We use wind and wave measurements from the Reducing the Uncertainty of Nearshore Experiment (RUNE) project to evaluate wind and wave simulations. RUNE was a collaborative research project that conducted a coastal offshore measurement campaign from 2 November 2015 to 1 March 2016, near the west coast of Jutland, Denmark. The experiment and data collected during RUNE are described in detail by and .

During the campaign, wind and wave measurements were taken approximately 7 km offshore. Wave measurements were obtained using a directional Triaxy wave buoy equipped with a downward-looking acoustic Doppler current profiler. This buoy was deployed at the beginning of the campaign at a water depth of 16.5 m. The hourly integrated wave parameters – including significant wave height (Hs), maximum wave height (Hmax), peak wave period (Tp), average zero-crossing period (T02), and mean wave direction (MWD) – are processed from the 7 Hz sampled data. A lidar buoy, positioned less than 200 m from the wave buoy, was equipped with a WindCube^® v2 Doppler wind lidar to record wind data. Mean wind speed and direction are available every 10 min at 12 different heights above the mean sea level: 40, 47, 59, 79, 97, 117, 134, 147, 172, 197, 209, and 247 m. Figure  shows the geographical location of the RUNE measurements as a red dot.

Figure  presents the time series of Hs and the wind speed at a height of 40 m, MWD, and the wind direction at a height of 40 m for a period of a week around our focus day, 5 December 2015. The wind measurements shown in the plots correspond to the lowest recorded height. We observe an overall wind–wave alignment from the southwest (less than 60° difference), which lasts for almost a full day on the focus day, marked in gray in Fig. . Additionally, the most intense wave event during the measurement period occurred on the same day at 18:00 UTC, with Hs=5.77 m and T02=8.7 s. During this storm, the average wind speed ranged from 21.3 m s⁻¹ at 40 m to 26.8 m s⁻¹ at 247 m. We use this day to investigate the wind–wave interaction in the COAWST modeling system in LES mode.

We utilize the WRF model, version 4.5 , and SWAN model, version 41.45 , through the COAWST modeling system version 3.8 to simulate wind–wave interactions in the North Sea for the selected storm. Other components of the COAWST system are not activated in this study. The WRF and SWAN models are two-way, online, coupled through the wave boundary layer model (WBLM) implemented in SWAN . The WBLM accounts for the vertical variation in stresses and energy in the wave boundary layer (WBL), which is the interface between the waves and the atmospheric boundary layer. In this layer, the wind speed profile deviates from the classical logarithmic shape due to wave-induced motions and momentum exchange. In this coupled system, the WRF horizontal velocity components at a height of 10 m (longitudinal U and meridional V) are sent to SWAN. The WBLM uses the former velocities along with local wave-induced and turbulent stress, as well as wave phase velocity, to calculate the vertical wind profile within the WBL by solving the kinetic energy conservation equation; computes the equivalent roughness length (z0) that conforms to the logarithmic wind profile; and finally transfers z0 back to the surface layer module of the WRF model . For the uncoupled WRF simulations, the surface layer parameterization relies on the revised MM5 Monin–Obukhov scheme , which uses the default Charnock-based formulation in its revised form following to diagnose the sea surface roughness length, computed as 1z0=αu*2g+0.11νu*, where the Charnock parameter α is a function of the 10 m wind speed U10, 2α=0.011,U10<10ms-10.011+0.018-0.01118ms-1-10ms-1×(U10-10ms-1),10ms-1≤U10≤18ms-10.018,U10>18ms-1, and u* is the friction velocity, g is the gravitational acceleration, and ν is the kinematic viscosity of air. The second term accounts for viscous effects and becomes important under weak wind conditions.

Therefore, the results from coupled WRF–SWAN simulations consider realistic wave growth and improved energy exchange at the air–sea interface compared to the uncoupled simulations.

Unlike most previous COAWST applications, which remain limited to mesoscale resolutions, our configuration extends the coupling to include LES domains. To make this framework operational, we applied two key adjustments. First, in domains with finer horizontal grid spacing than 100 m, we replaced the planetary boundary layer (PBL) scheme with LES. Second, we implemented the cell perturbation method (CPM) in the WRF model within the COAWST framework to enable turbulence simulations.

Our multiscale WRF simulations include six nested domains. The outer three domains run in mesoscale mode with horizontal grid spacings of 9.9, 3.3, and 1.1 km, denoted as D01, D02, and D03, respectively, while the inner three domains run in LES mode (denoted as D04, D05, and D06). The coarsest LES domain D04 has a grid spacing of 100 m. The grid spacing ratio between mesoscale domains is 1:3, while the ratio from the finest mesoscale D03 to the coarsest LES domain D04 is 1:11. In addition, we nest two more LES domains D05 and D06 with a 1:5 grid spacing ratio of 20 and 4 m, which are run for a shorter period (10 h). The time step ratio matches the grid spacing ratio, with a time step of 45 s for the outermost mesoscale domain. All six domains consist of 61 vertical levels, with the first level located at 10 m above the surface. The model's top is at 5000 Pa. The SWAN model adopts the same domain configuration as presented in Fig. . More details on the model domain specifications can be found in Table . Both coupled and uncoupled simulations employ the same domain configuration, nesting ratios, input data, and physical parameterizations. The simulations differ only in that the uncoupled simulation includes only the atmospheric model (WRF), whereas the coupled simulations additionally incorporate the wave model (SWAN).

A grid spacing of 100 m is intentionally used for the LES domain D04, as it reflects what is commonly used in industry and operational multiscale modeling , where computational constraints limit the LES domain sizes. Although the LES domains use a 1.5-order turbulence kinetic energy (TKE)-based subgrid-scale (SGS) model , the coarse horizontal grid spacing only allows a limited portion of the turbulence field to be explicitly resolved for this particular storm event, and therefore, a substantial fraction of the turbulent stresses originate from the SGS model. The finer-resolution LES domains (D05 and D06) are included to partly demonstrate how higher resolution increases the fraction of resolved turbulence.

The outermost domain is initialized and forced using ERA5 reanalysis data, updated every 6 h . In addition, the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) dataset is used to update the sea surface temperature and sea ice fields during simulations every 6 h. For static inputs, we utilize the default datasets provided by the WRF model, along with the CORINE land cover dataset and the ESA Climate Change Initiative (CCI) land cover datasets at resolutions of 100 and 300 m, respectively .

For the physics parameterizations of the WRF model, we employ the WRF Single-Moment 6-Class (WSM 6-class) graupel scheme for microphysics , which includes predictive variables for water vapor, cloud water/ice, rain, snow, and graupel. For radiation processes, we utilize the Rapid Radiative Transfer Model (RRTM) for longwave radiation and the Dudhia scheme for shortwave radiation, both executed every 9 min. The Kain–Fritsch scheme is employed for cumulus parameterization, activated every 5 min exclusively for the outermost domain. The Unified Noah land surface model is applied for land surface, while the revised MM5 Monin–Obukhov scheme is used for the surface layer . The Yonsei University (YSU) scheme is used for PBL parameterization, which was selected based on a sensitivity analysis among three other schemes: the Mellor–Yamada–Nakanishi–Niino (MYNN) , Mellor–Yamada–Janjic (MYJ) , and quasi-normal scale elimination (QNSE) schemes. PBL schemes are deactivated for the innermost domains as they run in LES mode. The SGS model prognoses the TKE, which is used to compute the local eddy diffusivity.

The SGS part of the stress includes the deviatoric component τijdev and the part from the SGS turbulent kinetic energy esgs. Using the 10 s model outputs (D04 outputs esgs and the deviatoric stresses), the SGS stress is calculated as 3τijsgs=23δijesgs+τijdev.

The resolved stress components (τijres) for each velocity pair are computed as 4τijres=-ρ〈ui′uj′〉, where ρ is the air density; ui and uj are the along-wind and cross-wind components; the primes (^′) denote fluctuations from the mean value, which are computed as a 10 min time average at the grid point closest to the measurement site; and the angle brackets 〈⋅〉 indicate a temporal average. The total stress components are obtained from 5τijtot=τijres+〈τijsgs〉.

In multiscale simulations using the WRF model, turbulence in the LES domain may not develop fast enough because of the smooth flow from the parent mesoscale domain and the time needed for high-resolution LES domains to develop turbulence. In contrast to the PBL scheme used within mesoscale domains, within the LES domains turbulence is partially resolved, and the SGS model represents the unresolved subgrid-scale turbulence, which further contributes to the Reynolds stresses and TKE . This challenge is more significantly intensified in offshore areas, where the absence of topographical features limits the production of turbulence. To address this issue and promote a seamless transition from mesoscale boundary conditions to fully developed LES turbulence, the CPM is applied at the inflow boundaries of the LES domain. In this study, for the first time, we integrate the CPM into the WRF model within the COAWST framework, enabling the application of this technique in coupled ocean–atmosphere–wave simulations. The CPM method introduces controlled perturbations on the potential temperature field. We apply the perturbations on three contiguous cells of the lateral boundaries to develop realistic turbulent fields . Additionally, we conduct a simulation without activating CPM in the LES domain D04 to assess its impact on the simulations, which is presented in Sect. .

For the wave modeling, we initialize the SWAN model using the output spectrum at each grid cell from a previous simulation conducted 24 h earlier to allow for spin-up and provide consistent boundary and initial conditions. The open boundaries of the outermost domain are set to zero. This does not impact the innermost domains due to the large domain size. We utilized 36 directional bins with a frequency exponent of 1.1. The frequency range extends from 0.03 to 10.05 Hz, resulting in a total of 61 frequency bins. The SWAN model operates with a time step of 6 min for the four outermost domains, and the time step is reduced to 4 min for D05 and D06. The EMODnet digital terrain model (DTM) with a grid resolution of 1/8 arcmin (approximately 230 m) is used for the bathymetry. In addition to the configurations mentioned above, the SWAN model incorporates several physical processes to accurately simulate wave dynamics relevant for our model domain, which is in the coastal zone with relatively shallow water. The depth-induced wave breaking is calculated using the parameters α=1.0 and γ=0.73, which control the intensity and the break threshold, respectively. Bottom friction is taken into account using the JONSWAP formulation with a friction coefficient of 0.038, representing energy dissipation due to seabed interactions. White-capping dissipation, which addresses the energy loss from wave breaking in deep water, is activated using the WAM Cycle 3 formulation with drag law fitting. In addition, SWAN considers processes related to sea spray, specifically by modeling white capping and wave-induced breaking. In the present coupled configuration, the effects of sea spray on atmospheric enthalpy fluxes and momentum exchange are indirectly represented through modifications of surface roughness and stress in the surface layer scheme. As the ocean component in COAWST is not activated, ocean mixing and feedback through sea surface temperature (SST) modification are not considered.

Coupled and uncoupled simulations for D01 to D04 are run over a 30 h period from 18:00 UTC on 4 December to 00:00 UTC on 6 December. Coupled and uncoupled simulations for D05 and D06 are run for a shorter period of 10 h with the same starting time. Results and analysis focus on all of 5 December for D01 to D04 and on the first 4 h of this day for D05 and D06, which we use for turbulence analysis. The SWAN model outputs are saved every 10 min for both D03 and D04. For the WRF model, outputs were saved every 10 min for D03 and every 10 s for D04, D05, and D06. All domains share the same spin-up period, despite the shorter total simulation time of D05 and D06.

Figure  shows distributions of the computed roughness length on 5 December for D03 and D04 from the coupled and uncoupled simulations. The distributions are computed from an area of 6 × 6 grid points in D03 and the corresponding 66 × 66 grid points in D04 around the RUNE location. The figure illustrates the effect of coupling and horizontal resolution on the variability and distribution of roughness length. Overall, mesoscale domains correspond to larger z0 than the LES domains. The atmosphere-only, non-coupled simulations also give larger z0. The shapes of WRF‐LES and WRF-LES–SWAN distributions differ: WRF-LES appears narrow and Gaussian, while WRF-LES–SWAN is broader and appears Weibull-like. Similarly, for the mesoscale data, the coupled WRF–SWAN also shows more variability compared to WRF. The differences are mainly due to the method used to calculate the sea surface roughness length in the coupled and uncoupled models. In the coupled system, roughness is dynamically derived from the wave state via the WBLM , whereas in the uncoupled WRF simulations, it is described by Eq. ().

Figure  presents a comparison of Hs, MWD, and Tp derived from SWAN when coupled with both the mesoscale (D03) and LES (D04) domains against RUNE buoy measurements. The 10 min simulation outputs were averaged over hourly intervals to match the temporal resolution of the hourly integrated measured wave parameters. The corresponding values of the root mean square error (RMSE) for each domain, calculated relative to the observations, are summarized in Table . The results indicate that, while model outputs in both domains follow the observed data, the LES-driven output provides improved wave characteristics, particularly for Hs, with an RMSE nearly half that of the mesoscale-driven domain output. The simulated Tp and MWD exhibit only minor differences between the two domains.

The time series of mean wind speed and direction output from both the coupled WRF–SWAN and WRF-only simulations of the mesoscale D03 domain and the LES D04 domain are compared against the lidar measurements at four different heights, 40, 79, 97, and 147 m, in Fig. . To ensure temporal consistency with the mesoscale results and measurements, the LES outputs were averaged over 10 min intervals from the 10 s output. At 40 m (Fig. a4), the lowest measurement height, simulations from the LES domain (both WRF-LES–SWAN and WRF-LES) show better agreement with observations than those from the mesoscale domain, in terms of magnitude and variability. At 79 m (Fig. a3), the WRF-LES–SWAN run exhibits the best agreement with measurements. Above 97 m, WRF-LES–SWAN tends to overestimate the wind speed compared to observations, and at 147 m, the WRF-LES run also overestimates the observed wind speed, which can primarily be attributed to the effect of boundary conditions, as ERA5 overestimates the measurements by up to 3 m s⁻¹ at some time steps. The higher simulated wind speeds in the coupled versus uncoupled simulations and the LES versus mesoscale simulations are consistent with the decreased simulated roughness length as shown in Fig. .

Figure  presents the vertical profiles of wind speed and direction during the 2 h period surrounding the time of maximum wave height (hours 17:00 to 19:00 UTC in Fig. ). Both WRF-LES and WRF-LES–SWAN simulations provide wind speeds lower than observations near the surface; however, they result in an overall good agreement with measured mean wind speed between 40 and 150 m, as also evident in the RMSE values (Table ) and the time series (Fig. ). However, this is likely due to excessive vertical wind shear, which is attributed to the type of SGS model used for the LES domains . In contrast, WRF and WRF–SWAN show wind profiles with vertical wind shears that are more consistent with those from the measurements, although both have a systematic bias at all measured levels. In addition, slightly higher wind speeds are observed in the coupled simulations compared to the uncoupled ones. The WBLM, which accounts for wave impacts and calculates an effective roughness length, yields lower roughness length values than those from the Charnock-based parameterization used by default in the WRF model, particularly under storm conditions. This is reflected in the analysis in Fig. . Similar results were previously reported in under stormy conditions. Lower roughness lengths lead to higher surface wind speeds under the same forcing conditions. In terms of wind direction, both WRF-LES and WRF-LES–SWAN runs show a slight eastward deviation, with a maximum of approximately 4° up to 100 m.

Although no high-frequency measurements are available for in-depth validation of the LESs of turbulence, we investigate the behavior of turbulent fluxes of the coupled and uncoupled simulations using results from the LES domains. For this, we compute both the resolved and the SGS stress components. To capture the extreme event at the RUNE measurement location, we use 10 s model outputs over a 2 h period from 02:00 to 04:00 UTC.

Figure  shows the vertical profiles of the velocity variances 〈u′u′〉, 〈v′v′〉, and 〈w′w′〉, as well as the covariances 〈u′w′〉 and 〈v′w′〉. The figure includes both resolved and total (resolved + SGS) fluxes from the WRF-LES and WRF-LES–SWAN runs at horizontal grid spacings of 100 m (D04) and 4 m (D06). The covariances 〈u′w′〉 and 〈v′w′〉 exhibit similar trends, with a smaller portion of resolved turbulence for D04 compared to D06, as expected from the effect of their spatial resolution difference. Results from both domains clearly show increased turbulence levels when wind–wave interactions are included in the simulation. Similar enhancements in velocity variances were also observed in an idealized simulation of the same case . For D04, the horizontal velocity variances have a maximum at around 70 m, which is rather far from the surface. This is argued to be an effect of the coarse horizontal grid spacing of D04 (100 m), a domain that cannot resolve the small eddies close to the surface. When finer horizontal grid spacings of 20 m (D05) and 4 m (D06) are used, the heights of the maximum turbulence fluxes appear closer to the surface, at a height of 60 and 30 m, respectively. In , a horizontal grid spacing of 1.25 m was used, and the corresponding height of the maximum turbulence fluxes was confined below the first 5 m. The contribution of SGS stresses is also more evident in D04 compared to D05 (not shown) and D06, as expected. The resolved vertical variances (dashed lines in Fig. c) are small in D04 and reach more realistic values (up to 0.1 m² s⁻²) in D06.

As no turbulence measurements are available from the RUNE campaign, these differences in turbulence should be interpreted as physics-based model behavior rather than validated improvement. It is also important to mention that all domains share the same spin-up period, and despite the shorter total runtime of D05 and D06, the turbulence fields in these fine LES nests are well developed, as indicated by the larger resolved variances relative to D04. The shorter runtime primarily limits the length of the available time series rather than the development of turbulence. The D05 and D06 domains are therefore included to illustrate how increasing horizontal resolution modifies the balance between resolved and SGS turbulence and to highlight the limitations of the 100 m LES configuration (D04) in representing near-surface turbulent structures. Consistent with previous LES studies, finer grid spacing is expected to increase the fraction of explicitly resolved turbulence and improve the representation of turbulent statistics, although no direct observational data are available for validation in this case.

Figure  shows the 24 h time series of wind speed at 40 m from the nested LES domain (D04), with and without CPM. The results highlight the role of CPM in enhancing wind speed variability and fluctuations.

To further detail the enhancement of turbulence by using CPM, we compute in Fig.  the wind speed spectrum from lidar measurements, the finest mesoscale domain D03, and the nested LES domain D04, both with and without CPM. The spectrum is an average of spectra derived within 5 h windows with a 15 min overlap. As illustrated, the spectrum from the no-CPM case fails to capture the levels of turbulent energy in the measurements even at timescales much larger than 10 min and closely resembles the mesoscale spectrum, which is not expected to resolve turbulence. In contrast, the D04 simulation with CPM activated matches the spectral energy distribution of the measurements more closely. The drop in energy at higher frequencies of the spectrum for WRF-LES with CPM can be noticed beyond the timescale of 1 min, which shows the limitation of coarse LES runs to properly reproduce a wide range of turbulence scales.