## 4 Discussion  
The investigation of the evolution of the horizontal wind field indicates that the wind intensifies gradually with growing distance away from the coast. Considering transects (Figure 2b) around the cluster N-4 the difference between horizontal winds offshore and the ones near the land is significant. The evolution of the horizontal wind fields can be defined as a two-phase process: The first phase concerns the rapid intensification of the wind speed and the second phase refers to the adaptation of wind to a relatively stable state far away from the coast. These observations are consistent with previous studies [57; 58; 59]. An average wind speed increase \(\Delta u\) of about 1.5 m/s and 1.3 m/s for all classes combined for easterly and southerly winds is, respectively, found. The scaling of the wind speed increase with respect to \(u_{land}\) yields a mean normalised wind speed increase of more than 18% for both wind directions. The parameter \(u_{land}\) is estimated through the fitting of an empirical model, which is more stable than a direct use of satellite signals close to land. The detailed analysis of the structure of horizontal wind speed gradients for easterly and southerly winds reveals different behaviours of the wind field, which are classified into three categories: The class \"INCS\" predominantly represents about 60% while the class \"DECS\" and \"LINCS\" constitute about, respectively, 20% and 15% of all cases. The \"INCS\" cases represent what should be expected when the wind blows over a discontinuity in the surface roughness [8; 60]. They obviously follow the two-phase process. Higher values for \(\Delta u\) of about 2.9 m/s and 2.3 m/s are consistently estimated by the empirical model for, respectively, easterly and southerly winds. The adjustment distance \(x_{95\%}\) is evaluated to 91 km and 38 km for, respectively, easterly and southerly winds. Overall, a maximum of \(R_{u_{10}}\) of about 46% is found for easterly winds and of about 32% for southerly winds. Hence, \(R_{u_{10}}\) for southerly winds is two thirds lower than that for easterly winds, although the wind rose and the average wind field indicate that the magnitude of the wind fields for both wind directions are quite comparable and small. In addition, southerly winds appear to increase rapidly and adjust to a stable state over shorter distance in comparison to easterly winds. There is a possible reason for these differences of the adjustment distance between the easterly and southerly cases. One hypothesis is that this has to do with differences in the overall structure of the eastern and southern coastline in the German Bight. The bathymetry shows that the eastern coastline has a more fuzzy geometric structure with the North Frisian islands spread over a wider range of distances from the mainland compared to the East Frisian islands. This could explain why the boundary layer transition process appears to be smoother for easterly winds. Another possible explanation is related to differences in the stability for easterly and southerly winds. It became apparent in Figure 14 that stable situations have a higher stability for easterly than for southerly directions and unstable situations have a higher instability for easterly than for southerly directions. This is to some extend consistent with the stability roses shown in [PERSON] et al. [61], although there is a strong stability increase in the south-west directional sector, that is partly included in the angular range used for our analysis of southerly wind directions. The empirical model introduced in this study depicts quite well the horizontal wind speed gradient for both considered wind directions. It demonstrates that the horizontal wind speed gradients can be described by an exponential function. The statistical analysis of different variables simulated by the model with respect to the SAR data show that the majority of computed adjustment distances \(x_{95\%}\) are below 100 km.