## 3 Results
### Example of Horizontal Wind Speed Gradient on 6 April 2018  
A typical example of increasing surface wind speeds with increasing distance from the shore is shown in Figure 6a,b. The 10 m SAR wind field displayed in Figure 6a was acquired on 6 April 2018 at 17:16 UTC. The wind direction is from the east-south-east (\(w_{d}\sim 109^{\circ}\)) as indicated by the DWD wind arrows in Figure 6b during the satellite overflight. The atmospheric condition is more stable (with higher thermal stability) as defined by Equation (21) (Figure 7c) closer to the coast than further offshore. Figure 7a shows the horizontal wind speed \(u_{10}\) computed over the transect \"Ref\" (rectangle in Figure 6a). The wind speeds increase gradually with distance away from the coast. In addition, the respective water depths along the transect is shown in green with a separate vertical axis on the right. Similarly, in Figure 7b the thermal stability is superimposed as a green curve showing a decrease as \(u_{10}\) increases away from the coast. It is clearly noticeable that following a more rapid wind increase in the initial part, the wind starts to adjust to an  
Figure 5: Mean SST and mean thermal stability for the seasons in (**a,b**) winter (DJF), (**c,d**) spring (MAM), (**e,f**) summer (JJA) and (**g,h**) autumn (SON) from DWD for the period 2017–2020. The black polygons represent the wind farm locations.  
equilibrium after roughly 130 km distance offshore. The horizontal wind speed obtained with the empirical model given by Equation (10) (red dashed curve in Figures 7c,d) closely follows the observed SAR wind field. Based on the fitting procedure the parameters \(u_{land}\) and \(u_{offshore}\) are estimated as 3.8 m/s and 11.7 m/s, respectively. This yields a maximal absolute increase of 7.8 m/s. This is in good agreement with the horizontal evolution of the parameter \(\delta u_{10}\) in Figure 7c, which also shows a wind speed increase exceeding 7 m/s. The adjustment distance \(x_{95\%}\) is estimated as 166 km and is indicated by a yellow dashed line in Figure 7c. The estimation of the maximum of \(R_{u_{10}}\) shows more than 180% wind speed growth. The modelled wind speed increase \(\delta u^{f}\) and normalised wind increase \(R^{f}\) using Equation (14), 15 (red dashed curves in Figure 7c,d), respectively, show good agreement with the observed quantities \(\delta u_{10}\) and \(R_{u_{10}}\) as well. \(R_{u_{10}}\) was estimated from Equation (17) with \(N_{p}=1\).  
The increase of the horizontal wind speed is also confirmed by DWD (Figure 6b and blue curves in Figure 7a-d). However, although the wind near the coast is higher for DWD, the magnitude of the increase is far weaker (\(\sim 4.8\) m/s and \(\sim\)120%) than for SAR. One explanation of this difference could be the coarser resolution of DWD. Therefore, in the following the statistical analysis are solely based on the high resolution SAR winds.  
Figure 6: (**a–c**): 10 m wind speed from SAR on 6 April 2018 at 17:16 UTC (**a**), DWD colocated 10 m wind (**b**), and thermal stability from DWD (**b**). (**c–e**): 10 m wind speed on 25 August 2019 around 05:48 UTC from SAR (**d**), colocated wind and thermal stability from DWD, respectively, in (**e,f**). The rectangular purple box represents the transect “Ref” in an area without any influence of atmospheric wakes. Red polygons indicate wind farm locations.