Comparing the NLLJ wind speeds and heights for long events (>3 h) and short events (≤3 h) at both sites highlighted different behaviors. The mean jet core wind speed of long events was stronger, 7.8 (8.4) m s-1 against 6.1 (7.0) m s-1 in Falkenberg (Lindenberg), but the extremes were more frequent for short events (Fig. ). The highest NLLJs were also the ones that were typically short. Also, the mean core height at 222.9 (218.8) m for long NLLJs was a bit lower than for short events at 244.3 (236.0) m in Falkenberg (Lindenberg). From Fig.  we can also see that the longer events had narrower distributions.

Table  shows the number of nights with at least one NLLJ event, as well as the number of nights with NLLJs classified by their duration. The percentage in brackets is the frequency of occurrence of NLLJs relative to the total number of nights (first column) and relative to the total number of NLLJ nights (latter four columns). We can see that 73 % (64 %) of the nights presented at least one NLLJ event in Falkenberg (Lindenberg) with a clear division of about half of those nights having events longer than 3 h. The presence of very long events (>6 h) was similar at both locations at 24 % and 29 % of the NLLJ nights, but the number of nights with only very short events (≤1 h) was more than doubled in Lindenberg (11) compared to Falkenberg (5).

Furthermore, we compared co-occurring NLLJs from both lidars. This assessment was inspired by the example of a long NLLJ that occurred during the night of 27–28 June 2020 at both locations but developed differently over time (Fig. ). While the nocturnal development was very similar between 22:00 and 02:00 UTC, there were differences during the early morning. Falkenberg saw a single long NLLJ that persisted until around 02:00 UTC when the NLLJ detection in Lindenberg was interrupted. In Lindenberg, the NLLJ was detected again around 03:00 UTC but not in Falkenberg. Such differences are associated with intermittent mixing and reflect the local differences in meteorological conditions and possibly the terrain. To better understand such effects, we assessed the spatial differences of co-occurring NLLJ profiles at both sites next.

We performed a statistical comparison of the core wind speed and height for co-occurring NLLJ profiles at the two sites (Fig. a and b). While the wind speeds were often similar at both places, the heights had larger differences between the two places. From the NLLJ profiles identified in Falkenberg, 75 % were also identified in Lindenberg, while for the opposite it was 87 %, underlining the frequent co-occurrence of NLLJs on the mesoscale. Restricting the analysis to short NLLJ events, the percentages were smaller, with values of 48 % and 53 %. This is to be expected since short NLLJ events can be associated with intermittent developments of long NLLJs (as in Fig. ), driven by density currents from convective cold pools that may not affect both sites simultaneously or even driven by local conditions like terrain differences. This behavior was also reflected in the lifetime of co-occurring NLLJs at the two sites (Fig. c). Co-occurring NLLJs lasting for more than 6 h had typically similar lifetimes at both places. This is consistent with the mesoscale spatial extent of NLLJs being driven by reduced frictional coupling of the wind field with surface friction in an inertial oscillation.

Looking at long NLLJ events in more detail revealed a nocturnal development similar to what one expects from inertial oscillations. Figure  shows the daily cycles of long NLLJs, including distributions of the jet core speed and height, as well as the normalized mean Ri (nRi) and dT (ndT) between 1 and 10 m a.g.l. The normalization was made by dividing the mean hourly values by their maximum positive values in order to better illustrate the daily cycle. The development of long NLLJs depended on the presence of the near-surface temperature inversion. Take for instance the temperature gradient ndT in Fig. a. After sunset, ndT increased, indicating the development of a surface inversion and leading to a reduction in frictional effects on the air flow at some distance from the surface. Stable stratification prevailed until the early morning hours when NLLJs also frequently occurred. It is important to mention that the average nRi and ndT had similar behavior when we included nights without NLLJs. This is a reflex of the higher stability of the atmosphere during night time. We also saw an increase in the mean core wind speed over time up to about 01:00 UTC when it started to decrease until the early morning. Up to 23:00 UTC, the mean jet height decreased and remained about constant thereafter. This behavior is broadly consistent with the process expected for an inertial oscillation, but there are also differences as would expected from the idealized assumption of stationarity in the theory. For example, longer periods of increasing wind speed are predicted from the theory, coinciding with half a period of the oscillation in mid-latitudes (approx. 8 h; ). This difference from the theoretical duration was apparent, especially for the short events. In addition to non-stationarity, reasons for differences between the measurements and the theory are the neglection or simplification of the smaller, yet still present, frictional effects . In reality, NLLJs are affected by intermittent mixing events, i.e., temporally variable frictional coupling of the jet with the surface layer and changes in the geostrophic wind along with the synoptic-scale weather conditions.

The wind directions changed in the course of the development of NLLJs but not as systematic as one would expect for a classical inertial oscillation. We selected the data from Lindenberg for quantifying the changes in wind direction in the core of the NLLJs. Most NLLJ events did not show large changes in wind direction in the course of their lifetime, falling between -40 and 40∘ total directional changes calculated as the total wind direction shift in the NLLJ core. NLLJs more frequently had a clockwise change (positive values in Fig. a) than counterclockwise. An inertial oscillation causes the wind field to veer in the course of the night. One therefore expects a larger directional shift in the NLLJ wind the longer the events are. We identified a total shift in the direction of the mean absolute values of 34∘ for short events, 107∘ for long events and 132∘ for very long events, consistent with veering in an inertial oscillation. Indeed, some of the longest events (marked by dashed lines in Fig. a) had large wind directional shifts, consistent with the theory of an undisturbed inertial oscillation.

The turning of the wind is very clear for the longest NLLJ event in Lindenberg during the night of 12–13 August 2020 (Fig. b). The NLLJ development began around sunset shortly after 18:00 UTC and ended due to turbulent mixing in the early morning hours (04:00–06:00 UTC), indicated by the morning time increase in dT. The perturbations in the turning of the wind are clearly related to fast changes in the geostrophic wind at about 00:00 UTC. This relationship between wind-turning perturbations and fast geostrophic wind changes also happens to other events from the campaign (not shown). This NLLJ event also led to supergeostrophic wind speeds consistent with the theory (Fig. c). The supergeostrophy, although already expected from theory, might at least in parts be explained by the slackening geostrophic winds in this example. Thus, changes in the synoptic-scale conditions affected the NLLJ development, although this event is close to characteristics expected from the theory. Other NLLJ events showed larger deviations from the theory (not shown), indicative of intermittent turbulence perturbing the nocturnal acceleration and turning of the wind field paired with temporal changes in the horizontal pressure gradients due to the evolving weather. The NLLJ of 12–13 August 2020 was associated with an anticyclonic southeasterly wind over the measurement sites due to a high-pressure system to the northeast.

We systematically investigated the occurrence of NLLJs under different synoptic weather patterns. Using the Großwetterlagen of the German Weather Service , we detected NLLJs in 13 out of 16 different weather pattern occurrences (Figure ). Three weather patterns had particularly favorable conditions for NLLJ development. The pattern with the largest amount of NLLJ events was the Scandinavian high, trough central Europe (HFz) pattern (Fig. a). The most efficient pattern was the anticyclonic south-easterly (SEa, Fig. b), with the highest overall probability, since all nine cases were associated with a NLLJ. Both weather patterns point to inertial oscillations being driven by the sufficiently large geostrophic wind at the margin of a high-pressure system paired with relatively dry conditions allowing stronger nocturnal radiative cooling of the surface. The two synoptic weather patterns are shown as composites in Fig. a and b, indicating high-pressure systems in northern Europe and lower pressure towards the south resulting in a large horizontal pressure gradient over the measurement site. The pattern with the largest number of short NLLJ events was the cyclonic westerly (Wz) (Fig. c), pointing to NLLJs associated with the passage of low-pressure systems. Northeast Germany was also found in a zone with a strong pressure gradient during this weather pattern.

These results are broadly consistent with findings by , based on data from May 2001 to April 2003 in Hanover (about 300 km to the west from our sites). They indicate that a short period can be sufficient to assess NLLJs associated with different weather patterns, although longer datasets would be needed for a full climatological assessment. It is interesting that we detected NLLJs during two patterns that were not detected in the previous study, namely cyclonic north-easterly (NEz) and anticyclonic north-easterly (NEa). These differences may be related to the different NLLJ identification methods, different locations or different time periods. In , SEa also had a very high efficiency; however, the high Scandinavia-Iceland, ridge central. Europe (HFNa), with the highest efficiency in his work, did not occur during our campaign.

NLLJs have a strong effect on wind power generation since they increase the wind speed at rotor heights. We quantified these effects using wind data at 100 m a.g.l. from lidar WL177 in Falkenberg, representative of typical rotor hub heights (Fig. a). The frequency distribution of these hub wind speeds during NLLJ events is clearly shifted to higher values compared to all data. For instance, the mean hub wind speed of 4.8 m s-1 from all data is smaller than the mean of 6.0 m s-1 during NLLJ events.

We calculated the wind power generation from two wind turbine models: Enercon E-126 and Vestas V112. The former has a much larger rated power and steeper increase in power generation with wind speed. We therefore normalized the wind power estimates by the respective rated power of the turbine for a better comparability of the results (Fig. b and c). The results highlighted the shift in the frequency distribution of wind power generation to higher values during NLLJ events. The distributions reflect the production in the lower half of the power curve since the wind speed rarely reached values needed for yielding the rated power.

The additional power generation during NLLJs nonlinearly depends on the turbine type. From the estimated total wind power potential during the campaign, 24 % (28 %) was generated during NLLJ conditions for the V112 (E-126). NLLJs increased the mean power generation of the same turbines by 53 % (80 %) compared to all conditions. This implies mean power values of 382.2 (583.3) kW for V112 and 785.2 (1412.2) kW for E-126 during all conditions (NLLJs). In comparison, the changes in wind speed at rotor heights were not as strong: 23 % for V112 and 32 % for E-126. This behavior reflects nonlinear dependencies of the power generation on NLLJ occurrence and characteristics, depending on the turbine type and hub height. Power production from the higher wind turbines with larger rated power therefore benefits more strongly from the occurrence of NLLJs.

Weak NLLJs (e.g., Fig. d) were rare such that most NLLJs were strong enough to reach the cut-in wind speed of both wind turbines and allowed power generation. We observed NLLJ profiles with wind speeds below the cut-in threshold at the rotor heights of the E-126 (135 m) in 12 individual profiles, translating to 0.2 % of all valid NLLJ profiles. For the V112 (94 m) this happened for 45 profiles or 0.7 %. These differences between the two turbine types are primarily explained by the different rotor heights since the cut-in wind speeds are identical.

While NLLJs are beneficial for the nocturnal power generation, their occurrence also has adverse implications for the turbines. Wind shear and veer in the rotor layer, here defined as 50–150 m a.g.l., were considerable during the occurrence of NLLJs, as indicated in the examples of wind profiles with different wind shear values (Fig. ). These are a case with (a) strong positive shear without the presence of a NLLJ, (b) strong positive shear due to a NLLJ, (c) a NLLJ with the core inside the rotor layer, causing positive shear below and negative shear above the core, and (d) a NLLJ with a core immediately below the rotor layer, which leads to negative vertical shear in the entire rotor layer. It is important to mention that when the NLLJ core falls within the rotor layer, care should be taken of how the shear, and thus the mechanical loading, is calculated. If we were to calculate the mean shear taking positive and negative shear together, it would result in a false impression of small shear. We therefore calculated the shear based on absolute values across the rotor layer for these conditions.

The shear was substantially larger during NLLJs events. The mean wind shear in the mean rotor layer (50–150 m) had an increase of about 67 % during NLLJ events. A similar value was found for V112 since that turbine type has a similar rotor layer (38–150 m). The higher E-126 (71.5–198.5 m) had a mean shear 53 % lower, but the increase during NLLJs was 84 %. We rarely saw negative shear values from cases like those illustrated in Fig. d, and those that occurred were often below the cut-in wind speed, consistent with having relatively few and weak NLLJs at very low levels.

Our results indicate that almost half (48 %) of all cases with extreme wind shear coincide with NLLJs (Fig. a). It implies that NLLJs are as important as storms for causing strong wind shear. Out of all occurring NLLJs, 37 % of NLLJs lead to extreme shear through the rotor layer. We here defined extreme wind shear through the rotor layer as the 90 % percentile, following , which corresponded to a similar threshold of 0.0354 s-1. The extreme shear was primarily explained by larger core wind speeds for NLLJs at similar heights rather than stronger NLLJs at higher altitudes. This can be seen by the similar distributions of the NLLJ height paired with a shift in the distribution of core wind speeds during NLLJs with extreme shear (Fig. b and c).

In addition to shear, the wind veer with height across the rotor layer also has implications for the mechanical loading on the rotors. We therefore quantified the absolute wind veer across the rotor layer during NLLJ events (Fig. ). The magnitude of the wind veer was typically larger during NLLJ events with a mean of 0.174∘ m-1 against 0.145∘ m-1 during all cases. It corresponded to a mean increase in the veer by about 20 %. The results for V112 were similar and slight differences were seen for E-126. For E-126, the average veer was 11 % lower than for V112 and the mean increase was 12 % during NLLJs.