the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Mar 2026
An in-depth observational and modeling analysis to explore long-range offshore wakes under different stability regimes
Abstract. As wind energy areas continue to be built out worldwide, it is increasingly important to understand the implications of long-range wind farm wakes on wind energy generation. While gross capacity factors can be estimated, the impacts of upstream wind farm wakes on downstream energy production, especially under stable conditions, are largely unknown. A clear understanding of marine atmospheric boundary layer (MABL) stability in offshore regions is still evolving, as continuous high-resolution thermodynamic profiles in the MABL are uncommon. Given the relationship between stability and long-range (>50 km) offshore wakes, it is increasingly important to reliably estimate stability conditions in offshore regions. With the lack of consistent observations in and around offshore wind farms, it is necessary to rely on mesoscale models such as the Weather Research and Forecasting (WRF) modeling system to estimate stability and wake lengths. For this work we test WRF's ability to reproduce wake effects and potential losses using flight data over wind farms in North Sea to evaluate its performance. As thermal stability is critical to understanding wake length, different metrics are evaluated to determine the best way to parameterize atmospheric stability from the WRF model. Results show that the bulk Richardson number derived from WRF can be used as a reliable metric to classify stability and that wake lengths are well represented under stable conditions.
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Status: final response (author comments only)
- CC1: 'Comment on wes-2026-55', Stefan Emeis, 19 Mar 2026
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RC1: 'Comment on wes-2026-55', Anonymous Referee #1, 17 Apr 2026
Revised Manuscript Assessment (wes-2026-55)
The manuscript entitled “An in-depth observational and modeling analysis to explore long-range offshore wakes under different stability regimes” presents a comparative study between aircraft-based measurement data—collected during the WIPAFF project—and WRF simulations for the corresponding period. The manuscript is well-structured and systematically addresses the research questions posed at the outset.
However, while the logical flow is sound, the manuscript would benefit significantly from a more robust discussion of the findings. Specifically, there is a lack of critical interpretation regarding the comparison of wake characteristics between the empirical measurements and the numerical simulations.
Recommendations:
- Model Reproducibility: While the WRF model setup is introduced in Section 3.1, a more comprehensive description of the configuration (e.g., specific parameterizations, domain nesting, and boundary conditions) is required to ensure that the results are reproducible by the broader research community.
- Data Methodology: The acquisition and post-processing of the airborne measurement data are currently described with limited detail. It remains unclear, for instance, what filtering criteria were applied to the raw data or how potential outliers were handled.
- Scientific Contribution: The inclusion of a dedicated Discussion section is highly recommended. This would allow the authors to contextualize their findings, highlight the most significant results, and explicitly state the contribution of this analysis to the fields of wind energy and mesoscale modeling.
Detailed Comments
Line 22: Please clarify the term "turbines facilities". It is recommended to use standard industry terminology, such as "wind energy converters" or "wind turbines."
Line 43: The current sentence structure, particularly the dependent clause in German, is difficult to follow. Please restructure this for improved readability.
Line 46: The authors should acknowledge the role of Lidar measurements in this context. Several studies have utilized such data; for example, Cañadillas et al. (2022) investigated offshore wind farm cluster wakes using long-range scanning wind Lidar and mesoscale modeling.
Line 69: Consider referencing Berge et al. (2024) regarding their comparison with X-Wakes measurement flights not WIPAFF.
Figure 1a: Please provide a justification for the selection of this specific vertical profile over others. There appear to be significant spatial and temporal discrepancies between the available profiles that should be addressed.
Line 219: The authors state that wakes from all 41 flights were compared; however, 16 of these are not wake measurements (line 94). Please clarify the methodology used to include these non-wake cases in the comparison.
Line 226: Siedersleben et al. (2018) already compared WIPAFF data to the WRF model for a single flight rather than the entire ensemble. So this sentence should be rephrased to accurately reflect the scope of that study.
Table 4: * Regarding the phase error: Were comparisons conducted only at full-hour increments, or did the error always result in full hours? Would analysis at smaller temporal increments yield more precise results?
- How were flights with mean altitudes significantly above hub height (e.g., 180 m + ) analyzed for wakes and subsequent time shifts? Please elaborate on this process.
Line 325: Please provide the relevant citations for the studies mentioned here.
Line 337: Have other vertical aircraft profiles been examined? The spatio-temporal bias noted may vary significantly depending on the time of day and the geographical position of the measurement.
Line 363: It is suggested to look into the X-Wakes dataset 8 https://doi.pangaea.de/10.1594/PANGAEA.955382), as it may contain extreme stability cases that could strengthen the analysis.
Figure 10: Please provide a potential physical explanation for the three outliers in subfigures (a) and (b), where the measured Capped Inversion Height (CIH) is more than triple the WRF-simulated CIH. Were there specific meteorological conditions during these flights that caused this divergence?
Line 390: Typo correction: "can be used."
Line 418: Grammar correction: "...profiles show that..." (or "...profile shows that...").
Figure 13: The text and labels in this figure are currently too small. Please increase the font size to ensure legibility.
Line 460: What is the hypothesized reason for the shift in the theta_v gradient observed around 2012/2013? Furthermore, do the subsequent years show an ongoing trend?
Line 489: The discussion comparing the measured and modeled (WRF) wakes requires significant expansion. While these results appear in Table 4, they are underrepresented in the text. Given that this is a core finding, more emphasis should be placed on interpreting the model's performance in both the near- and far-wake regions.
Line 503: Please justify the selection of 2012 for this analysis instead of the years during which the WIPAFF flights were conducted.
Citation: https://doi.org/10.5194/wes-2026-55-RC1 -
RC2: 'Comment on wes-2026-55', Anonymous Referee #2, 22 Apr 2026
Review of manuscript wes-2026-55
This manuscript investigates offshore wind farms wakes under different atmospheric stability conditions. The authors compare in situ measurements with model results from WRF.
Overall, the manuscript is clear and well-written. However, there are a few things that could improve the work. Specifically, the figures should be made clearer and the font must be made readable.
Specific comments
Specific humidity, as shown in Figures 6 and 11, is quite different for observations and model results. Please explain/discuss this further.
The results in part II seems a bit apart from the rest of the manuscript. Consider if it would make more sense to put it into an appendix.
Point 3 in Conclusions seems to introduce results not presented elsewhere. Please move this to an appropriate place in the manuscript (including Fig. 17).
Technical corrections
Line 22: Is “un-waked” an established term?
Line 53: “Phase error” is used frequently in the manuscript. Perhaps it would be clearer to specify, at least the first time, that it refers to a time shift?
Line 68: I guess “wake loses” should be “wake losses”?
Figure 2: It is very difficult to find the blue star of FINO3 against the background of black dots.
Line 155-156: U and V are referred to as gradients. Should it be ΔU and ΔV?
Figure 3: Please check if you can choose another color for “hour offset 0” as it is very difficult to separate from “hour offset 1” in a printed document.
Figure 3: Please add what the grey lines represent (like you do in Fig. 6)
Figures 4 and 5: Font for coordinates is too small to read.
Line 272: Here you write “time synching problem”. Is that the same as the “phase error”?
Figure 7: It is difficult to distinguish the “Stability measurement location” from the black dots of the wind turbines.
Line 376: Please remove extra “that”.
Line 418: “hows” -> “shows”
Figure 13: Font is too small to be readable.
Citation: https://doi.org/10.5194/wes-2026-55-RC2 -
RC3: 'Comment on wes-2026-55', Anonymous Referee #3, 10 Jun 2026
The manuscript investigates long-range offshore wind-farm wakes and how their behavior changes under different atmospheric stability regimes in the German Bight. The study combines observations and modeling by using airborne measurements collected between 2016 and 2017 over offshore wind-farm wake regions during the WIPAFF project and FINO3 met-mast data to validate WRF model simulations with Fitch wind farm parametrization.
The main scientific focus is on the influence of atmospheric stability, as characterized by the Bulk Richardson number and the atmospheric boundary layer height, on offshore wind-farm wake length and downstream wind-speed deficits, with additional validation of the capping inversion height.
The study finds that the Bulk Richardson number derived from WRF is a reliable metric for classifying offshore atmospheric stability, particularly when using the Businger-Hicks formulation. The paper also suggests that stable offshore conditions can lead to wakes longer than 50 km, and it finds good agreement between WRF-derived capping inversion heights and aircraft profiles.
This is an interesting topic and is relevant for wind-energy applications. However, there are a few limitations that should be addressed. I hope the following comments and suggestions will help improve the manuscript and make it more suitable for publication.
General comments:- The manuscript would be easier to follow with a clearer structure. The Results and Discussion sections should be more clearly separated before the Conclusions. At the moment, some discussion points are included in Sections 4 and 5, which mainly present the results. A separate Discussion section would help clarify the interpretation of the findings, the study limitations, and the broader implications for offshore wind-energy applications.
- It would be great if the study's main contribution and novelty were clearly stated.
- The connection between the validation parts and the climatology could be clearer. Why was the period 2010–2013 chosen for the climatology study?
- Not clear whether the validation of FINO3 data includes the cases where there is an impact of wakes from Sandbank or DanTysk.
- Some figures (for example, Fig 4, 5) could benefit from a colorbar that better highlights details between the observation and the model.
- Please add the correct reference to the WIPAFF data throughout the manuscript : Bärfuss, Konrad; Hankers, Rudolf; Bitter, Mark; Feuerle, Thomas; Schulz, Helmut; Rausch, Thomas; Platis, Andreas; Bange, Jens; Lampert, Astrid (2019): In-situ airborne measurements of atmospheric and sea surface parameters related to offshore wind parks in the German Bight [dataset publication series]. PANGAEA. https://doi.org/10.1594/PANGAEA.902845
Specific comments:- Line 50; 80: please add the reference Bärfuss et al., 2019
- Line 111—114: Depending on wind direction, measurements at FINO3 may be affected by wakes from the Sandbank and DanTysk wind farms. This means those measurements are not under fully free-stream conditions. Are those cases excluded from the analysis from FINO3? Please clarify.
- Line 145-148: Missing ‘)’ and sentence not clear; please check or reformulate.
- Line 256-261: Would the outcome of the study be different if the time phase difference were not taken into account?
- Line 280-290: Could the cold bias in the WRF model influence the stability calculation?
- Line 320: “before and after” : could it be clearer (for e.g., upwind and downwind?)
- Line 360 (profile): missing “s”?
- Line 376: “Using this method…”: Please remove the second “that”.
- In Figure 9, the agreement between WRF and FINO3 appears stronger than the agreement between WRF and the flight profiles, particularly for the lapse-rate metric. This difference should be discussed more clearly, as it may reflect differences in sampling strategy, measurement height ranges, temporal averaging, or the spatial representativeness of the aircraft profiles compared with the fixed FINO3 tower measurements.
- Line 402–404 and Figure 12: The distribution of points is strongly concentrated around neutral to stable conditions, with relatively few unstable cases. This uneven sampling may partly explain why the relationship between wake length and Rib is unclear. Platis et al. (2020, 2022 suggested that wake length is strongly linked to thermal stability. Could the authors discuss whether a thermal stability metric, rather than Rib alone, may better explain the relationship between wake length and stability? Ref: Platis, Andreas, Marie Hundhausen, Astrid Lampert, Stefan Emeis und Jens Bange. 2022. ‘The Role of Atmospheric Stability and Turbulence in Offshore Wind-Farm Wakes in the German Bight’. Boundary-Layer Meteorology 182 (3): 441–69. https://doi.org/10.1007/s10546-021-00668-4.
- Section 5: The term “climatology” is too strong for an analysis based on four years of WRF simulations and FINO3 observations. The 2010–2013 period provides useful information on multi-year variability. However, it is not long enough to support robust climatological conclusions. Please explain the choice of the period 2010—2013.
- Line 475: Is it Fig. 16 or Fig. 14? Please check.
- Figure 14: The results presented are only for 2011 and 2012. However, the climatology section discusses the full 2010–2013 period. It would be helpful to show all four years or provide quantitative evidence that 2011 and 2012 represent the full period.
- Line 483—484: Studies based on Satellite SAR also showed that atmospheric wakes can extend beyond 50 km for stable stratification. Please add relevant references here. Please add relevant references here (Christiansen and Hasager, 2006; Djath et al., 2018, 2022…)
- Line 502—505: Please clarify the criteria for selecting 22 cases from the 2012WRF simulation. This part of the analysis is not limited by airborne measurements. Could the number of cases be increased to achieve a better, more robust outcome?
- Line 506—508: These statements are important and should be supported by relevant references and further discussion. Please provide some references and further discussion.
Citation: https://doi.org/10.5194/wes-2026-55-RC3
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This is a very interesting paper dealing with an important issue: the wakes of larger offshore wind farms. This note is not to be considered as critics but just serves in order to give some hints to additional studies addressing the same subject.
First of all, atmospheric stability had been neglected in offshore wind energy projects for a long time. See Emeis (2010) https://onlinelibrary.wiley.com/doi/abs/10.1002/we.367?trk=public_post_comment-text for a first study wihich analyses the principle impact of atmospheric stability on wind farms wakes by a simple analytical model.
Atmospheric stability information could be displayed by so-called stability wind roses. Fig. 6 in Emeis et al. (2016) https://iopscience.iop.org/article/10.1088/1742-6596/753/9/092014/pdf gives an example how to do this. The stunning result is that stability and wind direction are strongly correlated for offshore areas of the midlatitudes. In the North Sea stable conditions are linked to southwesterly winds.
There had been earlier studies on how to reproduce WIPAFF data by WRF simulations. Maybe a look at Siedersleben et al. https://www.schweizerbart.de/papers/metz/detail/prepub/89817/Evaluation_of_a_Wind_Farm_Parametrization_for_Meso?l=DE may be helpful.
Anyhow, this paper deserves publication finally.