Classification and properties of coastal wind profiles with negative gradients – an observational study

Wind profiles with a negative gradient are frequently occurring over the Baltic Sea and are important to take into consideration for offshore wind power as they affect not only the power production, but also the loads on the structure and the behavior of the wake behind the turbine. In this study, we classified non-normal profiles as wind profiles having negative shear in at least one part of the profile between 28 and 300 m: low-level jets (with a local wind maximum in the profile), profiles with a local minimum, and negative profiles. Using observations spanning over 3 years, we show that the non-normal wind profiles 5 are common over the Baltic Sea in late spring and summer, with a peak of 40% relative occurrence in May. Negative profiles (in the 28–300 m layer) were mostly occurring during unstable conditions, in contrast to low-level jets that primarily occurred in stable stratification. There were indications that the the zone with strong shear during low-level jets could cause a relative suppression of the variance for large turbulent eddies compared to the peak of the velocity spectra, in the layer below the jet core. Swell conditions were found to be favourable for the occurrence of negative profiles and profiles with a local minimum, 10 as the waves fed energy into the surface layer, resulting in an increase of the wind speed from below.

investigated the vertical profile of turbulence intensity during LLJ events over the Baltic Sea, and concluded that during the events the turbulence intensity decreased in the layer below the LLJ core but increased in the layer above the core, compared to the average conditions before the onset of the LLJ (consistent with the theory of shear sheltering). Roy et al. (2021) found that for a coastal site in France, the nocturnal LLJ with an associated atmospheric gravity wave enhanced the turbulent kinetic energy close to the surface. 130 In summary, there are several interesting flow phenomena that may change the turbulent structure of the boundary layer, if the wind profile changes from a normal profile in a predominately shear driven boundary layer where the wind shear smoothly decreases with height. A selection of these phenomena include shear sheltering (reduction of variance at low frequencies close to the surface), dynamical instabilities (increased variances, and potentially fluxes, at specific frequencies related to the shape of the wind profile), Holmboe instabilities (Holmboe, 1962;Carpenter et al., 2012) (increased variances, and potentially fluxes, 135 at specific frequencies related to the combined shape of the wind and temperature profiles), modifications to transport of turbulence and/or pressure, and shear production close to the surface caused by momentum input from swell waves (Nilsson et al., 2012). Also, modifications of the turbulence transport and shear production by non-local gradients of wind and temperature can alter the turbulent characteristics. Experimental evidence into which of these effects dominate has so far diverged, which calls for further studies of field measurements.

Method
In order to analyze the occurrence and properties of wind profiles with negative gradients for a coastal site in the Baltic Sea, a data record covering 3.5 years of measurements, from 8 December 2016 to 24 June 2020, was used. In the following subsections, a site description is given followed by detailed information about the measurements of turbulence, the wind profile and the sea state. Also, the classification system for the wind profiles, the wave age, the stability of the atmospheric surface 145 layer is presented, and a presentation of how the turbulent properties were analyzed is given.

Östergarnsholm
Östergarnsholm is a 2 km 2 island located 3 km east of the larger island Gotland in the Baltic Sea, see Fig. 1. Östergarnsholm is relatively flat, the terrain reaching only 0-5 m above sea level in the southern parts of the island where the measurements were performed (57°25' 48.4" N, 18°59' 2.9" E). In the northern and northwestern parts of the island the terrain is higher, locally 150 up to 10-15 m above sea level. The research station has been in operation since 1995 and is presently part of the Integrated Carbon Observation System (ICOS) with research mainly focusing on the coastal wind profiles and the transfer processes of energy and greenhouse gases between the Baltic Sea and the atmosphere (see e.g., Smedman et al., 1997;Högström et al., 2008;Gutiérrez-Loza et al., 2019;Rutgersson et al., 2020).  Approximately 30 m north of the mast, a lidar (Light Detection And Ranging) device was located, measuring the wind profile up to 300 m height, details are presented in Sect. 3.3. Located 4 km east of the mast, a wave buoy (Directional Wa-verider™) measured the properties of the wave field and sea surface temperature, see Sect. 3.4 for details. Only occasions when observations were simultaneously available from the turbulence measurements in the mast, the lidar and the wave buoy were used in the analysis.

Turbulence measurements
At the Östergarnsholm station, the main mast is an open, steel-lattice construction that has lower flow distortion properties than a mast made of a solid material. The sensors are installed on thin booms projecting 4.5 to 5 m towards the open sea sector, and the electronic units are attached as far back as is possible. We restrict the analysis of turbulence measurements to wind directions between 45 and 355 degrees based on earlier studies about flow distortion and representative flux footprint areas (see 170 Rutgersson et al. 2020 and references within).
For this study, we use high-frequency (20 Hz) wind components and temperature measured with CSAT3 three-dimensional sonic anemometers (Campbell Sci, Logan, UT, USA) at two levels, namely, 10.4 m and 26.4 m above mean sea level. We use the lowest measurement level for calculation of half-hourly mean values (wind speed, wind direction, temperature etc.) as well as second-order moments (variances and covariances), spectra and the associated stability measure z/L, where L is the 175 Obukhov length (see Sect. 3.6) and z is the height of the measurements. The upper measurement level, as well as additional instrumentation e.g. precipitation detection using a distrometer and received signal strength indication from the gas analyzers LI-7500 (open path) or LI-7200 (enclosed path) (LI-COR Inc., Lincoln, NE, USA), was used for initial comparison and in tests of some earlier and recently introduced quality control routines Gutiérrez-Loza et al., 2019;Rutgersson et al., 2020) briefly discussed and summarized here. The time series of 20 Hz data was assessed for noisy signals and non-stationarity in several ways after the sonic anemometer crosswind corrections, which are done internally. The raw high-frequency wind components were first transformed to earthsystem coordinates and the angles were corrected using a double rotation method to avoid any effects caused by the tilting of the anemometer. Wind speed and wind direction were computed from the corrected wind components.
Any error flags indicating when sensors were not working properly, were used to remove those records prior to the calcula-185 tions. A non-linear median filter algorithm was then applied to the 20 Hz data over 30 min periods to eliminate outliers from the high-frequency time series (see Brock, 1986;Starkenburg et al., 2016). We assure to include in our analysis only half-hours when the longest duration of gaps are less than 3 minutes. Further, half-hours always contain more than 85% data coverage following the SevEr thresholds suggested by Vitale et al. (2020). Additionally, we used their suggested homogeneity test of fluctuations and differenced data based on Chebyshev's inequality theorem and the SevEr thresholds to avoid cases of large 190 aberrant structural changes (e.g. sudden shifts in the mean value or changes in variance) which could lead to violation of the assumption of stationarity (Vitale et al., 2020).
Further tests were also discussed in Vitale et al. (2020), and several such criteria and choices of thresholds were initially studied. We chose here to not include the detection of poorly developed turbulence regimes, which uses the assumption that the ratio of standard deviation of vertical wind speed and friction velocity should follow closely earlier observed measurement 195 results in the surface layer (Mauder and Foken, 2004;Foken et al., 2012). More work is needed to reveal if this type of test is appropriate for data selection on sites that often experience low turbulence levels (e.g. low values of σ w ) and observe small friction when the flow is coming from coastal or open-sea sectors. A simpler criteria was used to remove a few cases of unrealistic low turbulence when the variance of the vertical wind speed was less than 0.0001 m 2 s −2 . and requiring that results for second-order moments (variances and covariances) were not sensitive to being defined based on fluctuations from simple time means using block averaging or by using a linear fit over 30 min as a de-trending procedure.
Non-stationarity typically increases with decreasing wind speed (Mahrt, 1998) and we chose to keep more strict limits for the stationarity tests (Vitale et al., 2020) only for higher wind speeds to be able to include sufficient data in our analysis in all wind speed intervals (see Mahrt 1998 for further discussion on this issue). At very low wind speeds we allowed a maximum 205 on the non-stationarity ratio of 15, which could imply severe non-stationarity. However, this also allowed us to keep wind and wind stress climatology fairly intact. If we used a threshold for the non-stationarity ratio of maximum 3, as suggested in Vitale et al. (2020), an overall decrease of available 30 min statistics kept for analysis was estimated to be 16%. This may at first seem acceptable but the reduction of low wind speed data was severe: it would imply a decrease of approximately 46% for 10 m winds below 3 m s −1 and a 71% decrease of data availability for wind speed conditions below 1 m s −1 . This would have 210 caused severe restrictions to the analysis at the Östergarnsholm site of especially swell conditions. Instead, physical reasons for non-stationarity was initially investigated and found to occur frequently during precipitation events. Signal strength quality control parameters from the gas analyzers (see Nilsson et al. 2018) as well as unusually high temperature variances was used to identify, flag and exclude suspicious outliers. Finally comparisons between sonic anemometer wind speeds, wind directions and temperature to other in-situ sensors on the site (Rutgersson et al., 2020) were used to manually flag a smaller amount of 215 data points.
Fluxes were calculated in a rotated coordinate system (Kaimal and Finnigan 1994, natural wind coordinates with double rotation) and each 20 Hz time series that contained missing data or eliminated outliers was gap-filled with linear interpolation.
The turbulent fluctuations of each variable were then calculated using a Reynold's decomposition and block averaging over 30-min periods was selected for all further analysis in this study. The turbulent fluctuations were used to calculate the variances 220 and covariances, as well as other statistical moments used during the flux calculations and analysis. Bin-averaged spectra and cospectra for momentum and heat fluxes were also calculated for each 30 min time period (using 21 logarithmically spaced frequency bins) and analyzed together with wind lidar profile data.

Wind profile measurements
Vertical profiles of the wind speed were measured with a ZephIR-300 wind lidar (ZX Lidars), a conically scanning continuous 225 wave lidar. Data from the instrument have been used before by Svensson et al. (2019) and Hallgren et al. (2020) to study the wind profile at Östergarnsholm. The unit was modified to collect raw data and had an extended range of measurements up to 300 m, similar to the current ZX300 model. The measurement cycle consisted of focusing the laser on a specific height, making three revolutions (one revolution per second) to sample the Doppler shift before moving on to the next height. In addition to the scans at each measurement height, the cycle was completed by scans without focus which, in combination with a scan 230 at a lower height, was used for automatic data quality assessment. As such, increasing the number of measurement heights implies decreasing the amount of data available at each height for constructing the average wind profile. Reflecting the goal of detecting LLJs, the unit was set to measure at a relatively large number of heights; 28,39,50,100,150,200,250, and 300 m above sea level, which was considered a reasonable trade off between the number of heights and the statistical convergence, keeping in mind that a 30 minute averaging window was used for individual wind profiles.

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The technology of optically focusing the laser beam to set the measurement height implies that the vertical extent of the measurement volume is small at low heights, but quadratically grows with height. Using a Cauchy-Lorentz distribution to determine the probability of backscatter following Mann et al. (2010; see also Svensson et al. 2019), we determined that 50 % of the measurement was coming from within ±0.7 m at 28 m, ±8.9 m at 100 m and ±79.9 m at 300 m -assuming backscatter elements to be homogeneously distributed in the boundary layer and that the beam attenuation could be considered 240 minor. However, the thick tails of the Cauchy-Lorentz distribution implied that there still is a significant probability that the measurement became contaminated with Doppler shifts from lower or higher heights when the target height increased, especially for heterogeneous distribution of aerosols, but also in ideal conditions. In practice, the wind profiles will be somewhat smoothed by this effects, particularly the non-linear variations of the wind speed in the upper part of the wind profile.
In addition to the quality control from the manufacturer, an extra quality control was performed on the 10 minute output 245 averages which were then used to calculate 30 minute averages. In this additional quality control 6.7% of the data were removed (removal of spikes, removal of profiles with data missing on two or more of the eight height levels and manual control of all non-normal profiles classified as negative, LLmin, weak LLJ or strong LLJ, see Sect. 3.5). There were two longer breaks in the lidar measurement campaign (see Fig. 2): first the removal of the lidar from the site for testing and comparison at another site (23 January -29 April 2019), then due to service and maintenance from the manufacturer (11 August -2 December 2019).

Wave measurements
Since 1995, wave measurements at 57°25' 0.012" N, 19°3' 11.988" E (see Fig. 1) have been performed with a Directional Waverider™ buoy, owned and run by the Finnish Meteorological Institute (FMI). The water depth on the buoy location is 39 m. The wave spectrum was calculated on board the buoy from a time series of 1,600 seconds every half hour and quality controlled by FMI. The frequency at the spectral peak and the local water depth was used to calculate the phase speed c p of 255 the dominant waves. Then, the wave age c p /U was calculated using the horizontal wind speed U as measured by the sonic anemometer at 10.4 m in the tower. Based on the wave age, three classes were defined: growing sea (c p /U < 0.8), mixed sea (0.8 ≤ c p /U < 1.2) and swell (1.2 ≤ c p /U ). The wave age was only calculated for the open sea sector, since the location of the buoy is not representative for neither the Gotland sector nor the Östergarnsholm sector. Further, the land masses in these two sectors may have influenced the atmospheric properties as measured by the tower, which in turn complicates the analysis 260 of the impact of the wave field.
Data from the buoy have previously been used to analyze the behavior of the wind profile and the turbulence properties of the atmospheric surface layer as measured by the mast on Östergarnsholm, see e.g. Semedo et al. (2009) and Mahrt et al. (2021).

Wind profile classification
All lidar wind profiles were classified into one of the following six classes: normal, negative, LLmin, transition, weak LLJ or strong LLJ.
As the definitions of LLJs vary in the literature, we follow the most recent recommendation by Aird et al. (2021), applying both a fixed and a relative criterion for LLJ classification. A profile was classified as a strong LLJ if there was a well-pronounced local maximum in the wind profile where the core speed was both at least 20% and at least 2 m s −1 stronger than the weakest 270 wind speed in the lidar profile both above and below the jet core. Thus, for core speeds below 10 m s −1 , 2 m s −1 is the strongest criterion and for core speeds above 10 m s −1 , 20% is the strongest criterion. Similarly, for weak LLJs, the absolute and relative criteria were 10% and 1 m s −1 respectively.
Transition profiles were considered to be transitions between normal profiles and LLJ profiles. They do display a local maximum in the profile, but fulfilling only criteria of 0.5 m s −1 and 5% differences between the core speed and the lowest 275 wind speed above and below the core.
For profiles with a local low-level minimum in the profile (LLmin), the wind speed above and below the 'core' had to be both at least 10% and at least 1 m s −1 stronger than the speed at the local minimum.
Negative profiles were defined as lidar profiles (28 -300 m) where the wind speed decreased with height by at least 1 m s −1 between the maximum and minimum wind speed and the profile was not fulfilling the criteria to be classified as an LLmin, a 280 transition profile, a weak LLJ or a strong LLJ.
All profiles that were not categorized as any of the non-normal types described in the above, were classified as normal profiles. Note that profiles with only a very slight negative shear and profiles with a very weak local minimum or maximum could be classified as normal profiles. Also, note that only wind data from the lidar was used to classify the profiles (i.e. data from the meteorological mast was not included in the profile classification). Wind profile behavior above 300 m was not 285 possible to assess using our data, and our main focus the shape of the profiles in the height range most relevant for wind energy.

Classification of atmospheric stability
The Obukhov length L was calculated as where κ = 0.40 is the von Kármán constant, g = 9.82 m s −2 is the gravitational constant, w ′ θ ′ v is the vertical flux of the virtual 290 potential temperature (K m s −1 ) and u * is the frictional velocity (m s −1 ). Using standard notation for Reynolds decomposition, the prime denotes the turbulent fluctuations from the mean of the variable and the overbar denotes the mean of the product.
The potential temperature, θ 0 , used in Eq. 1 was calculated as in which T is the temperature measured by the CSAT3 sonic anemometer (K), p 0 is the reference pressure (1000 hPa), p is the 295 air pressure measured by the LI-7500 gas analyzer (hPa), R d is the gas constant for dry air (287.06 J kg −1 K −1 ) and c pd is the isobaric specific heat capacity for dry air (1004.71 J kg −1 K −1 ).
To obtain a frictional velocity for the total stress magnitude we used the definition given in Stull (1988), Using standard notation, u is the horizontal wind speed in the dominant wind direction during the 30 min period of averaging, 300 v is the wind speed in the cross-wind direction during the averaging period and w is the vertical wind speed. Thus, in Eq. 3, u ′ w ′ is the momentum flux in the along wind direction and v ′ w ′ is the cross-wind momentum flux, both measured in m 2 s −2 .
Using the stability parameter z/L, where z = 10.4 m is the height of the measurements, the local stability of the atmospheric surface layer could be classified. We used a five class system, unstable (U) when z/L < −0.2, weakly unstable (WU) when (2015), which in turn was based on Sorbjan and Grachev (2010).

Normalization of spectra
Similar to Smedman et al. (2004), we analyzed the turbulent u-and w-power spectra. The frequency n was normalized by the horizontal wind speed and the height of the measurements, z, to obtain a normalized frequency, f , such that Following Sahlée et al. (2008), u-spectra, S u (n), were normalized bŷ where ϕ ε is the non-dimensional dissipation rate of energy The turbulent dissipation rate of energy, ε, was calculated as where n ε is a selected frequency in the inertial subrange and α is the Kolmogorov constant for u. For n ε we chose the frequency 1.5 Hz and for α we used 0.52 (Högström, 1996).
Using this representation of the u-power spectra, all spectra should coincide in the inertial subrange, independent of stability, 320 with a slope of −2/3 of the spectra in the inertial subrange, if depicted in a log-log representation.
The w-power spectra was normalised by the variance of w, To compare the spectral values at a low frequency, the normalized frequency 0.01 was arbitrarily selected after visual inspection and with previous experience to predominantly represent a lower frequency than the spectral peak for the specific 325 measurement height used. Spectral values were then interpolated to this frequency from the neighbouring frequencies using linear regression in the log-log representation.

General meteorological and oceanographic conditions
The general meteorological (temperature, wind speed, wind direction, stability of the atmospheric surface layer) and wave 330 conditions during the period of measurements are presented in Fig. 2. In Fig. 2(d), the data availability is plotted. Typically the data availability -when data from all three instruments (sonic anemometer, lidar, buoy) were simultaneously availablewas approximately 50-80% per month. Note that all wind data from the sector 355°-45°was excluded from the analysis, as mentioned in Sect. 3.1 and Sect. 3.2. For some months, such as April 2019, the data availability was very low (see Sect. 3.3 for details) and the monthly statistics presented in Fig. 2 should be interpreted with care.

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Throughout the year, the temperature at 10 m height varied from −5°C in winter up to 25°C in summer, with a monthly mean above 0°C for all months. No ice cover was reported in the vicinity of Östergarnsholm in the winters during the time period.
The monthly median wind speed at 10 m height was typically between 5 and 10 m s −1 , with winter (DJFM) and fall (ASON) being the windier seasons and spring/summer (AMJJ) being less windy, especially in terms of extremes. In Sect. 4.2 the reason 340 for grouping the month into three seasons is presented.
The dominant wind direction at the site was from S-SW, and thus winds from the open sea sector or from Gotland were most common. When the wind was from the open sea sector, it was most often mixed waves or swell and less frequently growing sea. The waves were mostly directed from NE to SW, with waves coming from NE and SSW being more common than waves directed from E (results not shown). The wind roses in Fig. 3 show the average wind speed and wind direction at the site for the 345 three seasons. Also, for the open sea sector, the median wave age and the 25 and 75 percentiles of the wave age are presented, showing slightly higher wave age on average during AMJJ due to typically lower wind speed compared to the fall and winter seasons.
The stability of the atmospheric surface layer followed a yearly cycle where typically the unstable conditions dominated during fall and winter while stable conditions were more common in spring and early summer.

Average profiles and monthly occurrence
The average wind speed and wind shear profiles from the lidar for the different types of profiles are presented in panels (a) and (b) in Fig. 4. Negative profiles and profiles classified as LLmins typically occurred at lower wind speeds than other profiles and, in turn, transition profiles and weak LLJs occurred at lower wind speeds than the normal profiles. However, when a strong LLJ was present, the core speed was typically stronger than the average normal wind speed at the same height. The average shear profiles tell the same story as the average wind speed profiles, but from a different perspective. In the lowest layer of the profile, the average shear for the LLJ profiles was much stronger than the average shear for a normal profile.
By definition, the shear goes to zero at the jet core and is negative above the core, even though the absolute value of the shear tend to decrease with height. Negative profiles had a shear that was relatively low all the time, although mostly on the negative side. Also, for LLmins, the absolute value of the shear was lower than for normal profiles, except above the core where the 360 wind speed increased with height.
The monthly average occurrence of the non-normal profiles relative to all wind profiles are presented in Fig. 4(c). For all of these, there was a peak in the relative occurrence in the season April-July (AMJJ), reaching 35% in common, with a peak value of approximately 40% in May and June. However, the year to year variability was large. In May 2018, dominated by extended periods of atmospheric blocking and high temperatures, non-normal profiles occurred almost 60% of the time, while 365 in May 2019 and May 2020, when the synoptic situation was more variable, the relative occurrence was around 30%. LLJs were more common in August-November (ASON) than in December-March (DJFM), but for the LLmins and negative profiles the difference was less clear.
Based on the seasonality seen in Fig. 4(c), we divide the months into three seasons: winter (DJFM), spring/summer (AMJJ) and fall (ASON). No clear diurnal pattern could be seen in the occurrence of the different types of profiles during the different 370 seasons (results not shown).
The total occurrences of the different profiles are presented in the legend in Fig. 4(b) and, notably, negative profiles occurred as often as 4% of the time. Strong LLJs occurred 2% of the time and weak LLJs 6%. Transition profiles were rather common, occurring 8% of the time. LLmins were however rare, appearing approximately only 1% of the time. Please note that these numbers represent the record of the data as it is, and thus the summer season is slightly over-represented (since e.g. no data for 375 February, March and September-November 2019 were available, see Sect. 3.3 and Fig. 2).

Occurrence in different wind speeds and wave ages
To assess when the different types of wind profiles appeared, normalized distributions of 10 m wind speed and wave age for the three seasons are plotted in Fig. 5. Both in DJFM and AMJJ it is clear that the peak of the distributions for the non-normal profiles were shifted towards weaker wind conditions at 10 m compared to normal profiles, see also Fig. 4(a). On the other 380 hand, Fig. 4(a) suggests that at heights relevant for wind power, LLJs occur in the range of wind speeds where the power curve typically is steep, implying that the power production could be very sensitive to the speed of the jet core. In ASON, the difference between the distributions of wind speeds for non-normal profiles and normal profiles was less pronounced, even though a larger share of the negative profiles were occurring in weak winds. Although rare, it is interesting to note that negative profiles sometimes occurred in stronger winds (> 10 m s −1 ), primarily in ASON. Regarding the LLJs, it was very unlikely 385 that they would appear if the wind speed surpassed 10 m s −1 at 10 m height. As the wind speed decreases with height for the negative and LLmin profiles, most of these profiles occurred in wind speeds that were below typical cut-in wind speeds at standard hub heights for offshore wind turbines.

Occurrence in different wind directions and stabilities
Comparing the polar scatter plots in Fig. 6abc with the wind roses in Fig. 3, it is clear that strong LLJs were over-represented in the open sea sector during AMJJ and ASON. However, during DJFM, a much larger share of the season's strong LLJs were from the Gotland sector.

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For the strong LLJs, the average core height was highest for all sectors during winter. The average core height was also highest for LLJs that occurred when the wind was directed from the Östergarnsholm sector and lowest when the wind was from the open sea. In general, the lower the core height, the higher the average shear below the core. Also, naturally, the higher the LLJ core is located, the higher the core speed. As a consequence of the height discretization in the lidar data, LLJs were the other types of profiles, the other seasons and in other sectors, the wind distributions followed the 3.5 year climatology for that respective sector (or the amount of data was too small to draw any conclusions).

Spectral analysis
The normalized u-power spectra was interpolated to a fixed set of logarithmically spaced non-dimensional frequencies and then 430 the median value of the spectra for each frequency and each type of profile was calculated. The results, divided into different stability classes and different sectors, are plotted in Fig. 8. The Fig. is accompanied by Table 1, summarizing the number of individual spectra (for each type of profile) that constitutes the statistics for each median spectra presented in Fig. 8 and for the boxplots in Fig. 9 and Fig. 10. In all stabilities and for all sectors, the normal wind profile is the most common type of profile.
However, in stable stratification and when the wind is directed from the open sea, the total amount of non-normal profiles

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(1,335) is greater than the amount of normal profiles (1,079). profile per category was used as a limit to include the statistics for the profile. Table 1. Overview of the number of profiles (#) and the median stability (z/L) for the spectral values plotted in Fig. 8 and Fig. 10 for the different wind direction sectors and under different atmospheric stabilities. Note that (z/L) values for profile types with less than 20 occurrences (per sector and stability) were omitted from being presented in the table. For each sector and each stability class, the values of (z/L) that are higher than the corresponding value for normal profiles are marked in bold (representing a shift towards less unstable conditions or more stable conditions) and the lower values are marked in italics (representing a shift towards more unstable conditions or less stable conditions).  Fig. 8, differences in the shapes of the spectral curves for the median values can be seen comparing different stabilities (for the same type of profile) or comparing different types of profiles (in the same stability class). The total spectral energy was lower in the weakly stable/stable conditions compared to more unstable conditions and the peak of the spectra was located at higher frequencies (smaller eddies) for stable conditions than in unstable conditions. Within a single stability class, differences 440 between the median spectra for different types of profiles could be observed, especially in the low frequency range (large eddies). To analyze this further, the normalized frequency nz/U = 0.01 was selected and the spectral values at this frequency is presented in Fig. 9, following the methodology described in Sect. 3.7. Starting by comparing the boxplots for transition profiles, weak LLJs and strong LLJs to the normal profiles for the open sea sector, there was a significant difference in the median spectral value at this selected low frequency for all stability classes.

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For the Gotland sector, there was a significant difference in the normalized spectral values at this frequency between these profiles and the normal profiles in weakly unstable, near neutral and weakly stable conditions with the non-normal profiles having lower spectral values. There was also a significant difference between the strong LLJs and the normal profiles in stable stratification. Although less data in the Östergarnsholm sector, there are indications of lower spectral values at the selected low frequency for wind profiles with an LLJ compared to normal profiles.

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In the results for the negative profiles and the LLmins there were no clear patterns detected. The median spectral value for the selected frequency varied between being higher or lower than the median spectral value for the normal profiles, comparing between different stabilities and between different sectors.
The boxplots for extracted spectral values from the normalized w-power spectra for the same selected frequency nz/U = 0.01 is presented in Fig. 10. For the open sea sector, similar results as for u-power spectra could be seen with significantly lower values for profiles with a local maxima in the profile compared to the normal profile. Also for the Gotland and Östergarnsholm sectors, the results for the w-power spectra resemble the results for the u-power spectra. As the grouping of the data is the same as in Fig. 8 and Fig. 9, the numbers in Table 1 also represents the data presented in Fig. 10. Figure 10. Distribution of normalized spectral values of w-power spectra for the different wind profile classes for the selected normalized frequency 0.01. The data are presented in the same manner as in Fig. 9.

Discussion
Several types of wind profiles, different from what here is classified as normal profiles, are frequently occurring over the 460 Baltic Sea and presumably in any coastal area (e.g., Møller et al., 2020). For the case of Östergarnsholm, the non-normal wind profiles occurred on average 20% of the time during the 3.5 years of measurements. In the spring and summer season AMJJ, the stratification of the marine atmospheric surface layer was typically stable (see Fig. 2) as the water was still cold after the winter and warmer air was advected over the water surface, resulting in non-normal profiles being even more frequent, occurring 35% of the time. Numerical weather prediction models, as well as other atmospheric models, struggle with resolving processes in 465 the stable boundary layer (e.g., Holtslag et al., 2013;Sandu et al., 2013) and this work strive to highlight some of the processes occurring in the stable boundary layer and their turbulent properties.
To assess the wind power production in the Baltic Sea area it is crucial to be aware of the frequent occurrence of the different types of wind profiles and their implications on the turbulence, loads on the turbine and wake behavior. Improving forecasts to be able to give information in advance about the occurrence of the wind profile type within the next few hours would provide a better basis for decision-making for wind power operators. Note that the typical core height of an LLJ is similar to the hub height of an offshore wind turbine (e.g., Gaertner et al., 2020) and that the core speed is comparable to the average wind speed at that height. However, LLmins and negative profiles most commonly occur in weak winds, often below typical cut-in wind speed. Smedman et al. (2004) found that during LLJs over the Baltic Sea, the energy in the low-frequent turbulent part of the 475 spectra was suppressed compared to corresponding cases without a low-level maximum in the wind profile. Although this is in contrast to results from other studies of energy spectra and turbulent processes below LLJ cores (see e.g., Duarte et al., 2012;Karipot et al., 2008), we can now strengthen the results by Smedman et al. (2004), concluding that this is the case for Östergarnsholm when the wind is from the open sea. Furthermore, we conclude that the suppression of larger eddies, compared to normal profiles, occurred for LLJs in all stabilities, not only in stable stratification which was the only stability 480 class analyzed by Smedman et al. (2004). When the fetch was affected by land surfaces (i.e. the wind was directed from the Gotland and Östergarnsholm sectors) the results were less clear. However, it is important to note that the stability was measured locally at 10 m height in the mast. As such, it might not fully represent the stability conditions when the air was directed over non-homogeneous terrain, as an internal boundary layer might be advected to the measurement site, affecting the wind profile at higher levels, or the measurements of turbulence and stability in the mast. Additional measurements in the vicinity of the 485 site and on Gotland would be needed in future work to investigate these situations further.
As seen in Fig. 5 and Fig. 6, LLJs occurred in a wide range of wind speeds and there was a large spread in shear between the lowest level of the lidar measurements and the jet core. Since normal profiles (occurring 80% of the time) cover a wide range of shear, a perfectly fair analysis would require that only spectral values for LLJs and normal profiles with similar shear in the lowest part of the profile were compared. However, using observational data and limiting to cases when the lower part 490 of all profiles are similar and all governing atmospheric and oceanographic conditions are the same, is a hard restriction on the data. Thus, general practice in the literature covering e.g. shear sheltering on atmospheric flow is to compare turbulent features for all LLJ profiles with all non-LLJ profiles (given the same stability close to the surface). For further analysis focusing on differences in shear and their implications for the turbulent structure of the boundary layer comparing normal profiles with LLJs, we suggest a modeling study that systematically investigates the impact on the spectral density in the case of boundary 495 layers with strong low level shear and weak upper shear, ideally both including and excluding the effect of buoyancy.
Although the spectra were classified according to their stability, the median values of z/L given in Table 1 indicate that there was some spread within each stability class. Differences in the stability parameter z/L within the same class implies that the spectral values for cases with higher values (more shifted towards stable stratification, marked in bold in the table) should have lower normalized variances in Fig. 9 and Fig. 10. Compared to the normal profiles, the values for z/L during strong LLJs there still exists an uncertainty with regards to the role of the stratification in the upper layer, above the jet core. Large eddy simulation (LES) studies or intensive campaigns with e.g. radio soundings or drones, or remote sensing devices, such as e.g.
Radio Acoustic Sounding System (RASS) would be interesting to shed light on this.
In contrast to the LLJs, the negative profiles typically occurred in unstable conditions and also at higher values of c p /U (Fig. 7). This suggests that the momentum flux was directed upwards (from the sea and the waves to the atmosphere), feeding energy into the lower part of the atmospheric boundary layer and thus also increasing the wind speed from below. In studies by 510 e.g. Hanley and Belcher (2008) and Smedman et al. (2009), it was seen that a wind maxima can form at very low heights (∼ 10 m) during swell, and thus it is likely that the swell can contribute in creating a profile with negative shear (see e.g., Nilsson et al., 2012) as measured by the lidar. The validity of using z/L to describe the stability in situations with small (positive) fluxes could be questioned as these fluxes in reality could represent a turbulence regime that is very different from what we can attempt to describe with Monin-Obukhov similarity theory, see e.g. Drennan et al. (1999) and Högström et al. (2013). Using

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Eq. 3 to describe the frictional velocity gives the magnitude of the stress, but information about the direction is lost. In total, positive longitudinal u ′ w ′ momentum fluxes occurred 3.5% of the time in the time period analyzed. For many of these cases the value of the momentum flux was so small that it could be considered to be within the uncertainty of the measurements if the flux should be considered positive or negative.
The lidar measurements used in this study were performed on eight height levels, most levels separated by a distance of 50 520 m. As LLJ cores can be of varying vertical extent, it is likely that this vertical resolution might not capture all LLJs. We refer to Nunalee and Basu (2014) and Aird et al. (2021) for discussion on the sensitivity of detecting LLJs to the height resolution.
Also, as the measurement volume increases quadratically with height, the lidar is biased to capture sharper gradients and more localized extreme points in the lower part of the boundary layer. Therefore, there will likely be the case that using continuous wave lidar data for any long term classification of wind profiles, cases with strong lower level shear and weak upper level 525 shear will be overestimated. Further, temporal averaging results in fewer LLJs. Testing the sensitivity of temporal averaging, comparing the number of LLJs found in the time period 1 January 2018 -24 June 2020, we conclude that approximately 5% more strong LLJs (3% more weak LLJs) were found using the 10 min data than in the 30 min data, analyzing comparable numbers.
To explore the three-dimensional structure of different types of wind profiles and processes related to their formation and 530 dissolution in different boundary layer stratifications and wind directions, model data are needed or an array of horizontally and vertically scanning lidars. Using fully resolving turbulence models would allow for an explicit analysis of the turbulent properties above and below the jet core. This could also be performed using approximate calculations of the momentum flux or turbulent kinetic energy from the lidar (Svensson et al., 2019;Thomasson, 2021), or at sites with tall meteorological masts, reaching up above the average LLJ core height and equipped with high frequency measurements at the top level.

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For modeling the wind profiles in offshore conditions it is important to utilize a fully coupled model (Wu et al., 2020;Li et al., 2021), as feedback processes from the waves are crucial for the formation of e.g. negative profiles. This was confirmed from an observational perspective by the results in this study. An analysis of wind turbine wake behavior under different stabilities and for different shapes of the wind profile would be an interesting and important contribution in research related to wake steering and also to be able to accurately describe the wind resource in the vicinity of other (offshore) wind parks. The extent 540 of the wake behind a wind park is likely to be very sensitive to LLJ conditions as the potential to mix down momentum from above the jet core is greatly diminished. Also, studies on the impact from non-normal profiles on the loads on a turbine and the total power production would be interesting as well as an assessment of methods to improve short-term forecasts with regard to these types of wind profiles. Clustering non-normal profiles into events could give further information about the synoptic and/or mesoscale conditions necessary for the formation of wind profiles with negative gradients.

6 Summary and conclusions
Wind profiles with negative shear in at least one part of the profile between 28 and 300 m (LLJs, transition profiles, LLmins and negative profiles) are frequently (∼20% of the time) occurring over Östergarnsholm, a coastal site in the Baltic Sea. From an offshore wind power perspective it is important to know when these profiles occur and how they might affect the turbulent properties of the boundary layer, which in turn affects the loads on the wind turbine and the behavior of the wake behind the 550 turbine. Also, improving the understanding of the physical processes in the boundary layer, especially in stable stratification, is important in order to improve the performance of numerical weather prediction models under these conditions.
By providing a systematic analysis of meteorological data and ocean wave conditions from over 3 years of measurements at Östergarnsholm, we concluded that: -The non-normal profiles exhibited a clear annual cycle; they were most common in AMJJ with a peak in May.

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-The LLJs at Östergarnsholm were most frequently occurring in stable or weakly stable stratification but could appear in any stability. Also, LLmins primarily appeared in stable stratification while negative profiles were more frequent in unstable stratification.
-Most of the negative profiles and LLmins occurred during swell conditions.
-For all stability classes and during LLJs when the wind was directed from the open sea sector, lower normalized variances 560 were found in the low frequency range of the spectra. This follows the results found by Smedman et al. (2004). Further analyzes, considering processes both above and below the LLJ core, are needed to fully explain the cause for the observed change in turbulence properties.
-For LLmins and negative profiles there were no clear signals that these profiles altered the low frequency part of the uand w-power spectra.
Data availability. The data from the meteorological mast and the lidar are available from Erik Nilsson upon request. The data from the wave buoy are available from Heidi Pettersson upon request.
Author contributions. The project was conceptualized and administrated by CH and ES, with input from JA, EN, MS and SI. Funding acquisition was carried out by ES and SI. The methodology, programming, validation, formal analysis and visualization was performed by 570 CH. CH also wrote most of the original draft, except Sect 3.2 (written by EN), Sect. 3.3 (written by JA) and Sect. 3.4 (written by HP). CH was supervised by ES and SI. AT performed the pilot study, supervised by CH. Data curation was performed by JA, EN and HP. All authors participated in reviewing and editing the manuscript.
Competing interests. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.