Offshore wind farm global blockage measured with scanning lidar

The objective of this paper was the experimental investigation of the accumulated induction effect of a large offshore wind farm as a whole, i.e. the global blockage effect, in relation to atmospheric stability estimates and wind farm operational states. We measured the inflow of a 400 MW offshore wind farm in the German North Sea with a scanning long-range Doppler wind lidar. A methodology to reduce the statistical variability of different lidar scans at comparable measurement conditions was introduced and an extensive uncertainty assessment of the averaged wind fields was performed to be able to identify 5 the global blockage effect which is small compared to e.g. wind turbine wake effects and ambient variations in the inflow. Our results showed a significant decrease in wind speed at platform height in front of the wind farm of 4.5 % within an accuracy range between 2.5 % and 6.5 % with the turbines operating at high thrust coefficients in a stably stratified atmosphere, which we interpreted as global blockage. In contrast, at unstable stratification and similar operating conditions we identified no wind speed deficit. We discussed the significance of our measurements, possible sources of error in long-range scanning 10 lidar campaigns and give recommendations how to measure small flow effects like global blockage with scanning Doppler lidar. In conclusion, we provide strong evidence for the existence of global blockage in large offshore wind farms in stable stratification and the turbines operating at a high thrust coefficient by planar lidar wind field measurements. We conclude that global blockage is dependant on atmospheric stratification.


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Wind turbine wakes can cause negative effects at downstream turbines due to decreased wind speeds and increased turbulence (Porté-Agel et al., 2019). This was intensively studied in the last decades and is considered in all wind farm projects planned today (Rohrig et al., 2019). Recently, the so-called global blockage effect came into the research focus. It denotes the reduction of the wind speed in a comparably wide area upstream of large wind farms. The effect is supposed to be caused by an interaction of the wind farm as a whole with the atmospheric boundary layer since it can not be sufficiently described by a simple 20 superposition of the induction zones of individual turbines in a large wind farm. Global blockage is usually not considered in the planning of wind energy projects and could therefore lead to non-negligible uncertainties in the assessment of the wind resource (Bleeg et al., 2018). rent overview of engineering models including global blockage and compare their performance with an actuator disk RANS 60 simulation as reference. They find the different models to show varying levels of accuracy with a mean error level below 1 % in the induction zone.
These numerical studies agree on the magnitude of the wind speed deficit in the wind farm induction zone to be in a lower one-digit percentage range. Nevertheless, most numerical studies lack measurement data for validation since experimental investigations on global blockage have been rarely performed. Segalini and Dahlberg (2019) measured the effect of a model wind farm on a row of upstream turbines in different distances in a laminar wind tunnel. They observed a decrease in wind speed at the turbine row in distances of up to 30 rotor diameters (D=45 mm) upstream and with a maximum of 2 %.
To our knowledge the only study presenting free field measurements of global blockage was performed by Bleeg et al. (2018), who analysed wind measurements of meteorological masts upstream and lateral to three different onshore wind farms 70 before and after the commercial operation date and for high thrust coefficients of the turbines. Deficits in wind speed upstream compared to the lateral reference mast of around 2 % and up to more than 6 % appeared typically in front of the farms after the turbines went into operation. The authors relate this mainly to the global blockage effect.
Open field measurements of global blockage are challenging. Classic anemometry is limited in its possibilities to study the 75 induction zone of a wind farm since just a limited number of masts can be placed in front of it due to mainly financial constraints. In the last decade, the remote sensing methods Doppler wind lidar (light detection and ranging) has become a common tool in many fields of wind energy research and applications (Hasager and Sjöholm, 2019). Lidar devices offer the possibility to scan whole wind fields with ranges of several kilometres. Commercial scanning lidar systems allow to measure the line-ofsight (LOS) component of the wind vector on several hundred positions along the emitted laser beam and to orientate the beam 80 in any direction. Scanning lidars have enabled many new insights in different fields of wind energy research, like wind turbine wakes (Käsler et al., 2010;Trabucchi et al., 2014), wind farm cluster wakes , resource assessment in complex terrain (Menke et al., 2020) and minute-scale wind power forecasts (Theuer et al., 2020b).
The current knowledge on global blockage is mainly based on modelling activities or wind tunnel studies. Compared to 85 well-known phenomena like wind turbine wakes with significant wind speed deficits in the order of tens of percents of the inflow wind speed in a well defined downstream region, global blockage is much harder to study especially due to the larger spatial expansion over typically several square kilometres and the smaller wind speed differences in a single digit percentage range. Furthermore, the effect of global blockage needs to be separated from other spatial and temporal variations in the wind field. Averaged field measurements on single points (Bleeg et al., 2018) lack information on superposed flow features like local 90 wind speed variations due to orography, wind farm layout or varying meteorological conditions. Since it is not possible to distinguish these flow features, this adds uncertainty to the identification of global blockage. Therefore, accurate field measurements spatially resolving the induction zone of the wind farm are of major importance to validate the modelling results already achieved. The extent of global blockage in operating wind farms and its dependency on wind farms is still missing.
Compact Doppler lidar systems offer the possibility to scan large parts of the inflow of a wind farm with measurement ranges up to 10 kilometres. Nevertheless, to obtain wind data for a quantitative analysis all measurement parameters of the lidar device such as its orientation and tilt due to platform movements need to be carefully selected and accurately controlled. Furthermore, environmental parameters and conditions like curvature of the earth, knowledge of the current wind profile and atmospheric 100 stability for height correction need to be known and accounted for.
The objective of our paper is the experimental assessment of the global blockage effect in a large offshore wind farm dependent on atmospheric stability estimates and wind farm operational states. In addition to this, we are proposing a method to examine comparably small flow effects like global blockage with long-range scanning lidar. Our approach includes:

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analysing horizontal long-range Doppler lidar plan position indicator (PPI) scans upstream of a 400 MW offshore wind farm, deriving atmospheric stability from local meteorological measurements and performing a detailed uncertainty assessment and error correction on all measured quantities. Furthermore, we provide recommendations for measurements of global blockage or similar small flow effects with scanning 110 Doppler Lidar.
In this paper we use the terms blockage effect and wind turbine blockage effect for decreased wind speeds in the induction zone of single turbines while we call the accumulated blockage effect of all turbines within a wind farm or wind farm cluster global (wind farm) blockage or global (wind farm) blockage effect. This paper is structured as follows. In Section 2 we introduce our experimental setup including lidar measurements and 115 atmospheric stability estimations. We place special focus on the uncertainty assessment of the lidar data. We present the results of four different inflow situations varying in atmospheric stability and wind speed in Section 3. In Section 4 we discuss our findings and give recommendations for lidar measurements of flow effects like global blockage with a magnitude of typical ambient wind speed fluctuations. We conclude and close the paper in Section 5.

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In this section we describe the analyzed wind farm (Section 2.1), lidar measurements (Section 2.2), meteorological measurements and atmospheric stability characterization (Section 2.3), lidar data analysis (Section 2.4) and lidar wind speed uncertainty estimation (Section 2.5).

Offshore wind farm Global Tech I
At the time of our measurement campaign in the first half of 2019, several offshore wind farms had been installed in the German 125 and Dutch North Sea. In the focus of this work is the 400 MW wind farm «Global Tech I» (GT I). It features 80 turbines of type «Adwen AD 5-116» with a rotor diameter of 116 m and a rated power of 5 MW at a rated wind speed of 12.5 ms −1 .  The «BorWin 1» cluster is located in a distance of about 24 km in south-west direction. During our measurements the wind farms «Hohe See» and «Albatros» (c.f. Figure 1 (b)) were build in the direct south west vicinity of GT I with several transition pieces, turbines and two sub-stations installed. Measurements after the first power was fed in on 15 July 2019 were not considered (EnBW, 2019).  135 We used a scanning long-range Doppler wind lidar of type Leosphere Windcube 200S (Serial no. WLS200S-024) which we installed on the transition piece (TP) of turbine GT58 in GT I (red filled in Figure 1 (b)). The height of its scanner was approximately 24.6 m above mean sea level (MSL), 67.0 m below hub height and 9.0 m below lower blade tip height of the turbine. The measurement campaign started in August 2018 and ended in January 2020. We consider data from a period between February 2019 and June 2019. We performed plan position indicator scans (PPI) with an elevation of 0 • , resulting in 140 a measurement height of 24.6 m MSL plus a correction due to the earth's curvature (up to 5 m in 8 km distance). Further, a turbine thrust-dependent tilt of the lidar was observed, resulting in varying measuring heights across range gates and azimuth angles (c.f. Section 2.5). We set the lidar's pulse length to 400 ns, the acquisition time to 2.0 s, the scanning speed to 1 • s −1 and scanned the upstream flow in different azimuth sectors of 150 • that we aligned manually to the wind direction. Range gates were defined between 500 m and 7990 m with a 35 m spacing. Hence, one lidar scan took 150 s and resulted in 215 range 145 gates (also referred to as "measurement points") on each of the 75 beams. The further processing of the lidar scans is described in Section 2.4. Schneemann et al. (2020) give further information on the measurements and Schneemann et al. (2019) provide some exemplary lidar scans from this campaign.

Atmospheric stability characterization and meteorological measurements
For the analysis of the global blockage effect knowledge about wind speed at one common height across the whole scan 150 is required. The varying measuring height, as a consequence of the tilt of the lidar device and the Earth's curvature, thus necessitate the extrapolation of wind speed to that altitude. In order to keep extrapolation distances small, we here chose the height of the transition piece. For the extrapolation, knowledge of the wind profile and thus also estimates of atmospheric stability are required. Information regarding stability further allows us to analyse the effect of atmospheric conditions on global blockage. 155 We used a similar methodology to derive atmospheric stratification as in Theuer et al. (2020b) and Schneemann et al. (2020), which is described here for completeness. To characterize atmospheric stability (Emeis, 2018) we used local measurements as well as reanalysis data. On the transition piece of turbine GT58 close to the lidar's position, we measured air temperature and humidity (Vaisala HMP155) and air pressure (Vaisala PTB330). Additionally, we used the sea surface temperature (SST) from the OSTIA data set (Good et al., 2020). We utilized a methodology introduced by Rodrigo et al. (2015) to estimate the Bulk 160 Richardson number Here, g is the gravitational acceleration, T v the virtual temperature at sea level and Θ TP and Θ 0 the virtual potential temperature at TP height z TP and sea level respectively. u li describes the wind speed at the lidar position, determined utilising lidar measurements up to range gates of 600 m. The height used to calculate Ri b is defined as the mean between the two height 165 levels, i. e. 0.5z TP . After estimating Ri b we obtain the dimensionless stability parameter and finally the Obukhov length with z = z TP and u = u TP . Here, κ = 0.4 describes the von Kármán-constant and α c = 0.011 the Charnock parameter, often used in an offshore context (Smith, 1980). The stability correction term was defined following Dyer (1974) with γ = 19.3 and β = 6 (Högström, 1988).

Lidar data processing
We filtered the lidar scans using a carrier-to-noise (CNR) threshold filter, considering only values with −26 dB < CNR < 0 dB.
With a Velocity-Azimuth-Display (VAD) algorithm, we calculated a mean wind speed u and wind direction χ individually for each scan assuming a homogeneous wind field and neglecting the vertical wind speed component (Werner, 2005). At each 180 measurement point we projected the line-of-sight (LOS) wind velocities u LOS onto the mean wind direction by means of with horizontal wind speed u h and azimuth angles ϑ. Sectors with azimuth angles almost perpendicular to the wind direction, i. e. Only scans with a data availability of at least 60 % were considered for further analysis. Data availability was calculated individually for each scan, including measurement points up to a range gate of 7000 m and not considering critical sectors as defined in Equation 7.
Finally, we interpolated all valid scans to a Cartesian grid with a spacing of ∆x = ∆y = 50 m to be able to average data of 195 varying scanning sectors.
For further analysis, the lidar scans were categorised according to their respective mean wind direction χ, mean wind speed u and atmospheric stability characterized by L. In each category, consisting of N individual lidar scans i, we performed the following steps: First, the mean wind speed within the scan i at TP height u TP,i was derived and used to normalise the wind 200 speeds on all grid points, yielding u TP,norm,i . Second, all normalised scans were averaged to u TP,norm . Hereby, Cartesian grid points with data availability < 80 %, i. e. N r < 0.8N , with N the number of all available scans within the category and N r the number of valid scans at each grid point, were neglected. Third, normalised and averaged wind speeds u TP,norm were interpolated onto a virtual line in mean wind direction upstream of the lidar.

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For the blockage analysis we decided to distinguish between two stability classes, i. e. unstable and stable situations, and three different operational states respectively wind speed ranges. The operational state of the wind farm was estimated using SCADA power data and the wind speed range based on the wind speed at TP height. These states are namely the wind farm not operating (wind speed below 4 ms −1 , low thrust coefficient), the wind farm operating at rated power (wind speed above 12.5 ms −1 , moderate to high thrust coefficient) and the wind farm operating below and up to rated power (wind speed below 210 13 ms −1 , high thrust coefficient). In total, the combination of these two categories left us with a number of six possible cases to be analysed. However, for brevity we omitted the combinations unstable, not operating and unstable, operating above rated wind speed. With the comparison of the four remaining cases we aimed to cover both scenarios where global blockage is likely to occur and those where an occurrence is less likely. This "cross-check" allowed us to better interpret the obtained results.
We start with the analysis of the remaining unstable scenario and then continue with the stable cases, sorted according to their 215 thrust coefficients. The values of the thrust coefficient were estimated from a generic 5 MW wind turbine model with same rated wind speed. The four scenarios are summarized below.
Scenario 1 Wind turbines operating below and up to rated power with a moderate to high thrust coefficient. We chose a wind speed interval of 10 ms −1 < u < 13 ms −1 , unstable atmospheric conditions and a total power production of the wind farm with at least 50 % of wind farm's rated power and 80 % of the wind farm's estimated power. Here, 220 the wind farm power is estimated by extrapolating u TP to hub height using an average logarithmic profile (see Section 2.3, with L = −300 m) and transferring the result to the whole wind farm considering wind farm effects.
Further, only situations with high power production at GT58 (P GT58 ≥ 4000 kW) were considered to make the experienced tilt of the lidar device comparable to that of Scenario 4.
Scenario 2 Wind farm not operating with wind speeds below cut-in wind speed. Here scans with wind speed u TP from 225 3 ms −1 < u < 4 ms −1 , during stable atmospheric conditions and a wind farm power production < 5 % of the wind farm's rated power were selected.
Scenario 3 Wind farm operating at rated power with wind speeds u TP above rated wind speed and low thrust coefficient. This comprises scans with 16 ms −1 < u < 22 ms −1 , stable atmospheric conditions and a total wind farm power >80 % of the rated power. Further, only cases with a blade pitch from SCADA data > 5 • at GT58 were considered. Scenario 4 Wind turbines operating below and up to rated power with a high thrust coefficient. Same as Scenario 1, however here we chose scans within the wind speed interval 7 ms −1 < u < 10 ms −1 and stable atmospheric conditions. In this case the estimated wind farm power was determined using an average logarithmic profile with L = 300 m.

Uncertainty estimation
For the further analysis and interpretation of the results, several uncertainties introduced in the course of the measurement 235 campaign and data analysis procedure are important to consider. In this section, we qualitatively summarise the most important error contributions and subsequently estimate uncertainties using three different methodologies. First, we calculate the total propagated uncertainty using the uncertainties assigned to the individual components with Gaussian error propagation, second we determine the total propagated uncertainty as before but distinguish also between range gate-independent and range gatecorrelated input variables, and third we derive the statistical standard error of the mean. platform like the TP of an offshore wind turbine. Aside the general uncertainty in the LOS wind speed measurement the main source of uncertainty is the varying measurement height due to lidar scanner misalignment (dark red) and platform tilts and movements (light red) e.g.
due to the turbine's thrust. Curvature of the earth (blue) and tide (light blue) adds on the height uncertainty. As a consequence of known height errors measured wind speeds need to be transformed back to the desired height, thus the lack of knowledge of the prevailing wind profile introduces additional uncertainty (orange).

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We summarise sources of errors and uncertainties that need to be considered in offshore lidar measurements of flow effects with small deviations with respect to the mean flow in Table 1 and visualise them in Figure 2. It becomes clear that several of the error sources are directly or indirectly linked to the alignment of the lidar: The device's tilt causes the need for a height extrapolation, thus wind profile information is required, introducing additional uncertainties. Considering a measurement scenario with perfect horizontal measurements, the error sources could be significantly reduced. However, as in this set-up an 245 extrapolation of wind speed u m at measuring height z m to lidar height z TP is required we estimated the uncertainty associated with it in more detail in the following.

Total propagated uncertainty
As stated earlier the height extrapolation of lidar data is performed by means of a stability corrected logarithmic wind speed profile (Equation 4). The wind speed at height of the TP u TP can thus be expressed as Gaussian error propagation yields the total propagated uncertainty with the corresponding uncertainty in the stability correction term The indices of the correction terms Ψ refer to the height at which it is determined. The uncertainty of the Obukhov length L is also determined by means of Gaussian error propagation of Equations 1 to 3, leading to 265 The uncertainties ∆T v , ∆Θ 0 und ∆Θ TP are hereby assessed using air and water temperature, humidity and pressure uncertainties. We set ∆T air = 0.1 K, ∆T water = 0.2 K, ∆p = 0.3 hPa and ∆H = 1.2 %, following typical uncertainties suggested in the sensors' user manuals. to be expected especially during very stable atmospheric conditions. Even though the study uses different input parameters, this also holds valid for our analysis.
We determined the total propagated uncertainty ∆u TP for each scan and grid point. Values were normalised within each 280 scan i using u TP,i and averaged across all valid scans, yielding ∆u TP,norm .

Corrected propagated uncertainty
In the uncertainty estimation of the total propagated uncertainty (Section 2.5.1) we defined ∆u TP,norm in a way that assumes none of the input uncertainties are correlated across range gates. That means, we also assume it is possible that the signs of the errors vary between range gates. While this might be true for wind speed errors ∆u m and roughness length errors ∆z 0 , it 285 does not hold for measurement height errors ∆z m , which are directly related to the tilt of the lidar, and the Obukhov length error ∆L, which we consider to be constant across the whole measurement domain. Since these assumptions could influence the interpretation of the results, we decided to determine the uncertainty additionally only considering measurement range independent input variables. That means, we set ∆z m = ∆Ψ TP = ∆Ψ m = 0 to calculate the corrected propagated uncertainty 290 Also ∆u TP,cor is normalised within each scan and subsequently averaged across all valid scans to ∆u TP,cor .
We examine the uncertainty contributions of ∆z m , ∆Ψ TP and ∆Ψ m for relevant cases separately in a case distinction in Section 3.4.

Standard error of the mean
As an alternative to the total propagated uncertainty we calculated the statistical error, i. e. the standard error of the mean 295 SEM = 1.96 for each grid point, considering all valid scans N r with the standard deviation of the normalised wind speed at each grid point σ uTP,norm . We included the factor 1.96 already in the definition of the variable to cover the 95 % confidence interval for normally distributed errors. The SEM estimates the deviation of the sample mean from the true mean (McKillup, 2005) and thus yields information regarding the statistical significance of the results. While the total propagated uncertainty regards the 300 accuracy of single input variables, the statistical error quantifies the precision of the results from different scans. A higher number of scans typically reduces measurement noise from the statistical error, i. e. wind speed fluctuations around the mean.

Results
In the following we present results of the four scenarios introduced in Section 2.4.
3.1 Scenario 1: Wind farm operating below and up to rated power at unstable atmospheric conditions with moderate 305 to high thrust coefficient This can be attributed to the relatively small change of wind speed with height during unstable conditions. Generally slightly larger values can be observed for the SEM as compared to ∆u TP,cor . For far range gates from approximately −38D onward, the SEM increases significantly as a consequence of lower data quality and the lower number of values considered here (c.f. Figure 3 (c)). We found no evidence for a decreasing trend in wind speed upstream of the wind farm GT I for Scenario 1.    the SEM exceeds ∆u TP,cor and increases strongly for far distances due to decreasing N r (see Figure 5 (c)) and decreasing 340 data quality for far range gates. The difference between ∆u TP,cor and ∆u TP,norm increases with distance to the wind farm as a consequence of the increasing measuring altitudes and the shape of the wind profile. Also considering the larger mean wind speed, the impact of the uncertainties of L and z m is here stronger as compared to the unstable cases in Scenario 1. uncertainty ∆u TP,norm reaches values of up to 3 %. As the analysed scans are attributed to stable atmospheric conditions, the impact of L and also z m is large.

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As defined in Section 2.5, the width of the uncertainty contributions are considered to cover 95 % of all cases. Figure 6 indicates a significant decrease of wind speed closer to the wind farm when considering the corrected propagated uncertainty ∆u TP,cor . This is not true anymore when including all error contributions, i. e. considering the width of the total propagated uncertainty ∆u TP,norm . In Figure 7 we visualise how the decrease of wind speed changes when assuming the largest uncertainties for L and z m to analyse the error contributions of the range gate-correlated variables in more detail. We consider the 360 same data set in Figure 7 as in Figure 6. Here, we show the two most extreme scenarios with L − ∆L, z m + ∆z m (blue, largest reducing effect on the deficit) and L + ∆L, z m − ∆z m (red, largest enhancing effect on the deficit) respectively. As explained earlier, we assume ∆L and ∆z m to be correlated across range gates within the same scan and thus consider the corrected propagated uncertainty ∆u TP,cor more valuable than the total propagated uncertainty ∆u TP,norm depicted in Figure 6 (b).
As clearly visible in Figure 6 (b) and Figure 7, misestimations of Obukhov length and measurement height have a significant 365 impact on the magnitude and shape of the observed wind speed decrease. In the blue graph in Figure 7 the wind speed deficit is reduced as a consequence of the more stable conditions and larger differences between measuring height and hub height assumed here. Considering the associated uncertainty, the observed wind speed deficit of approximately 2.5 % for this case with the largest reducing effect tends to be within the range of the corrected propagated uncertainty. When considering errors with less reducing effect, i. e. errors with the same sign but smaller magnitude, the wind speed deficit increases towards a 370 significant value. If maximal errors occur in the opposite direction (red curve), the effect would be maximally enhanced to a wind speed decrease of 6.5 %. Here, the observed decrease is large compared to the uncertainty intervals and thus clearly significant. Considering the range gate-correlated error contributions the wind speed deficit of 4.5 % lies within an uncertainty interval between 2.5 % and 6.5 %.

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We analyzed averaged long-range Doppler lidar PPI scans at TP height in the inflow of the 400 MW offshore wind farm GT I and found wind speed deficits upstream in stably stratified boundary layers with wind turbines operating at high thrust coefficient in the upper partial load range. In contrast, at unstable stratification and similar operating conditions, no effect was visible. We identified the comparably small wind speed difference by performing a data correction and by averaging the normalised lidar scans. We analyzed the effect considering a detailed uncertainty estimation. In this section, we discuss our  in Figure 6 (a), with the corrected propagated uncertainty ∆uTP,cor visualised as colored shaded area. For the blue curve L was additionally reduced by ∆L and zm increased by ∆zm, for the red curve L was increased and zm reduced respectively. These cases represent the two combinations of ∆L and ∆zm that yield the most extreme results.

Global blockage dependant on atmospheric and operational conditions
To distinguish between different wind turbine operational states and atmospheric stabilities we divided our measurement data into four different scenarios (c.f. Section 2.4).

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In unstable conditions with wind speeds from 10 m s −1 to 13 m s −1 and a moderate to high thrust coefficient (Scenario 1, Figure 3) we could not identify decreasing wind speeds in front of the wind farm and thus no global blockage effect. This result is plausible since wind speed fluctuations in unstable flows are much higher due to convection than the assumed magnitude of global blockage. Convection leads to more mixing in the boundary layer and thus repeals global blockage. Furthermore, in unstable stratification, the boundary layer is typically higher and thus the flow can pass obstacles like hills (Stull, 1988) or 390 in this case a wind farm more easily. Additionally to Scenario 1 we performed the analysis for unstable stratification and the wind speed ranges above rated wind speed and below cut-in wind speed respectively (c.f. Section 2.4). In both cases, we could not identify decreasing wind speeds in the inflow of the wind farm. As explained earlier we do not show these results here for brevity.
In stable atmospheric stratification and with low wind turbine thrust coefficients due to low wind speeds (i.e. not operating 395 turbines, Scenario 2, c.f. Figure 4) or due to high wind speeds (i.e. turbines operating with pitched blades above rated wind speed, Scenario 3, c.f. Figure 5) no wind speed reductions upstream of the wind farm were identifiable. When the turbines are out of operation there should not be any reason for global blockage to appear due to the very low thrust. For turbines operating above rated wind speed a small global blockage effect might occur. However, it is unlikely that the effect would be clearly visible in the data as a consequence of high wind speeds and the reduced thrust. Since the turbines operate at rated power 400 global blockage, if any, would not have a negative impact on power production in this wind speed range.
In stable atmospheric conditions with a high wind turbine thrust coefficient (i.e. wind turbines operating in the partial load range, Scenario 4, c.f. Figure 6) we found the wind speed to decrease towards the wind farm by approx. 4.5 % over a distance of 25 D = 2.9 km. For larger distances upstream, the wind speed approaches a constant value. The wind speed reduction is significant when considering range gate-uncorrelated uncertainties. It is considered meaningful for global blockage to be most 405 significant in stable stratification and for higher thrust coefficients.
Despite the intensive uncertainty analysis and error correction we performed in this work (c.f. Section 2.5), how certain can we be that our observations are caused by the global blockage effect? To consider the effect of the correlated error sources that we excluded from the calculation of the total propagated uncertainty, namely ∆L and ∆z m , Figure 7 shows the two most extreme cases with the largest reducing effect (blue) and the largest enhancing effect (red) of both error values. Assigning these 410 combinations of errors, the extent of the global blockage wind speed deficit is limited by 2.5 % to 6.5 %. In the latter case, the wind speed deficit is clearly significant, while for the first one, it could be explained by the correlated propagated uncertainty.
However, considering more likely error magnitudes in between those two most extreme cases, the wind speed deficit would become significant. Thus, we consider the wind speed deficit in front of the wind farm to be caused by the global blockage effect.

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Our measurements of global blockage were performed at a height of approx. 9 m below the rotor area while Bleeg et al. (2018) used measurements at hub height. An extrapolation to hub height instead of lidar height would not have a significant impact on our findings as it would only result in an upscaling of the observed effect to a higher altitude. Further, we assume extrapolation uncertainties would increase significantly when extrapolating across larger height differences (Theuer et al., 2020a). We do not know whether the global blockage effect is distributed equally over height but expect it to be most distinct 420 in the rotor area especially at hub height. With our measurement data, we were not able to study global blockage induced flow deflections upwards, downwards or sideways which could lead to increased wind speeds above, below or aside the wind farm's rotor area. The vertical extent of the global blockage effect in front of a wind farm needs to be assessed in future experimental or numerical studies. Schneemann et al. (2020) show the existence of cluster wakes in the inflow of GT I using data from the same measurement 425 campaign as used here. In the wind directions, we chose for the analysis of global blockage no distinct wind speed gradients are present in the inflow. Generally, the data we present here could be influenced by cluster wakes. We do not expect disturbances of the global blockage measurement since the centre flow of a cluster wake in the far-field is comparably homogeneous and would only reduce the mean wind speed in the whole lidar scan.
We found the magnitude of the global blockage induced deficit of approx. 4.5 % (uncertainty range 2.5 % to 6.5 %) in stable 430 stratification to correspond well with values measured in an onshore free field experiment by Bleeg et al. (2018) based on met mast point measurements at three different wind farms of typically 2 % to 4 %. One possible explanation of the comparably lower deficits of Bleeg et al. (2018) is the lack of stability information and thus the comparison of long intervals including the climate mean of stratifications. Our results suggest less or no global blockage effects in unstable stratification, this effect possibly reduced the average values of Bleeg et al. (2018). RANS simulations performed by Bleeg et al. (2018) typically simulations of large finite-size wind farms of 1.3 % and 3 % for different farm layouts in a weak free-atmosphere with neutral stratification across the rotor area, which is slightly lower than our findings.
Aside from results from wind tunnel experiments (Segalini and Dahlberg, 2019) and onshore free field point measurements (Bleeg et al., 2018) our lidar measurements represent the first areal free field investigation of the global blockage effect offshore.

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Spatial analysis of global blockage has only been reported from numerical studies so far. RANS simulations performed by Bleeg et al. (2018) for three different large onshore wind farms reveal homogeneous induction zones upstream of the farms with spatial extents of more than 2 km for a deficit of 1 %. Such distances correspond well to our findings in Scenario 4. The higher wind speed deficits in our data could possibly be explained by the restriction to stable stratification. Nevertheless, the shape of the induction zones in their RANS simulations seem to smoothly follow the first row of turbines. The contours we 445 show in Figure 6 tend to have the same shape in the middle sector of the wind field but deviate from that shape on the sides. We To assess the impact of the global blockage effect on a wind farms annual energy production (AEP) more research and development on the implementation and validation of the effect in wind farm planning tools is needed. A detailed AEP assessment then needs to consider particularly the local undisturbed wind speed and stability wind roses. The consideration of global blockage in the future could further increase the accuracy of wind energy site assessment which is especially important for 455 the financing process of wind farm projects. Despite its possible negative impact on energy production, global blockage seems not to have a critical impact on wind energy utilization. In our study, we observed the effect only below rated power, in stable stratification and with a magnitude of 4.5 % within the uncertainty range of 2.5 % to 6.5 %. Consequently, we expect global blockage to have a much lower impact on the power production than other wind farm flow features like inner wind farm wakes.

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Compared to wind turbine wake effects with several ms −1 wind speed deficit over a distance of less then one rotor radius between wake centre and free flow the global blockage effect has a comparably small magnitude. Scenario 4 reveals a deficit of about 4.5 % of the average wind speed of 9.0 ms −1 which equals approx. 0.4 ms −1 . This difference builds up over a distance of 25 D = 2.9 km. This is well below typical fluctuations in wind fields due to e.g. orographic or thermal influences which makes global blockage hard to identify in measurement data.

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There are no further areal wind field measurements of global blockage in literature. The shape of the zone with reduced wind speeds in front of the wind farm and comparisons of different locations could not be analyzed using single-point measurements like presented by Bleeg et al. (2018). Spatial characteristics of global blockage inflows of wind farms that were generated by numerical simulations and modelling (Bleeg et al., 2018;Branlard and Meyer Forsting, 2020)  zone with wind speed reduction can allow for a more detailed analysis.
Generally, we do not expect global blockage to be significantly identifiable in single flow measurements like an individual lidar scan. The effect is much smaller than the common fluctuations in wind farm inflows and needs to be derived from averaged measurements where the influence of local turbulence and coherent turbulent structures is reduced in the averaging process.
The lidar measurements we analyse in this paper were originally performed to study the effect of cluster wakes in the inflow 475 of GT I  and to perform minute-scale power forecasts (Theuer et al., 2020b). Due to the comparably small global blockage effect, all errors influencing the accuracy of lidar measurements need to be carefully examined and reduced wherever possible. We give an overview on sources of uncertainty in Table 1. For lidar measurement campaigns aiming at the assessment of global blockage or similar small flow effects we recommend to calibrate the lidar before the campaign. This includes the measurement of radial velocities, the range gate distance from 480 the device and especially the scanner orientation and movements. Here especially the scanners elevation angle deviation is crucial since it results in height errors of the measurement.
carefully align the lidar at the measurement location and to monitor the lidar's tilt dynamically. We recommend using accurate inclinometers and accelerometers and in offshore campaigns the method of "sea surface levelling" for lidar tilt alignment and the method of "hard targeting" for alignment of the north direction (Rott et al., 2017.

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perform independent measurements of the prevailing wind profile either by e.g. met mast, VAD lidar or virtual met masts spanned by scanning lidars (Bell et al., 2020) to be able to perform a proper height correction of the scanning lidar data.
perform measurements of meteorological quantities for characterization of atmospheric stability to support a more precise interpolation of the wind profile (e.g. Schneemann et al., 2020).
The stronger tilting on the nacelle compared to the transition piece and the resulting large errors in the measurement height 490 introduce increased uncertainties to nacelle-based measurements especially when aiming to achieve several kilometres of range or to detect small flow effects like global blockage. Active motion compensation of the lidar's scanner or similar measures could enable the possibility of nacelle-based measurements.
Further, the use of overlapping Dual Doppler measurements could be beneficial to better resolve local flow characteristics like global blockage induced flow deflections and to overcome the need for basic assumptions like the homogeneity of the 495 wind field in the VAD algorithm (c.f. e.g. van Dooren et al., 2016;Stawiarski et al., 2013). Another measurement system to assess global blockage could be the remote sensing method Doppler radar which was successfully deployed for wind turbine and wind farm wake measurements (Nygaard and Newcombe, 2018).

Conclusions
This paper has pursued the objective to analyze whether it is possible to measure global wind farm blockage with long-range lidar PPI measurements of the inflow of the 400 MW offshore wind farm Global Tech I. In stable stratification and with the turbines operating below and up to rated power with a high thrust coefficient, the measurements revealed reduced wind speeds at the height of the transition piece in the approaching flow. At unstable stratification and similar operating conditions, however, no effect was visible. We relate this upstream wind speed reduction to the presence of the wind farm, namely to global wind 505 farm blockage. Therefore, we conclude global blockage to be dependant on atmospheric stability.
Compared to wind turbine wakes or cluster wakes, global blockage is a very small effect that is overlaid with different atmospheric phenomena and thus very hard to detect. Nevertheless, based on our detailed uncertainty assessment we arrive at the conclusion that the wind speed deficit in front of Global Tech I in our lidar measurements is caused by global blockage.
Generally, we assume long-range Doppler lidar to be able to accurately measure global blockage and recommend to carefully 510 align and calibrate the used lidar systems.
Our measurements agree with recent findings of the magnitude of the global blockage effect to range from 2 % to 6 %. At platform level, we found a wind speed reduction of 4.5 % within an uncertainty range from 2.5 % to 6.5 %, over a distance of approx. 2.9 km or 25 D. The influence of the global blockage effect on the annual energy production of a wind farm requires further experimental and numerical investigations. Due to the expected limited appearance of global blockage only in special 515 atmospheric situations and wind farm operational states and its small magnitude, we expect the impact on power production to be much smaller in comparison to inner wind farm wakes. Accurate estimates of the global blockage effect by means of well-calibrated engineering models could further decrease uncertainties in wind farm site assessments and power calculations in the future.
In this work, we demonstrated scanning long-range Doppler lidar to be a suitable tool to study global wind farm blockage 520 and provide strong evidence for the existence of the global blockage effect for a wind farm with the turbines operating at high thrust coefficients in a stably stratified atmosphere.
Data availability. Lidar data are not published and could be made available on request. The OSTIA data set can be obtained from http: //marine.copernicus.eu/.
Author contributions. JS initiated the research, performed the measurement campaign, was heavily involved in funding acquisition and 525 research discussion, wrote Sections 1, 2.1, 2.2, 4 and 5 and prepared Figures 1 and 2. FT performed the data analysis, was heavily involved in research discussion, wrote Sections 2.3, 2.4, 2.5 and 3 and made Figures 3, 4, 5, 6 and 7. AR was heavily involved in research discussion and supported paper writing. MD initiated the research and was heavily involved in funding acquisition and research discussion. MK was heavily involved in funding acquisition and supervised the research. All authors contributed intensively to an internal review.
Competing interests. The authors declare no conflict of interest.