## 4 Discussion
The horizontal wind speed gradient is therefore slightly reduced behind the cluster in unstable conditions for the two wind directions. In stable stratification, wakes strongly impact the horizontal wind speed gradient because these conditions are favorable for wakes. A strong wind deficit downstream the cluster N-4 changes the gradient of the horizontal wind speed. The resulting strong wind gradient affects the adjustment distance, which may become longer The adjustment distance can also depend on the wake length and recovery. This need to be further investigated. The coastal gradients are important for offshore wind energy [10]. The location of the wind farms regarding the horizontal wind speed transects of \(u_{10}\) appears to be critical for the power production. The cluster N-4 is closer to the eastern than southern coast. The cluster N-4 is situated in-between the acceleration phase, where the wind speed is still at its lowest amplitude regarding easterly wind directions. This is the opposite for southerly winds, with the winds almost at the equilibrium level. This situation also applies to the cluster N-5, which is far from the southern coast. Consequently, the power production will be much more affected with easterly than southerly winds. However, this may not be the case for the cluster N-8 located far away from the eastern coast. In addition, the wind speed at the cluster N-8 has a higher wind amplitude than the one at the cluster N-4 and has almost recovered from the wake effects. Considering \"INCS\" measurements from both easterly and southerly winds, the average power-density \(\psi\) (Equation (19)) and the average normalised power density \(R_{\psi}\) (Equation (20)) are computed. The power-density increase is estimated as about 0.3 kW/m\({}^{2}\). As for the horizontal wind \(u_{10}\), the magnitude of \(R_{\psi}\) is lower close to the shore, but increases moving with distance from the coast and levels off at 160%. The magnitude of \(R_{\psi}\) represents more than twice the maximum of the \(R_{u_{10}}\) for horizontal wind gradients associated with stable conditions for easterly winds. It is also about four times as big as the respective normalised wind speed increase. These estimations refer obviously to the 10 m wind speeds provided by SAR, and are independent of any particular wind farm characteristics. These numbers show that coastal effects are significantly amplified if wind power is considered instead of wind speed. Further studies are required to translate these results to wind turbine hub heights. The analysis of horizontal wind fields has also shown a significant number of cases with decreasing wind gradients (\"DECS\"). The wind at its highest amplitude at the coast, decreases gradually towards an equilibrium. Here, the first phase concerns the decrease, while the second phase refers to the adjustment towards an equilibrium state. The analysis of such cases reveals that \"DECS\" occur predominantly in stable conditions. The investigation of LIDAR profiles acquired over the same period suggests the occurrence of LLJs at low altitude at the coast in these situations. The higher wind speed amplitude near the coast could be explained by the presence of LLJs. Offshore winds are associated with the occurrence of an IBL due to the change in roughness. The IBL height grows with increasing distance from the coast until an equilibrium is reached. In the case of an LLJ the situation in the lower boundary layer is very much dominated by the high wind speeds within the jet. However, the relative warm water temperatures and the resulting instabilities lead to vertical diffusion of the jet with growing distance from the coast, i.e., higher near-surface wind speeds are predominantly found close to land where the LLJ originated. In stable stratification, the LLJs initially at the coast propagate gradually with distance away from the shore. While moving away from the coast, the LLJs are shifted to higher altitudes and leave lower wind speeds below.