Wind observation and power production data have been collected from two wind parks, wind park A and wind park B, located on the large island Kvaløya in northern Norway. Figure  shows the location of the wind parks and the surrounding terrain. The topography in the surrounding area is characterised by fjords, straits, and islands, as well as mountains, with elevations ranging from sea level (brown) up to 1800 m above sea level (m a.s.l.) (light blue). The prevailing wind direction in the wind parks is from the southeast (SE), and the observed yearly mean wind speed, prior to the wind park development, was 7.86 and 7.39 m s⁻¹ at 80 m above ground level (m a.g.l.) at A and B, respectively . The SE wind direction is particularly common during the winter months, when the cold inland climate and relatively warm North Atlantic Ocean current give rise to a pressure gradient in the east–west direction and a strong land breeze . In addition, during winter, high-pressure systems building up over land, in combination with low-pressure systems frequently present over the North Atlantic Ocean , can further reinforce the pressure gradient and the wind field. Mountain waves are expected to occur more frequently during the winter months, when the stability in the lower part of the atmosphere is typically relatively strong at these latitudes . Stably stratified air, approaching the coast from the east and southeast, will be affected by the topography and form complex wind patterns such as wakes, gap winds, mountain waves, and strong downslope winds . The operator of the wind parks frequently experiences strong winds on the lee side of the mountain during periods of wind from the SE, although this has not yet been documented scientifically (Andreas Schmid, personal communication, 2021).

Figure  shows a close-up view of the wind parks and the topography, with dark green indicating sea level and yellow indicating altitudes up to 560 m a.s.l. The black dots and squares indicate the locations of the wind turbines that in total cover an area of approximately 7 km × 7 km. Wind park A (dots) consists of 47 wind turbines, evenly distributed over the mountain at elevations ranging from 300 to 557 m a.s.l. Wind park B (squares) consists of 20 turbines distributed in row-like formations at elevations ranging from 359 to 514 m a.s.l. The wind turbines are of the type Siemens SGRE-DD-130, with a rotor diameter of 130 m, a hub height of 85 m a.g.l., and a rated capacity of 4.2 MW. Observation data with a 10 min resolution between 4 September 2020 and 24 January 2021 have been used in this study, including wind speed and wind direction taken at hub height, as well as the power production from each turbine.

In order to study how these particular wind parks are affected by mountain waves, only hub height winds from the SE are considered, more specifically wind from the 120–165° sector. This is the prevailing wind direction in the wind park and the direction from which strong downslope winds are expected to occur frequently. The selection of time slots where the wind comes from the SE is based on the observations at the turbines and is referred to as SE events. For a time period to be considered an SE event, the wind direction observed at 40 turbines or more must be within the selected wind sector. In addition, only periods that last for more than 4 h are considered, and if a period lasts for more than 48 h, the first 24 h is considered to be a separate event.

The marked areas in Fig.  show selected clusters of wind turbines that, under SE wind directions, are located upstream of the mountain top (A1 and B1), at the mountain top (A2 and B2), and downstream of the mountain top (A3 and B3). For the purpose of this study, the mean values of the wind speed, wind direction, and power production of each turbine cluster are considered. By evaluating the mean values of the wind turbines within each cluster, instead of values from single turbines, the impact from small local topographic effects is reduced. In the case studies in Sect.  and , wind and power data from each of the 67 turbines of the wind parks are included.

The formation and development of mountain waves depend on the atmospheric conditions upstream of the mountain. In order to evaluate the state of the atmosphere upstream of the study location, and as an alternative to in situ observations, meteorological parameters have been retrieved from the fifth-generation atmospheric reanalysis (ERA5) provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) . The global reanalysis is produced by combining weather observations with numerical weather prediction modelling. With a spatial resolution of approximately 31 km and hourly output, ERA5 provides detailed information on the evolution of the atmosphere. Relevant meteorological parameters at the 137 vertical model levels of ERA5 have been retrieved at the model grid point location indicated by a P in Fig. .

The Scorer parameter indicates how a mountain wave develops depending on the atmospheric stability and the wind speed and is given by the following equation: 1l(z)2=N(z)2U(z)2-1U(z)d2U(z)dz2, where the Brunt–Väisälä frequency N(z) and the wind speed U(z) are a function of the altitude z. The Scorer parameter is calculated at each ERA5 model level. The horizontal wind speed is decomposed such that only the wind speed in the SE wind direction of 135° is considered and is referred to as the tangential wind speed. For simplicity, the curvature term has been omitted in the calculations, so l(z)≈N(z)/U(z). When the Scorer parameter l decreases strongly with height, the formation of trapped lee waves can be expected . Favourable conditions for vertically propagating mountain waves are found when l is nearly constant with height. A Scorer parameter that increases with height indicates conditions allowing for the mountain wave amplitude to grow until breaking occurs. If l increases abruptly with height, as when the cross-barrier flow becomes zero, or reversed, a critical layer exists where vertically propagating mountain waves can be absorbed and reflected, causing strong downslope winds.

Another parameter frequently used to describe the development of mountain waves is the non-dimensional mountain height denoted H^. This parameter combines the cross-barrier wind speed U, the mountain height h0, and the stability, in terms of the Brunt–Väisälä frequency N, as follows: 2H^=h0NU.

If the non-dimensional height H^≪1, the flow will pass easily over the mountain. However, there will not be any wave breaking that causes strong downslope winds. In contrast, if H^≫1, a stagnation point will occur on the windward side, and the flow will be blocked and deflected around the mountain. When H^∼1 and the flow is normal to the mountain ridge, a stagnation point is formed above the mountain, where the horizontal wind is much lower in comparison to the wind at lower levels, causing the vertically propagating mountain waves to break .

The theory of the non-dimensional mountain height was developed primarily for idealised flows, in which U and N are constant with height. Real-world flows will typically display vertical variability in wind speed, wind direction, and stratification; consequently, U and N must be approximated as constant with height . Despite the limitations of the concept, H^ is widely used to indicate real-world flow behaviour (e.g. ; ). In this study the Brunt–Väisälä frequency is estimated by the following bulk method: 3N=gθΔθΔz, where θ is the potential temperature. It is assumed that the mountain will have an impact on the stable layer closest to the mountain top, and this layer is taken to have a depth of about 1 km, based on the typical stable layer in the selected cases. Δθ and Δz are therefore calculated between the lowest ERA5 model level (about 310 m a.s.l.) and model level number 120 (varying between 930–1000 m a.s.l.), noting that the ECMWF model levels are numbered from the model top downward. The potential temperature θ in Eq. () and the tangential wind speed U in Eq. () are calculated using model level number 127. With heights varying between 553–586 m a.s.l., the model level number 127 is the level closest to the real height of the mountain of wind park A. The mountain height h0 is set to 550 m, according to the real terrain within the A2 turbine cluster (Table ).

Additional non-dimensional parameters describing mountain wave characteristics are the vertical aspect ratio h0/L and the hydrostaticity parameter NL/U, where L is the half width of the mountain. These are metrics describing whether the wave developing will be within the hydrostatic or non-hydrostatic regime. Mountain waves only exist when NL/U>1. For NL/U≫1, vertically propagating waves dominate with minimal wave motion downwind .

For the purpose of this study, the WRF model version 4.3 is configured to include three two-way nested domains, D01, D02, and D03, with horizontal resolutions of 10.5 km, 3.5 km, and 700 m, respectively. The locations of the domains can be seen in Fig. . D01 and D02 consist of 101×101 and 112×112 grid points, respectively. D03 consists of 121 grid points in the north–south direction and 146 grid points in the east–west direction. Static fields with 30 arcsec resolutions are applied. The static fields are retrieved from the NCAR database and provided by the 20-category Moderate Resolution Imaging Spectroradiometer (MODIS) and the Global Multi-resolution Terrain Elevation Data 2010 (GMTED 2010). Table  summarises the real range of elevations within each turbine cluster of wind park A, along with the corresponding model elevations in D03. The vertical structure of the model consists of 51 terrain-following sigma levels, with the lowest five levels located below 100 m a.g.l. and the upper boundary at 50 hPa. The model is configured without Rayleigh damping.

The physical configuration of the model consists of the Thompson microphysics scheme , the Rapid Radiative Transfer Model for Global applications (RRTMG) scheme for long- and shortwave radiation , the MYJ surface layer scheme , the Unified Noah Land Surface Model , the Mellor–Yamada–Nakanishi–Niino (MYNN) planetary boundary layer scheme , and the Tiedke cumulus parameterisation scheme . For D03, the cumulus scheme was turned off due to the high resolution to allow the model to resolve the convective processes explicitly. Wind turbine parameterisation is applied by the Fitch scheme . The power curve and thrust coefficient included are specific to the wind turbines in the park, with a default correction factor of 0.25, as suggested by .

The ERA5 global reanalysis is used as initial and boundary conditions for the simulations. The simulations are run for 8 d, with the first 12 h considered spin-up time. The next 12 h of the simulation period has been interpolated with the last 12 h in the previous simulation to allow for smooth overlap of the time series. The simulations cover the period from 4 September 2020 to 24 January 2021. The wind data are retrieved 85 m a.g.l. by vertical interpolation of the model levels and from the given turbine locations by horizontal bilinear interpolation between the grid points. Similar to the observations, the cluster wind values and power production are the mean values of each parameter at the turbines within each cluster.

This section investigates the relationship between the upstream weather conditions at location P (Fig. ), calculated from ERA5 data, and the accelerated downslope winds in wind park A. The Scorer parameter and how this parameter changes with height indicate which type of mountain wave will develop during a mountain wave event. A cross-mountain wind decreasing with height, i.e. a reversed wind shear, is a condition where the Scorer parameter increases with height (Eq. ). In addition, if the cross-mountain flow becomes zero and further reversed, the Scorer parameter goes to infinity with increasing height. Figure  illustrates the vertical profile of the tangential ERA5 wind speed at point P averaged over all SE events, with the tangential wind speed being the component of the horizontal wind in the SE direction. It is apparent that there is on average, for all 67 SE events, a reversed wind shear from about 900 m a.s.l. in the cross-mountain flow and a mean state critical layer at just below 8000 m a.s.l. This distinct signature in the upstream large-scale wind profile is quite striking and indicates upstream weather conditions in which mountain waves may either grow sufficiently to break and form a so-called “self-induced” critical level or propagate vertically, until they break at the mean state critical level. It is expected that the vertical wind profile will vary between the different events.

Figure  illustrates the relationship between the downslope winds at A3 and the non-dimensional mountain height H^. The y axis shows the A3 wind speed values normalised with respect to the wind speed at A2. The cluster wind speeds are the mean value of the observed nacelle wind speeds at the three turbines within each cluster, as defined in Sect. . A normalised wind speed above 1 means the wind speed is higher at the lee side than at the mountain top. The x axis shows the values of H^ calculated from ERA5 data extracted at the upstream location P. The green dots show the hourly values, while the thicker blue dots represent the same values averaged over the period of each SE event. During the SE events studied, the wind speeds at the lee side of the mountain are typically stronger than the wind speed at the mountain top. When considering the hourly values of all SE events, the wind speed at A3 is higher than at A2 80 % of the time. In addition, 18 % of the time, the wind speeds are 1.5 times higher or more at A3 compared to A2. The non-dimensional mountain height varies mainly between 0 and 5 during the SE events considered. In addition, there are 10 sporadic timestamps (green dots) with H^ values above 5 that are not included in the figure. As H^ increases from zero to a value of about 1.5, there is a tendency of an increasing normalised wind speed. When H^ increases further, the normalised wind speeds decrease. As H^ increases above 3, the normalised wind speeds are typically below 1. These results correspond well with previous studies, such as and . studied idealised airflow over a mountain barrier and found that for H^ lower than 0.25, mountain waves are created over the barrier, but no wave breaking is present, resulting in only slight enhancement of the wind speed downstream of the barrier. When the wind speed is increased such that H^ equals 1.4, the wave breaks over the ridge and the wind speed increases in a narrow zone downstream of the barrier. In , there is partial upstream blocking for H^=2.8 and full upstream blocking for H^=5.0. The current study shows a similar pattern with lower wind speeds at A3 than at A2 for H^ above 3 according to Fig. , indicating upstream blocking and less air over the mountain. found similar H^ values for wave breaking in idealised flow over an obstacle. However, at what H^ value the wave breaking first occurred also depended on the vertical aspect ratio. For aspect ratios of 0.1 and 0.05, wave breaking occurred when H^=1. For vertical aspect ratios outside of this range, wave breaking did not occur before H^=1.25 . Along the SE direction, the mountain of wind park A is approximately 12 km wide at sea level, corresponding to a half width of 6 km and a vertical aspect ratio of about 0.09. The hydrostaticity parameter, given by NL/U, is estimated to be above 4 for all SE events and hence within the hydrostatic regime where waves propagate nearly hydrostatically.

Figure  displays a strong relationship between H^ and the A3 wind speeds, and for this particular wind park, the non-dimensional mountain height is to some extent able to indicate when to expect enhanced lee side winds due to mountain waves and when to expect lower wind speeds on the lee side of the mountain. The single parameter calculated from readily available meteorological data can hence be useful both in planning and for power prediction purposes. One reason the results appear to agree reasonably well with the theory may be that the lower-resolution ERA5 data, as opposed to local observations or high-resolution WRF simulations, provide a mean state of the atmosphere free of local terrain effects at location P. The apparent relationship between H^ and the A3 wind speeds suggests that breaking of internal gravity waves is the dominant mechanism responsible for the strong downslope winds in wind park A.

Although the result of this study indicates a relationship between H^ and the downslope winds at A3, the results should be interpreted with caution. In particular, the approximation of a constant Brunt–Väisälä frequency is not straightforward, as demonstrated by . applied two common approximations for N, referred to as the averaging method and the bulk method, to multiple cases with vertically nonuniform stability. Neither of the two methods provided a single best method to estimate a constant N. However, compared to the averaging method, the bulk method provided a better prediction of whether a flow will pass over the mountain or around it. To account for the uncertainty in estimating N and U, sensitivity analyses are performed. As described in Sect. , N is estimated using the bulk method in Eq. () between the ERA5 model levels spanning the surface up to a height of about 1 km. The sensitivity in the approximation of N is tested by changing the upper level to heights of about 855 and 1172 m a.s.l. The results (not shown) appear to be only weakly sensitive to the choice of the upper vertical level used to calculate N, with the overall findings remaining consistent. U in Eq. () is approximated from the single ERA5 level closest to the mountain peak (about 580 m a.s.l.). The sensitivity to the approximation is evaluated by calculating U at heights slightly below (500 m a.s.l.) and above (677 m a.s.l.) mountain top level. The results (not shown) are only weakly sensitive to the choice of the model level.

The sensitivity to upstream geography is tested by dividing the SE wind sector into two smaller sectors. In the first sector (120–140°), the nearby upstream terrain is characterised by several high mountains (Fig. ). In the second sector (140–165°), the airflow approaches the wind parks rather undisturbed through a long fjord. The distinction between the two sectors is made based on observed wind directions from one of the A2 turbines. Figure a shows the results for the first sector and Fig. b for the second sector. Within the first sector, there is a tendency of increasing normalised wind speeds as H^ increases towards 1; however, similar to Fig. , there are some deviating wind speed values for H^∼ 1. Within the second wind sector, the relationship between H^ and the normalised A3 wind speed appears to agree better with the theory, with less spread in the normalised wind speeds when H^∼ 1 and no normalised wind speed values below unity for H^<1.6. Figure b supports our view that one of the reasons why the rather simple theory of the non-dimensional mountain height appears to hold to some extent in this real-world case, as opposed to an idealised model, may be the long and well-defined fjord that channels the wind from location P towards the mountain.

Although many of the events appear to be consistent with the theory, there are also several events that deviate. This is not unexpected, as the concept of the non-dimensional mountain height is developed based on linear flow with approximately uniform U and N. However, the apparent relationship between the non-dimensional mountain height and the A3 wind speeds is encouraging. Future work should address additional metrics, such as the Froude number, developed based on hydraulic theory. In addition, future research should test whether a similar relationship exists in other wind parks located in comparable terrain.

The impact of mountain waves and strong downslope winds on wind power production is evaluated in terms of the wind speed distribution and the power production at the three wind turbine clusters. These results include only wind and power production for the SE events selected as described in Sect. . Figure a shows the variations in the observed wind speed distribution between clusters A1 (blue), A2 (green), and A3 (red) when only the SE events are included. The histogram bins have been divided into intervals of 0.5 m s⁻¹ along the x axis, and the frequency on the left y axis is given in 10 min values that have been converted to hours. In order to allow for a comparison of the wind speeds and the potential power production, the power curve for the turbines has been included in the same figure (black dashed line) with power along the right y axis. The power curve consists of four power curve zones (PCZs): PCZ1, with wind speeds below the cut-in threshold and no power production; PCZ2, with wind speeds between the cut-in wind speed and the rated wind speed, i.e. where the power increases from zero and up to the rated power; PCZ3, where the turbines operate at rated power until cut-off wind speed; and PCZ4, the zone where the turbines are shut down due to high wind speeds. For the turbines in these particular wind parks, the cut-in wind speed is at 3.0 m s⁻¹, the cut-off wind speed is at 28.5 m s⁻¹, and the rated wind speed is 14.5 m s⁻¹.

The A3 wind cluster has a higher frequency of wind speeds favourable for wind power production in comparison to A1 and A2. While the A1 and A2 wind speed distributions have similar shapes, shifted towards the left, with peaks at approximately 6 and 7 m s⁻¹, respectively, the A3 wind speeds are more evenly distributed, with a peak around 11 m s⁻¹. At A1 and A2, the frequency of wind speeds within PCZ2 is considerably higher than at A3. Consequently, the A1 and A2 turbines operate below the rated power more often compared to A3. In addition, small variations in wind speed within PCZ2 result in large variations in power production. At A3, on the other hand, the frequency of wind speeds within PCZ3 is considerably higher than at A1 and A2; hence the A3 turbines will more often operate at their maximum power. In addition to the enhanced power production on the lee side of the mountain of wind park A, the same wind turbines record wind speeds above the cut-off threshold and below the cut-in threshold more often than the turbine clusters upstream. The large difference in the wind speed distribution between A3 and the two other clusters has a clear impact on wind power production and is expressed through the capacity factor Cf in Table . The capacity factor is a parameter commonly used to evaluate how well sited a wind turbine is and is defined as the ratio of the actual energy produced to its maximum possible energy output over the same period. For the purpose of this study, Cf is calculated from the power produced during the SE events only. The A3 turbines operate considerably closer to their maximum in comparison to the turbines in the other two clusters. During the selected SE events, the A3 turbines produce 51 % and 21 % more energy than the A1 turbine and A2 turbines, respectively.

Similarly, the wind speed distributions (not shown) for the three clusters in wind park B, as indicated in Fig. , reveal a higher frequency of higher wind speeds on the lee side compared to the upstream turbines, although the difference between the clusters is not as pronounced as in wind park A. The capacity factor in Table  reflects the spatial variations within wind park B, with Cf being the highest at B3 and the lowest at B1.

The result of this study emphasises the importance of an extensive understanding of the wind flow in complex terrain during various atmospheric stability conditions, both in the planning phase and for wind power production forecasts. Although there were no observations of severe wind speeds in these particular wind parks during the study period, downslope windstorms can result in severe and occasionally damaging wind speeds, large wind speed fluctuations, and turbulence and wind gusts and should therefore be considered in the planning phase.

The ability of the WRF model to reproduce the observed wind patterns in the wind parks is evaluated in terms of the mean features during the SE events, such as the wind speed distribution, the mean wind speed, and the capacity factor calculated over the same periods. In addition, the ability of the model to reproduce the temporal pattern of the observations is evaluated in terms of the mean absolute error (MAE) and the correlation coefficient (R). These statistical parameters and the bias are also provided in Table  and are calculated as described in . In addition, the ability of the WRF model to reproduce the wind directions during the SE events is evaluated in terms of wind roses (not shown) for all nine turbines within the clusters in wind park A. WRF is able to reproduce the wind directions with only small deviations from the observations.

In agreement with the observations, the simulations show a higher mean wind speed at the lee side of the mountain (A3) compared to the mean wind speeds at the mountain top (A2) and at the upstream location (A1). When evaluating each turbine cluster separately, the wind speed bias indicates that the model tends to overestimate the wind speeds at A1, while underestimating the wind speeds at A2 and A3. The negative bias at A3 is considerably larger than at A2. The larger negative bias at A3 suggests that the model is not fully able to reproduce the accelerated downslope winds. The WRF model is also able to reproduce the spatial variations in power production, with the highest Cf at A3 and the lowest Cf at A1. Although the model is, to some extent, able to reproduce the relative power production of the three turbine clusters, the increase in Cf from A1 to A2 and A3 is not as pronounced as what is seen in the real Cf. Similar wind speed biases are found in the clusters of wind park B. Although the model is able to reproduce the higher mean wind speed at B3, compared to B2, WRF is not able to reproduce the increase in Cf from the B2 cluster to the B3 cluster.

When comparing the temporal patterns of the simulations and observations, the MAE is the lowest at A1, higher at A2, and the highest at A3. The correlation coefficient is the highest at A1 and the lowest at the A3 cluster. Wind park B exhibits similar patterns in MAE and R (Table ), with higher error and lower correlation at B3 compared to the turbine clusters upstream. The reduced accuracy in the temporal pattern at the lee side turbines is also seen in the study by and can be linked to the increased complexity of the wind patterns from the windward side to the lee side due to mountain waves. The MAE and the R of the current study are of similar values as in previous studies conducted in the same area . In addition, the MAE and the R in the current study, with a 700 m horizontal grid resolution, are slightly improved compared to what was found in the 1 km simulations by at the same location. However, the results are not directly comparable due to differences in the model configurations and study periods.

Figure b presents the wind speed distributions of the simulated wind speeds at the three turbine clusters in wind park A. The WRF model is able to reproduce the observed differences between the A3 wind speed distribution and the distributions of the other two clusters. In agreement with the observations, there is a high occurrence of wind speeds above 12 m s⁻¹ at A3, including wind speeds above the cut-off threshold, while at A1 and A2 there is a lower occurrence of the same wind speeds. The higher occurrence of the PCZ3 and PCZ4 wind speeds at A3 compared to A1 and A2 indicates that the model is able to simulate the formation of mountain waves above the wind park causing the accelerated winds on the lee side of the mountain. For the lower wind speeds, below the cut-in threshold, the model succeeds in reproducing the higher occurrence of these wind speeds at A3 compared to A1 and A2. This result suggests that the model is also able to reproduce periods where the airflow is blocked by the mountain and diverted around.

Although the model is able to reproduce the distinct wind speed distributions observed at the three clusters, the distributions also reveal some shortcomings in the ability of the model to accurately reproduce the complex wind patterns in the wind park. For instance, the differences between the simulated wind speed distributions of the three clusters are not as pronounced as they are in the observations. In particular, the A1 and A2 wind speed distributions appear to be more similar in comparison to the observed wind speed distributions at the same locations. When comparing the simulations with the observations at the A3 cluster, it is apparent that the model underestimates the high occurrence of the PCZ3 wind speeds. The underestimations of these higher wind speeds suggests that the model is not fully able to reproduce the frequency and the strength of the downslope windstorms. It is worth noting that for the highest wind speeds at A3, above the cut-off threshold, the simulated wind speeds are more accurate. At A2 the simulated wind speed distribution skews left in comparison to the one of the observations. In particular, the model overestimates the frequency of the lower wind speeds and underestimates the higher wind speeds. At A1, the model considerably underestimates the lower PCZ2 wind speeds, while overestimating the occurrence of the wind speeds within the PCZ3. The shift in the simulated wind speed distribution, with under- and overestimation in PCZ2 and PCZ3, respectively, agrees well with previous studies conducted in the same area . However, for the lower wind speeds, below the cut-in threshold, the model overestimates the frequency at all three turbine clusters. A similar overestimation of the lower wind speeds is not seen in the studies of and .

Several factors may impact the accuracy of the model simulations. For instance, found that small variations in the initial conditions led to substantial differences between forecast ensembles of downslope windstorms, including qualitative differences in the characteristics of the upper-level wave breaking, as well as in the strength of the downslope winds, while highlighted the importance of micro-physical processes in the formation of downslope windstorms. The accuracy of numerical simulations of downslope winds is also highly sensitive to the accuracy of the roughness length, land use, and surface friction parameterisation .

A higher horizontal resolution, hence, a better representation of mountain peaks in particular, is also expected to improve the accuracy of simulated meteorological metrics during mountain wave events . Although the mountain peaks appear to be sufficiently represented in the model (Table ), a higher resolution could improve the representation of the terrain, as well as some smaller-scale terrain features that are missing in the model and may impact the accuracy of the simulations. In addition, the terrain model used to configure WRF has a resolution of 30 arcsec and is part of the default setup of the WRF model. However, higher-resolution terrain models are available and could potentially improve the terrain representation in D03.

For the purpose of the current study, the horizontal resolution is carefully selected to balance the benefits of higher-resolution details with the constraints imposed by the Fitch wind farm parameterisation, which recommends a grid size of at least 5 rotor diameters . For this particular study, given that the mountains of the wind park are approximately 10 km across, a 700 m grid resolution, corresponding to an effective resolution of 7×Δx≈ 4.9 km, may not adequately resolve the mountain-induced flow perturbations. Perturbations, such as mountain waves, on scales smaller than the effective resolution are damped and likely contribute to the model not being able to reproduce some of the observed variability in the wind . Future studies should evaluate the potential benefits of a finer grid resolution, though this would require reconsideration of the turbine representation.

Another factor impacting the wind flow within the park is the wakes created by the wind turbines. Studies suggest that under stable conditions, the strength of the wakes is higher and the recovery slower than during unstable and neutral conditions . For the purpose of the current study, the Fitch wind farm parameterisation scheme is employed in the model to allow for the impact from the wind turbines on the simulated wind flow. However, the accuracy of wind power parameterisation schemes under stable atmospheric conditions is not thoroughly explored. For instance, found that when comparing mesoscale simulations with large-eddy simulations, the Fitch scheme exhibits larger deviations under stable atmospheric conditions than during neutral or unstable atmospheric conditions. In addition, the Fitch scheme does not take into account mechanical and electrical losses, resulting in an overestimation of the turbulent kinetic energy (TKE) generated by the turbines in the model . In order to reduce the TKE source, suggest the introduction of a correction factor. Due to the lack of a reliable estimate for the correction factor during stable atmospheric conditions, the initially suggested correction factor of 0.25 is employed in the simulations of the current study. However, the study by suggests that under stable conditions, as compared to neutral conditions, an increased correction factor could improve the simulation results.

This study demonstrates the ability of the WRF model to reproduce spatial patterns of hub height wind speeds relevant for wind power production in complex terrain. It is possible that tuning the model configuration to more optimal settings could further improve the simulation results, particularly if the stability is affected . A future study should therefore include a sensitivity analysis and investigate the impact of the wind farm parameterisation on the wind field within the parks during periods with strong downslope winds.

The following analysis investigates two different events. Case 1 represents a typical SE event, with stronger winds at A3 compared to A2. Case 2 represents a less frequent event, with weaker wind at A3 compared to A2. The analysis is motivated by the observations showing that under comparable wind directions, the wind speeds and power production at A3 relative to A2 can vary substantially.