The Rødsand II wind farm (54.5799° N, 11.8903° E), in operation since 2010, is located in the shallow waters of the Baltic Sea, south of the island of Lolland (Fig. ). The farm consists of 90 Siemens SWT–2.3–93 turbines, each with a nominal capacity of 2.3 MW, a hub height of 68.5 m, and a rotor diameter (D) of 93 m. The farm is arranged in five curved rows of 18 turbines each, with inter-turbine spacing ranging between 5D and 8D (see also the bottom panel of Fig. ). Approximately 3 km to the east lies the Nysted wind farm, commissioned in 2003, comprising 72 Bonus 2.3 MW turbines with a spacing ranging from 6D to 10D. The nearest landmass, the island of Lolland, is characterised by low-lying, flat terrain with sandy beaches, coastal dunes, agricultural fields, small settlements, and patches of forest. The region experiences high average wind speeds of about 9.6 m s⁻¹ at 100 m, predominantly from the west to the south-west, influenced by weather systems passing over the North Sea and Baltic Sea see also https://globalwindatlas.info/en/, last access: 22 September 2026.

During more than a decade, Rødsand II and Nysted have been used for studies on the interaction between atmospheric flow and wind farm arrays, in particular wind turbine wakes and wind farm interactions, also called cluster effect . Previous studies focusing on wake loss for these two farms used simulations alone , combined SCADA data and numerical simulations or simulation and mast-based measurements .

There have, however, been only a few measurement campaigns that have focused on wake flow characteristics and the structure of the ABL above Rødsand II. In 2013–2014, a scanning lidar campaign under the lead of the Carbon Trust Offshore Wind Accelerator program was performed. It was aimed at investigating wake flow and boundary layer dynamics at Rødsand II. Only a limited portion of the results from this campaign has, however, been openly published .

The LOLLEX campaign builds on these foundations and introduces several novel and complementary elements: a long-range scanning lidar deployed on the offshore transformer platform north of the wind farm and a dual scanning-profiling lidar setup mounted on a CTV as an observational platform of opportunity.

To complement the lidar data, high-resolution mesoscale wind speed data from the 3 km Norwegian Hindcast Archive (NORA3) were used. NORA3 is a state-of-the-art hindcast dataset produced by dynamically downscaling ERA5 reanalysis data . It provides hourly wind conditions over Northern Europe at a horizontal resolution of 3 km. The dataset has been validated against both in-situ observations and remote sensing data , demonstrating excellent performance in coastal and offshore environments.

During the LOLLEX campaign, a specific subset of the NORA3 database, containing wind speed data at seven vertical levels from 10 to 750 m, was used in combination with the lidar observations above the wind farm, as shown in . It was also used to complement the Range Height Indicator (RHI) scans from the lidar installed on the transformer platform (see Sect. ).

The backbone of the campaign was the installation of two DWLs onboard a CTV serving the Rødsand II wind farm, using it as an observational platform of opportunity. This mobile measurement set-up over several months was complemented by the shorter fixed deployment of an additional scanning lidar system on the transformer platform of the wind farm.

The WindCube100S occasionally produced short or incomplete scans when deployed on the vessel, likely due to its sensitivity to rapid translation and acceleration. This can be attributed to its mechanically rotating scanning head for beam steering, in contrast to the WindCubeV2 Offshore, which operates without moving parts and is designed for dynamic buoy deployments. For the vertical staring mode conducted between 25 January and 28 August 2023 (approximately 9900 scans), 65 % of the WindCube100S scans were flagged as incomplete (scan duration <10 min) and excluded, while 30 % achieved the full 25 min duration.

All lidar measurements were subjected to a two-step quality control procedure to ensure high-quality data for further analysis. In the first step, a signal-quality filtering was applied using the Carrier-to-Noise Ratio (CNR), which is provided by both the WindCubeV2 and WindCube100S. A fixed CNR threshold was applied at each time and range gate to remove low signal-to-noise measurements. Following earlier studies , thresholds of -24 dB for the WindCubeV2 and -27 dB for the WindCube100S were used.

In the second step, statistical outliers were removed using a moving median absolute deviation (MAD) filter with 3 MADs away from the median, following and , to eliminate spurious values that passed the CNR threshold but were inconsistent with local temporal variability. After signal-quality filtering and statistical outlier removal, data availability was range-dependent. That is, within a given scan, valid data could be retained at lower ranges while being filtered out at higher ranges. Therefore, data availability could not be represented by a single campaign-wide percentage. After quality control, motion correction was applied to the WindCubeV2 data and to the DBS-mode scans of the WindCube100S, as described in Sect. . Unless otherwise stated, all results presented in this manuscript are based on motion-corrected wind speed data.

Following , a signal-to-noise ratio (SNR) threshold of -20 dB is commonly recommended for radial velocity data from the Halo Photonics StreamLine XR+. In the present case, this threshold appeared overly conservative. The lidar data were used solely for mean wind speed estimation, and the beam was frequently oriented at angles close to 90° relative to the mean wind direction, resulting in generally low SNR values. In addition, the SNR was originally provided on a linear scale, with a substantial fraction of values being negative, preventing a consistent conversion to dB.

For case study 4, a moderate correlation (ρ≈-0.63) was found between the SNR and |vr-v0|, where vr is the along-beam (radial) velocity and v0 denotes the most probable radial velocity. However, substantial overlap between low- and high-deviation data across the SNR range indicates that SNR alone is not a reliable indicator of data quality. Consequently, no SNR-based filtering was applied. Radial velocity data were first filtered to remove implausible values by discarding samples with |vr|>30ms-1. The most probable radial velocity v0 was then estimated as the mode of the vr distribution. Only samples satisfying |vr-v0|<kMoAD were retained, where MoAD=median|vr-v0| denotes the median absolute deviation about the modal radial velocity v0, and k=3 is a dimensionless threshold parameter.

The ABL top is inferred from vertical-stare lidar measurements using both CNR and σw profiles when these diagnostics are well defined. Aerosol- and backscatter-based methods are commonly used to estimate ABL height from lidar and ceilometer observations , but the resulting height should be interpreted as a proxy rather than as an exact thermodynamic inversion height. This is particularly important in cloud-topped conditions, where cloud droplets may dominate the CNR signal and the CNR maximum may correspond to a cloud-related backscatter feature that is not necessarily collocated with the actual ABL top. When a distinct local minimum is visible in the vertical profile of σw, it is used as an additional turbulence-based indicator of ABL depth, following previous Doppler-lidar studies based on vertical velocity variance profiles: used the altitude where σw2 drops below an empirical turbulence threshold, whereas used the minimum of σw2 under stable conditions.

A lidar wind profiler mounted on a moving platform, such as a buoy or ship, is subject to six degrees of freedom (DOF) of motion. These include translational movements, such as surge, sway, and heave along the platform’s x, y, and z axes, as well as rotational movements, such as roll (β), pitch (φ), and yaw (ψ) around these respective axes. These motions alter the measurement geometry and introduce artificial velocity components that affect both the observed radial wind velocity (vr) and the reconstructed three-dimensional wind vector (u^).

For a lidar mounted on a buoy, the 10 min average wind speeds are only marginally impacted (typically by 1 %–2 %) due to averaging over periodic quasi-random motion . However, instantaneous measurements can be significantly affected. Therefore, motion correction is essential when high-resolution wind data is required, especially in offshore environments.

Several motion correction algorithms have been developed to compensate for the motion-induced errors in lidar measurements from floating platforms . These efforts primarily target periodic wave-induced motions, typically observed in buoy-based systems. However, ship-based systems experience both rotational and non-periodic translational motion patterns that can be challenging to correct with standard correction techniques.

In this study, we adopt the correction method described by and , which is suitable for periodic and aperiodic motion conditions. The algorithm corrects each lidar beam's line-of-sight (LOS) velocity in two steps: (1) translational motion correction: The platform's instantaneous translational velocity vector ut, comprising surge, sway, and heave, is projected onto the beam direction and subtracted from the measured vr; (2) rotational motion correction: At each time step, the platform’s orientation is used to construct a rotation matrix R based on the roll, pitch, and yaw angles.

In the absence of motion, u at one altitude can be reconstructed using the vr obtained from one full DBS scan of WindCube lidar and the beam direction matrix N as 1vr=Nu, where u is the true wind vector in the inertial frame. For a WindCube wind lidar operating with a 5-beam DBS setup, vr and N are defined as 2vr=vr(α=0°)vr(α=90°)vr(α=180°)vr(α=270°)vr(ϕ=90°),3N=cos⁡ϕ0sin⁡ϕ0cos⁡ϕsin⁡ϕ-cos⁡ϕ0sin⁡ϕ0-cos⁡ϕsin⁡ϕ001, with α being the azimuth angle and ϕ the beam elevation angle.

In the presence of motion, considering the translational and rotational motion, Eq. () can be rewritten as 4vr-vr,t=NR(u), where R is the the rotation matrix, and vr,t is the projection of translational speed ut to the beam as 5vr,t=NR(ut).

The rotation matrix R is computed from the time-resolved attitude data using standard Euler rotations 6Rx=1000cos⁡βsin⁡β0-sin⁡βcos⁡β,7Ry=cos⁡φ0-sin⁡φ010sin⁡φ0cos⁡φ,8Rz=cos⁡ψsin⁡ψ0-sin⁡ψcos⁡ψ0001, where β, φ, and ψ correspond to roll, pitch, and yaw in the inertial coordinate system. These matrices are combined as R=RzRyRx to account for the platform's full attitude. The best estimate of the wind velocity (u^) is then obtained by using the least-squares method: 9u^=[(RN)TRN]-1(RN)T(vr-vrt).

In practice, the motion correction is implemented at each synchronised time step. For the WindCubeV2, one beam is recorded per second (5 s per complete five-beam scan), whereas for the WindCube100S, one beam is recorded every 3 s (15 s per scan). To ensure temporal consistency, both radial velocities and motion signals (translational velocities and attitude angles) are interpolated onto a common 1 Hz time base. This enables temporal collocation and synchronisation of the five beams forming each scan. The correction is then applied simultaneously to each synchronised beam set using the corresponding rotation matrix and translational velocity vector, and the wind vector is retrieved via Eq. (). Although wind vectors are computed at 1 Hz after interpolation, this upsampling does not introduce additional physical information and is used only for subsequent statistical aggregation (e.g., mean estimates).

In this study, the WindCube100S operates in DBS mode twice per hour using five beams, yielding five equations for the three unknown wind components, which enables dynamic motion correction of the retrieved wind speeds. When operating in vertical stare mode, however, only one equation with three unknowns is available, making such dynamic correction impossible.

Hereinafter, u, v, and w denote the along-wind, across-wind, and vertical velocity components in a streamline coordinate system as defined by . In , a method to correct for static tilt angle error was presented and applied to a single 30 min scan. Here, we extend this static tilt correction to the full campaign duration to assess its robustness (Fig. ). We compare this correction to a simpler tilt angle correction based on the assumption of mean horizontal flow at 400 m above the surface and to the uncorrected case. For completeness, the method is summarised below, and its performance is discussed.

In vertical stare mode, the LOS velocity component closely approximates the vertical velocity component, unless tilt angles differ significantly from zero. The static (time-averaged) tilt angle can be estimated and used to correct the lidar-retrieved vertical velocity component. The method is inspired by the double rotation algorithm commonly used for tilt correction of sonic anemometers . Prior to applying this correction, the horizontal wind components are rotated into a coordinate system aligned with the mean horizontal wind direction. In this wind-aligned frame, yaw misalignment is removed, and the projection of the mean flow onto the vertical axis depends only on the inclination angle θ. The following formulation therefore represents a physically prescribed static tilt correction rather than a statistical double- or triple-rotation enforcing w‾ to be zero. Hereinafter, the overline denotes temporal averaging; for example, u‾ and w‾ denote the mean along-wind and vertical velocity component, respectively.

The tilt-corrected horizontal and vertical components u‾ and w‾ at height z are 10u‾uncor=u‾cos⁡θ-w‾sin⁡θ≈u‾,11w‾uncor=u‾sin⁡θ+w‾cos⁡θ, where u‾ is the mean horizontal wind speed at the same height, w‾uncor is the uncorrected mean vertical velocity component recorded by the lidar (i.e., the along-beam velocity), and θ is the static tilt angle. Depending on the application, the equation can be solved for w‾, u‾, or the height-independent tilt angle θ. The angle θ can be determined either through visual inspection of the lidar's inclinometer or estimated using w‾ and u‾ from the lidar wind profiler WindCubeV2, as done in . Both visual inspection and the application of Eq. () using data from WindCubeV2 yielded, on average, a static tilt angle of θ≈2.7°.

In Eq. (), the influence of the mean vertical component on the mean horizontal wind speed is negligible for such a small tilt angle, as the correction term associated with the mean vertical velocity scales with w‾sin⁡θ, with w‾≪u‾. The tilt angle derived from visual inspections represents the initial geometric alignment. During operation, quasi-static changes in vessel attitude (e.g. due to varying mass distribution) may occur and introduce a vertical velocity bias of approximately w‾bias≈u‾sin⁡θ. In principle, the effective static tilt angle can be estimated for each measurement period using the Eq. (). In this study, however, a constant value of 2.7° is used for simplicity and to preserve high data availability.

Figure  presents the probability density function (PDF) of the vertical velocity difference between the WindCube100S and the WindCubeV2, using three different methods for tilt correction: no correction, a correction assuming w‾=0 at 400 m, and tilt correction with θ=2.7° derived from Eq. (). The corrected WindCubeV2 is used as the reference instrument due to its dedicated wind-profiling configuration, continuous DBS operation, lower mechanical complexity, and consequently higher robustness and lower measurement uncertainty compared to the scanning WindCube100S.

The PDF is computed from all available high-quality data collected between 1 January and 12 July 2023 (>6000 samples). Without correction, the vertical velocity from the scanning lidar exhibits a positive bias, with a median of 0.28 m s⁻¹ and values reaching up to 1 m s⁻¹. Applying a constant correction based on the assumption of zero mean vertical velocity at 400 m reduces the bias but over-corrects, resulting in a negative median of -0.20 m s⁻¹. The tilt-correction method based on Eq. () yields the lowest absolute bias (-0.05 m s⁻¹), the lowest root-mean-square error relative to the WindCubeV2, thus producing a noticeably narrower PDF, indicating improved accuracy and precision compared to the other approaches.

It should be noted that in turbulence analysis, velocity components are decomposed into mean and fluctuating parts using Reynolds decomposition 12i=i‾+i′, where i={u,v,w}. The static tilt correction is therefore applied to obtain an unbiased estimate of the mean vertical velocity without assuming it to be zero. This correction removes the mean bias associated with the static tilt. However, an unresolved tilt of the measurement axis can also affect second-order turbulence statistics, because the measured fluctuating velocity may contain a projection of the horizontal turbulent velocity component onto the nominally vertical beam. For a tilt angle θ in the streamwise direction, the measured fluctuation can be written as 13wtilt′=u′sin⁡θ+w′cos⁡θ so that (wtilt′)2‾ includes contributions from u′2‾ and u′w′‾. In the present analysis, the tilt correction is applied to reduce the mean vertical-velocity bias, while any residual influence of unresolved tilt on w′w′‾ is treated as a source of uncertainty. Hereinafter, the scanning lidar data are shown with tilt correction using Eq. ().

Periods with precipitation can occasionally introduce spurious vertical velocity signals in Doppler lidar measurements due to backscatter from falling hydrometeors . Such events were rare in the dataset and were not analysed here, as this study focuses on mean flow and vertical turbulence in the marine atmospheric boundary layer and the associated momentum entrainment under typical atmospheric conditions.

In wind energy, momentum entrainment is defined as the divergence of Reynolds stresses that transports high-momentum fluid from the freestream into the wake and drives wake recovery . The streamwise, lateral, and vertical momentum entrainment terms are defined as 14Ex=-∂u′u′‾∂x15Ey=-∂u′v′‾∂y16Ez=-∂u′w′‾∂z where Ey (lateral entrainment) and Ez (vertical entrainment) represent the dominant wake recovery mechanisms through spanwise and vertical stress divergence, while Ex (normal stress divergence) represents streamwise turbulent diffusion and is typically much smaller than the combined lateral and vertical contributions.

In first-order turbulence closures, vertical turbulent momentum transport is linked to the local mean-wind shear and a turbulent velocity scale through a characteristic mixing length . The lidar measurements provide the vertical mean-wind shear, ∂u‾/∂z, and the standard deviation of vertical velocity, 17σw(z)=w′w′‾(z), which is used here as a proxy for the intensity of local vertical turbulent mixing. The momentum flux u′w′‾ is not measured directly. Therefore, its vertical divergence Ez cannot be quantified. Instead, in this study, the local vertical shear and σw estimated by the DWLs are used to identify conditions favourable for increased vertical turbulent momentum transport and, where this transport varies with height, enhanced vertical momentum entrainment. In these cases the averaging time ranged from five to 13 min.

The moving standard deviation σw(t) was also used to characterise short-term variability of turbulence. This moving standard deviation was estimated using a centred sliding window of 60 s, which, for a sampling frequency of 1 Hz, corresponds to 60 data points. The choice of the 60 s window represents a compromise between capturing minute-scale variations in turbulence and including a sufficient number of samples to obtain a representative estimate of the vertical velocity standard deviation. This window length was, therefore, selected to retain relatively rapid changes in turbulence while avoiding an overly noisy estimate of σw(t). No additional filtering was applied when computing σw(t). High-frequency variability is usually partly filtered by the along-beam spatial averaging of the lidar. In a correction for potential high-frequency noise to 10 min data was applied. This correction, however, requires a sufficiently robust estimate of the power spectral density, which cannot be reliably obtained from a 60 s window. The 60 s window also limits the contribution of variability at time scales longer than 60 s.

The approach adopted here complements direct Reynolds-stress retrievals from five- and six-beam DBS scans with DWL profilers, in which line-of-sight velocity variances are combined to estimate components of the Reynolds-stress tensor . Existing multi-beam retrieval methods have primarily been evaluated for fixed-platform profiler lidars, while their application on moving offshore platforms remains an active research topic because platform motion affects the effective beam geometry, sampling, and uncertainty of the retrieved turbulence statistics. Recent work by on Reynolds-stress-tensor recovery from a floating five-beam pulsed lidar illustrates this ongoing development. Validation of such retrieval methods against collocated in-situ turbulence measurements is beyond the scope of the present study.

Figure  shows the data availability of the WindCube100S, the WindCubeV2, and the Halo Photonics (scanning lidar on the transformer platform) throughout the campaign. In 2022, the WindCube100S lidar was located in the harbour but had not yet been installed on the vessel. In January 2023, the WindCube100S was mounted on the CTV, allowing for direct measurements within the wind farm. For the WindCube100S, high data availability was recorded from September 2022 to July 2023, except during the period between December 2022 and January 2023. The WindCubeV2 exhibited even higher availability, with only one significant gap in April 2023. The scanning lidar on the platform recorded reliable data from May to August 2023. As a result, overlapping measurements from all lidar systems were available between May and July 2023 and again at the end of August 2023.

The CTV was located primarily in the harbour during the night and inside the wind farm during the day, as illustrated by Fig. . This figure uses a pseudocolour plot to visualise the number of hours the CTV spent at each location. The map reveals several high-density clusters, some exceeding 50 h, near individual wind turbines and the transformer platform. These high-density areas correspond to the turbines most frequently visited for operation and maintenance, as well as offshore idle time. Most turbines were visited at least once, ensuring that lidar measurements were collected across the entire wind farm during stationary periods. This widespread spatial coverage is a clear advantage of the vessel-based lidar setup. Such extensive spatial sampling would not have been achievable using wind lidars mounted only on buoys or fixed platforms.

Figure  shows a comparison between the wind roses from NORA3 and WindCubeV2 data at 150 m above sea level. To improve clarity, only wind energy-relevant wind speeds (above 5 m s⁻¹) are included. The wind rose is based on 5623 h of data. Both NORA3 and the WindCubeV2 show that westerly winds dominate, with a median wind speed between 8 and 9 m s⁻¹ at 150 m altitude. The WindCubeV2 data indicate more frequent north-easterly winds and stronger winds from the sector between 210 and 260° than NORA3. Differences in wind direction between the NORA3 dataset and the WindCubeV2 measurements can be explained by two factors. First, the CTV carrying the lidar was not fixed in space and often remained near the harbour or inside the wind farm, while NORA3 data corresponds to a fixed offshore grid point. Second, the NORA3 model does not represent the effects of the Rødsand II and Nysted wind farms on the local wind field.

Motion correction was applied to the full dataset, including WindCubeV2 measurements and WindCube100S DBS data. The corrected and uncorrected results are compared with NORA3 in Fig. . For the WindCubeV2, the correction increases the regression slope from 0.85 to 0.91 and bias value from 0.1 to 0.24ms-1, improves R2 from 0.797 to 0.892, and reduces the RMSE from 1.9 to 1.5ms-1. For the WindCube100S, the correction increases the bias from -0.19 to 0.03ms-1, R2 from 0.737 to 0.814, and slightly reduces the RMSE from 2.2 to 2.1ms-1, with the regression slope moving closer to unity.

For the WindCubeV2 lidars, the error metrics relative to NORA3 are similar to those reported in , which were obtained using fixed lidar instruments. This suggests that the motion correction leads to performance comparable, in terms of these statistics, to that of fixed lidars. However, this does not imply that the motion correction is successful in all cases.

Figure  shows the ensemble-averaged bias and RMSE between NORA3 and the ship-based lidars' wind profiles during the campaign before and after motion correction. The WindCubeV2 and WindCube100S show a positive bias below 100 m, indicating that NORA3 overestimates wind speed at lower heights. The NORA3 hindcast does not consider wind-farm wakes, while the lidar measurements are affected by the flow deceleration caused by the farm, a phenomenon also documented at the FINO1 site . It is worth mentioning that NORA3 has a horizontal resolution of 3 km and represents boundary-layer flows more realistically than the earlier 10 km NORA10 hindcast . Nevertheless, uncertainties in the representation of near-surface wind processes may remain. Evaluations of similar high-resolution wind atlas datasets (3 km) show that they reproduce near-surface wind characteristics fairly well, although certain aspects of boundary-layer dynamics, such as the structure of low-level jets, may still be imperfectly represented .

As shown in Fig. a, the bias of the motion-corrected WindCubeV2 data becomes slightly more negative with increasing altitude. The variations in bias remain within ± 0.2 m s⁻¹ across the profile. For the WindCube100S, the bias is more positive below approximately 100 m, and its magnitude decreases, approaching -0.5 m s⁻¹ above 200 m after correction.

The RMSE between the WindCubeV2 and NORA3 decreases with height for both uncorrected and motion-corrected data, with the corrected data showing systematically lower values (Fig. b). Above approximately 150 m, however, the RMSE increases again. In contrast, the RMSE between the WindCube100S and NORA3 increases slightly with height, with typical values around 2 m s⁻¹ after correction. The magnitude of the bias and RMSE is consistent with earlier validation studies of NORA3 in offshore and coastal regions . A local maximum near turbine tip height may reflect increased flow variability not captured by NORA3. The contrasting RMSE trends suggest that part of the height dependence reflects measurement characteristics rather than changes in model performance, with increasing uncertainty for the WindCube100S at higher altitudes. This interpretation is consistent with previous findings that NORA3 performance generally improves slightly with height above the surface .

This case study was presented in detail in , but the analysis was limited to the period between 12:35 and 13:00 UTC on 22 February 2023. Here, we expand upon that work to highlight the influence of CTV motion on velocity retrieval and to provide recommendations for the use of a scanning DWL on a moving vessel. For completeness, we summarise below the context in which Kelvin-Helmholtz billows (KHBs) were observed, but refer the reader to for further details.

KHBs are wave-like structures caused by shear instability between air layers moving at different speeds . They typically form under hydrostatically stable conditions when vertical wind shear exceeds a critical threshold. This leads to dynamic instability and enhanced turbulent mixing, particularly vertical momentum transport. During the LOLLEX campaign, the scanning DWL on the CTV observed KHBs on several occasions. One of the clearest events occurred on 22 February 2023, between 12:30 and 13:00. The KHBs were captured in both the CNR and vertical velocity data, as shown in Fig. a and b. The time series reveals distinct KHB structures between 12:46 and 12:56 at altitudes ranging from 550 to 750 m. These structures evolved from small wave-like perturbations into billows that grew, overturned, and eventually dissipated. In the vertical velocity field, they appear as alternating zones of upward and downward motion.

Before the event, a bright and persistent CNR maximum is observed near 600 m (Fig. a). This maximum corresponds to aerosol accumulation beneath the capping inversion at the top of the stable boundary layer. Strong temperature inversions can suppress vertical turbulent mixing and limit dispersion, leading to the accumulation of aerosols below the inversion . Vertical wind shear due to the change from typical sub-geostrophic wind speeds in the ABL towards geostrophic winds in the free atmosphere above can create favourable conditions for Kelvin-Helmholtz instabilities.

The KHBs were advected across the lidar beam over approximately 11 min, and their passage caused vertical mixing. This mixing is visualised by the broadening and dimming of the CNR maximum, which progressively descended downward to around 400 m by 13:00. However, a local maximum in the CNR remained visible until 13:30, suggesting that elevated aerosol concentrations persisted at around 400 m altitude, even after the dissipation of the KHBs.

Coincidentally, the lidar measurements, located approximately 37 m downstream of the turbine, captured the effect of the turbine on the local flow field. This appears in the vertical velocity time series as a band of enhanced positive vertical velocity between 100 and 200 m height, visible between 12:35 and 13:12 (Fig. b). The spatial extent of the enhanced vertical velocity band indicates a rotor-induced streamline deflection in the near-wake region. This interpretation is consistent with previous studies of near-wake dynamics . SCADA data confirm that the turbine was operational during the observation period, with a nacelle orientation of approximately 167°, placing the lidar nearly directly downstream of the rotor.

The panel d and e of Fig.  show the vessel speed, roll, and pitch angles. Between 12:35 and 13:10, the CTV remained stationary with minimal roll and pitch. After 13:12, the vessel began moving away from the turbine, which led to a negative velocity bias in the WindCube100S data and the disappearance of the near-wake signature. The vessel speed increased to approximately 4 m s⁻¹ before becoming stationary again near 13:20, after which it resumed motion to a new location.

The observation of this KHB event revealed a significant increase in the variance of the vertical velocity component within a 400 m thick atmospheric slab, well above the region influenced by the turbine near-wake (Fig. c). In this case, no direct interaction between the KHBs and the wake was observed. However, such interactions may occur under different conditions, e.g. in a shallower ABL, within large wind farms where the internal boundary layer reaches the ABL top, or when KHBs form at lower altitudes, as briefly documented by . As highlighted by , the enhanced vertical mixing associated with KHBs, indicated by elevated vertical velocity variance, could accelerate wake recovery by entraining higher-momentum air downward. We therefore hypothesise that if KHBs overlap more directly with wind turbine wakes, they may enhance wake recovery under stable stratification. This hypothesis warrants further investigation.

Furthermore, when the CTV is in motion, the along-beam velocity data retrieved by the WindCube100S becomes significantly noisier, likely due to the combination of high translational speed and varying pitch and roll angles. This limits the instrument's ability to capture accurate velocity measurements and reduces the amount of usable data during periods of vessel motion. Consequently, operating the CTV in stationary mode is preferable when using scanning lidar for turbulence analysis, as it improves both the quality and availability of the retrieved data. Interestingly, the CNR data appear to be less affected by vessel motion. For instance, the dissipation of the KHBs into smaller wave-like patterns after 13:00 remains detectable beyond 13:10, even though the vessel was moving and the velocity data were considerably noisier. This highlights the utility of the CNR as a complementary data source, particularly under non-ideal motion conditions, for tracking coherent structures like KHBs.

The second case study documents observation of a local increase of vertical turbulence on the same day (22 February 2023). This increase may have been promoted through buoyancy-driven downward turbulent motion from the top of the ABL reaching down to approximately 200 m above the surface. These measurements were collected before the vessel entered the wind farm under south-east wind conditions. The sunrise and sunset times in Rødbyhavn on 22 February 2023 were 06:21 and 16:36 UTC, respectively. Thus, the start of the scan coincided with the sunrise. The CTV was stationary at the beginning of the case study and started moving at 07:12 UTC. Figure  presents the instantaneous profiles of CNR (a), vertical velocity (b), and the moving standard deviation of w (σw) (c).

To determine the ABL top in this case, in addition to the CNR profiles, the profiles of wind speed and σw obtained from lidar measurements are illustrated in Figs.  and  a, respectively. The wind speed profiles show a local maximum between 0.9 and 1.0 km from 06:35 to 06:47 before decreasing significantly above 1 km, whereas the σw profiles, do not show a clear minimum. The ABL top is therefore inferred primarily from the CNR signal and is estimated to lie between 0.9 and 1.0 km.

Within this layer, the WindCubeV2 and WindCube100S DBS measurements reveal a local wind-speed maximum of 6 m s⁻¹ near 200 m, with NORA3 showing a similar maximum of about 5.5 m s⁻¹ around 150 m (Fig. ). A strong negative wind-speed gradient occurs above this maximum. Consistent with this, the vertical wind velocity in Fig. b shows coherent regions of upward and downward motion emerging around 06:47 and persisting thereafter, indicating substantial vertical transport within the ABL. Prior to 06:47, the moving standard deviation of w (σw) is relatively uniform between 100 and 800 m, with weak turbulence (σw<0.2 m s⁻¹) (Fig. c). From 06:47 onwards, σw increases locally near 600 m and subsequently reaches values of approximately 0.5 m s⁻¹ between 400 and 600 m. The corresponding vertical profile of σw (Fig. a, between 06:47 and 07:00) also shows local increase of the vertical turbulent fluctuations at heights between 200 and 800 m above the surface.

Figure  also presents the vertical profiles of kurtosis (b), skewness (c) for three observational windows (06:35–06:47, 06:47–07:00, and 07:05–07:12), and the corresponding power spectral densities of w at 430 m (d). Prior to 06:47, the power spectral density Sw exhibits pronounced white noise at frequencies above 0.1 Hz, indicating that turbulence fluctuations are too weak to be reliably resolved by the WindCube100S scanning lidar. Between 06:47 and 07:00, the Sw spectra indicate improved detectability of turbulent fluctuations, although noise levels remain sufficiently high to partially obscure the effects of along-beam spatial averaging. After 07:05, vertical velocity fluctuations peak near 430 m, and the corresponding Sw spectrum shows reduced noise levels, with along-beam spatial averaging associated with the lidar probe-volume length becoming apparent at frequencies above 0.1 Hz, where the spectral slope steepens relative to the -5/3 inertial subrange. The pronounced spatial and temporal variability of σw reflects a non-stationary and vertically evolving boundary layer, suggesting the onset of downward transport from the boundary-layer top.

Although strong vertical shear is present and may contribute to shear-driven instability, this does not by itself demonstrate the presence of KHB. In our previous KHB observations , the billows were characterised by a clear narrow-banded spectral peak, a well-organised periodic pattern in the time series, and a persistent kurtosis peak. In the present case, by contrast, the power spectral density of w shows a broader increase in energy across a range of frequencies rather than a narrow-banded peak, and the time series of w and CNR do not display similarly organised periodic structures. In this case study, the negative skewness peak around 300 m was used as an indicator consistent with turbulence generated by cloud-top radiative cooling; however, a negative skewness peak was also present in the KHB case of , indicating that this feature is not specific to one mechanism. In addition, local increases in kurtosis have previously been used as indicators of coherent KHB structures . In the present case, a local peak occurs between 06:45 and 07:00, which could suggest intermittent coherent structures consistent with KHB, but it disappears during 07:05–07:12, even though σw continues to increase. This behaviour contrasts with the persistent kurtosis peak observed during the KHB event reported in . Taken together, these features suggest that KHB cannot be excluded, but that the event does not exhibit the clear spectral and temporal signatures of a classical, well-organised KHB case; it is therefore interpreted more cautiously as intermittent mixing and entrainment near the ABL top.

Furthermore, radiative cooling at the top of stratocumulus clouds may be a plausible mechanism for triggering the observed buoyancy-driven turbulence . The resulting turbulence propagates downward, contributing to enhanced entrainment near the top of the cloud-topped boundary layer. This region is typically characterised by strong gradients in humidity and temperature that favour mixing processes. Following , turbulence influenced by cloud-top radiative cooling is often associated with negative skewness above the surface layer. In the present case, negative skewness of w, reaching values as low as -0.7 at 300 m (Fig. c), is observed between 07:05 and 07:12. This localised negative peak is absent before 06:47, prior to the increase in σw, while skewness becomes moderately negative (down to -0.4) between 400 and 700 m during 06:47–07:00. However, a negative skewness peak was also observed during the KHB event documented in , indicating that this feature is not unique to turbulence driven by radiative cooling. Although the present observations are qualitatively consistent with turbulence initiated near the ABL top, the absence of thermodynamic measurements near the boundary-layer top prevents a definitive attribution to radiative cooling. At the same time, the strong vertical shear suggests that shear-driven instabilities may also contribute, and the dominant mechanism therefore remains uncertain.

These observations demonstrate that turbulent mixing can develop under stable conditions and redistribute vertical momentum over several hundred meters, even without convective forcing or clear classical coherent structures such as KHBs. The non-stationary turbulence and its vertical extent suggest entrainment initiated near the ABL top and propagated downward through combined shear and buoyancy effects. Such vertically distributed entrainment may facilitate wake recovery in a wind farm by promoting the downward transport of higher-momentum air. These findings highlight the value of combining scanning and profiling DWLs on vessels to investigate entrainment processes.

Case study 3 addresses observations of internal waves conducted in the harbour after the CTV returned from the offshore wind farm. The evening of 22 February was characterised by stable stratification, a wind speed of 10 m s⁻¹ at 100 m, a strong near-linear shear of approximately 0.06 m s⁻¹ m⁻¹ between 40 and 100 m (Fig. a) and a cloud cover above 600 m as indicated by the CNR profiles in Fig. a. As shown in Fig. a, the WindCube100S detected the presence of a low-level jet, with a maximum wind speed of 15 m s⁻¹ between 300 and 500 m above the surface. From 22:05 to 22:30, the lidar recorded wind conditions suggestive of internal atmospheric waves below the cloud-topped ABL. Such waves are often associated with the presence of low-level jets . In the present case, the observed wave-like motions may have been triggered by shear instability near the maximum of the low-level jet, where vertical wind shear was strongest.

Wave patterns begin to form at 22:16 and become visible in both the CNR, above 400 m, and the vertical velocity fluctuations from 200 to 600 m (Fig. a and b). These waves are not generated by wind farms and are therefore distinct from the so-called farm-generated gravity waves . When internal atmospheric waves, including gravity waves, form upstream of a wind farm and at a height low enough to interact with the farm's internal boundary layer, they may enhance wake recovery by amplifying mixing and wake meandering .

Figure  shows the vertical structure of these oscillations, which span approximately 200 m in height. The wave-like motions are visible both in the instantaneous vertical velocity (panel b) and the corresponding standard deviation (panel c). The internal wave structure coincides with the nose of the low-level jet. A spectral analysis of the vertical velocity at 200, 400, and 600 m revealed a dominant periodic signal with a 2 min cycle during the wave event, as shown in Fig. b and c. The observed phase shift between altitudes suggests that vertical wind shear strongly influences the wave structure. No distinct spectral peak is observed prior to the occurrence of the waves (Fig. b), indicating the absence of wave activity during this earlier period. During the wave event (22:15–22:30), pronounced spectral peaks appear between approximately 200 and 600 m, consistent with the oscillations visible in the time series in Fig. c. After 22:30, clear spectral peaks remain visible between approximately 350 and 600 m, while no pronounced peak is observed at 200 m, suggesting that the wave packet initially reaches 200 m but later remains confined to higher altitudes near the nose of the low-level jet.

The spectral peak falls within the mesoscale range rather than the typical turbulence range, and is therefore more consistent with internal atmospheric waves than with turbulent eddies.

The observed period places these waves at the lower end of the internal gravity wave spectrum. For comparison, reported oscillation periods between 6.5 and 18 min in coastal terrain, while observed shear-driven gravity waves with periods exceeding 10 min. According to , internal gravity wave periods typically range from 1 to 30 min, indicating that the 2 min period observed here is short but still within the expected range.

As shown in Fig. c, the local increase in the standard deviation of vertical velocity extends to heights below 200 m, even though the CNR indicates that the wave-like pattern is strongest around 500 m. Given the proximity of the measurement site to the coast and its distance of about 20 km from the nearest offshore wind farm, it is possible that similar wave-like motions could occur above the wind farm itself. If so, such waves could enhance wake recovery by amplifying vertical momentum entrainment into the farm.

The previous case studies, along with this one, demonstrate the ability of scanning and profiling DWLs to capture dynamic processes in the ABL, including momentum entrainment associated with internal waves. However, limitations remain for a complete characterisation of internal atmospheric waves. In particular, the absence of co-located temperature and humidity measurements restricts our ability to study the stratification of the atmosphere in detail and, therefore, to identify the dominant wave generation mechanisms. While wind speed profiles confirm the presence of a low-level jet and support the interpretation of shear-induced wave activity, additional observations would be needed to distinguish between shear- and buoyancy-driven processes.

Moreover, although reanalysis products such as NORA3 could be used to estimate atmospheric stability (e.g., via the Bulk Richardson number), their temporal and spatial resolution is limited compared with the scales of the observed processes. A more robust assessment would require co-located, high-resolution profile measurements of temperature and humidity, e.g. by a passive microwave radiometer , a Raman lidar , or an infrared temperature profiler . To obtain such measurements, a HATPRO RG4 profiler was installed at Rødsand harbour at the beginning of the campaign. Unfortunately, the instrument was malfunctioning, and no usable data could be obtained.

This case study presents preliminary results from RHI scans performed by the long-range scanning lidar installed on the transformer platform north of the Rødsand II wind farm. The limited joint data availability from the floating WindCubeV2 lidar and the platform-mounted lidar prevented a systematic analysis; however, a few representative cases can still be highlighted.

Case study 4 corresponds to an easterly mean flow observed by the platform-mounted lidar on 13 June 2023 between 12:11 and 12:25. At 100 m, the WindCube V2 lidar measured 9.2 m s⁻¹, about 3 m s⁻¹ lower than the NORA3 estimate of 12.1 m s⁻¹. This further indicates that the lidar measurements were affected by wind farm-induced velocity deficits, unlike NORA3, which does not account for the presence of the wind farm. At 100 m, NORA3 indicates a mean wind direction of 71°, compared with 69° measured by the WindCube V2 lidar.

In the PyWake simulations, the ambient vertical wind-speed profile is prescribed directly from NORA3, while the wind direction is taken as a single value obtained by interpolating the NORA3 wind-direction profile at hub height. Data from the WindCube 100S were not available during this period. At the time of the observations, the CTV was located on the southeastern side of the wind farm (Fig. ), implying that the areas scanned by the platform-mounted lidar and the WindCubeV2 lidar were not collocated.

The NORA3 vertical wind-speed profile and the hub-height wind direction derived from NORA3 were used as input to the PyWake model for wind-farm flow simulations. Since NORA3 does not account for the presence of the wind farm, it provides an estimate of the undisturbed upstream flow, whereas the WindCubeV2 lidar measurements are affected by turbine and wind-farm wakes. PyWake was therefore used to simulate wind-speed profiles at the location of the WindCubeV2 lidar using different wake deficit models. In addition, virtual RHI scans were generated to mimic the measurements from the scanning lidar on the transformer platform. These virtual scans reproduce vertical slices of the mean along-beam velocity component as observed by the lidar.

The comparison serves two main purposes. First, it provides a novel approach to assess the performance of wake deficit models implemented in analytical wake modelling frameworks. Second, it enables a qualitative evaluation of the lidar measurements, i.e. to verify whether the observed wake structures are consistent with simulations.

It should be noted that NORA3 does not necessarily provide a perfect estimate of the true upstream wind conditions. Discrepancies between model predictions and observations may therefore arise from several sources, including measurement noise, limitations of the wake models in representing real atmospheric conditions, or inaccuracies in the initial and boundary conditions derived from NORA3. For the purpose of comparing wake deficit models, these sources of uncertainty are of secondary importance, as all simulations rely on the same NORA3 input and are evaluated against the same reference measurements.

In PyWake, the PropagateDownwind wind farm model was adopted, in which wake effects are computed by propagating the influence of upstream turbines downstream and superimposing their wake deficits onto the undisturbed inflow. This formulation neglects upstream blockage effects, which were therefore not considered. A set of analytical wake deficit models was evaluated under identical inflow conditions, including NOJ , TurboNOJ , BastankhahGaussian , NiayifarGaussian , ZongGaussian , TurboGaussian , and GCL . For Gaussian-based wake deficit models, a mirror ground model was used to account for sea-surface reflection. Wake superposition was treated using a squared-sum approach, and wake-added turbulence was modelled using the Crespo-Hernandez formulation , assuming a uniform ambient turbulence intensity of 0.07, representative of typical offshore conditions .

The inflow was prescribed using a UniformSite with a user-defined vertical wind-speed profile obtained by interpolating the NORA3 wind speeds as a function of height. The wind direction was prescribed as a single value obtained by interpolating the NORA3 wind-direction profile at hub height. Simulations were performed for the combined Rødsand II and Nysted wind farm layouts, implemented from measured turbine position data. All turbines were represented using a generic Siemens SWT-2.3-93 turbine (rotor diameter 93 m, hub height 69 m), with power and thrust coefficients prescribed from tabulated curves. No yaw misalignment, wind veer, or wake deflection effects were considered.

For each wake deficit model, the simulated flow field was sampled in two configurations. First, vertical profiles of the mean wind speed were extracted at the position of the floating WindCubeV2 lidar. Second, virtual RHI scans were generated by sampling the flow field in a vertical plane aligned with the scanning geometry of the platform-mounted lidar. The along-beam velocity was reconstructed by projecting the simulated horizontal wind vector onto the lidar line-of-sight, thereby neglecting any mean vertical velocity component. Differences between the present results and those reported by may partly arise from differences in wake model selection, configuration, and the treatment of wake superposition and turbulence.

Figure  shows the vertical profile of the mean wind speed above the CTV during case study 4. The WindCubeV2 lidar profile exhibits negative wind shear below approximately 60 m and positive shear above, which is characteristic of waked flow. This is consistent with the horizontal flow field in Fig. , which places the vessel within a waked region.

The PyWake simulations in Fig.  show that most wake deficit models underestimate the observed wake losses, resulting in higher wind speeds than measured by the V2 lidar. Only the TurboGaussian model provides close agreement with the observations. Although based on a single case, this result is consistent with , who reported that commonly used analytical wake models underestimate wake deficits and overestimate wake recovery between the Rødsand II and Nysted wind farms, but did not include the TurboGaussian model. The TurboGaussian model, closely related to Ørsted's TurbOPark concept, produces stronger far-wake effects; in the present simulations, it yields longer wake extents and larger velocity deficits than the other Gaussian-based models, leading to improved agreement with the lidar observations.

Figure  compares the 14 min mean along-beam wind velocity measured by the platform-mounted scanning lidar during an RHI scan on 13 June 2023 at 12:11 with corresponding virtual RHI scans obtained from PyWake simulations. The comparison is performed using an averaged flow field, consistent with the steady-state assumption of the PyWake simulations. Both measurements and simulations reveal multiple turbine wakes.

Both measurements and simulations capture wakes from individual turbines within the Rødsand II wind farm. The simulations primarily resolve three distinct wakes, while Fig.  suggests that the flow may also be influenced by additional far-wake contributions from the upstream Nysted wind farm. Such farm-to-farm interactions are known to enhance wake losses at Rødsand II ; however, this contribution cannot be unambiguously isolated in the RHI scans of the platform-mounted lidar. In Fig. , the wake of the nearest turbine, located approximately 0.7 km from the lidar, is clearly identified in both measurements and simulations. The alignment of subsequent wakes, around 1.0 km downstream, is slightly less consistent between simulations and observations. In particular, a third wake is predicted by the simulations but is not clearly visible in the measurements, likely due to measurement noise.

Discrepancies between simulated and observed wake structures can arise from several factors. Small variations in wind direction can significantly shift wake positions in virtual RHI scans when NORA3 is used to prescribe the inflow. Additional sources of mismatch include wind veering , yaw misalignment due to turbine control, and large-scale effects such as the Coriolis-induced deflection of the Nysted farm wake . Differences in wind speed between simulations and measurements are further influenced by uncertainties in the upstream inflow. During the campaign, upstream conditions were not systematically measured, as vessel-mounted lidars were often located in sheltered harbour environments or within the wind farm. Although NORA3 provides a practical inflow estimate, it may be less reliable under moderate and weak wind conditions. In periods of strong winds, when the vessel could not operate within the farm, wake validation relied solely on platform-based lidar observations.

Overall, several thousand RHI scans were collected during the campaign, providing a unique dataset for the validation of analytical wake models at Rødsand II. While the present qualitative comparison suggests that the TurboGaussian (TurbOPark-type) model performs well for this case, further work is required to better characterise inflow conditions, for example using SCADA data, and to extend the analysis to multiple cases. Future work should include systematic quantitative error metrics, such as root-mean-square error or bias, applied to both RHI scans and vertical wind speed profiles to identify the most suitable wake deficit models.