clear that the positive and negative tails of the filtered SSH distributions are better captured with wave coupling.

Figure 16 summarises the relative improvement in RMSD between CPL_DA and DA for each season at all UK coastal tide gauge sites. This shows substantially improved statistics at all locations, particularly during periods of highest SSH residual in winter 2016/2017 and autumn 2017 and focused in regions most susceptible to storm surges around north-western and eastern UK coastlines.

In summary, these results briefly highlight that inclusion of wave–ocean feedbacks in the operational NWS forecast system is expected to improve coastal SSH simulations, in particular by enhancing the simulated extreme values driven by positive and negative storm surges. This initial assessment also enhances the prospect for longer-term evolution towards the use of regional coupled systems for both operational ocean and storm surge prediction, converging with existing ensemble-forced barotropic ocean modelling approaches, as part of more integrated natural hazard prediction capabilities (e.g. O'Neill and Saulter, 2017).

The mean change in surface currents on the NWS due to wave coupling is small (Fig. 17). The impact of waves is found to be consistent across different seasons and independent of whether ocean assimilation was active. Figure 17 focuses on the impact of wave coupling during October 2019, a period coincident with acoustic Doppler current profiler (ADCP) observations at the FINO1 and FINO3 locations in the German Bight (Fig. 3a). This highlights a tendency for increased current speeds in the central and northern North Sea, and reduced to the west of the NWS in the southern North Sea and English Channel. This distribution is more consistent with Stokes drift speed computed from the wave model (Fig. 1c and f) than the net momentum storage and release by waves. Figure 17b shows a complex response to wave coupling but with large areas of enhanced wave-induced currents at coastlines, although the net impact is small when averaged over longer periods.

A comparison of current profiles with ADCP observations at the FINO3 location (green star in Fig. 17b and Fig. 3a) during October 2016 is shown in Fig. 17c. Comparisons between observations and simulations are made using the nearest grid cell value only (rather than a 5×5 region mean) in order to better capture extremes in a highly variable field. The FINO3 site is located in a region of enhanced currents with wave coupling, which is shown to have better agreement with observations of both the mean and standard deviation through much of the profile. This enhancement is consistent with previous results in the region described by Staneva et al. (2016), who found increased currents during storm conditions. Simulated current profile results at FINO1 (yellow star in Fig. 17b) show very little impact of wave coupling during this period, consistent with the distribution of surface changes in Fig. 17b.