Comment on "A theoretical upper limit for offshore wind energy extraction" by Sim&atilde;o Ferreira et al. (2026)

van der Laan, Maarten Paul; Watson, Simon

doi:10.5194/wes-2026-59

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https://doi.org/10.5194/wes-2026-59

Preprints

24 Apr 2026

| 24 Apr 2026

Status: this preprint is currently under review for the journal WES.

Comment on "A theoretical upper limit for offshore wind energy extraction" by Simão Ferreira et al. (2026)

Maarten Paul van der Laan and Simon Watson

Abstract. A theoretical limit for the energy extraction of offshore wind farms has been suggested by Simão Ferreira et al. (2026) based on a simple analytical model that was originally designed to provide an estimate of the wake loss of an infinite wind farm. Simão Ferreira et al. (2026) validated the model with 72 offshore wind farms using an ad hoc and undocumented method to correct the model for application to finite wind farms. In this work, we discuss a number of concerns regarding the reproducibility of the finite wind farm correction and its sensitivity to the model results and validation, as well as the application of the model to assess national policies. We conclude that the limit proposed in Simão Ferreira et al. (2026) is not a theoretical limit but a model limit that is strongly dependent on the finite wind farm correction.

Received: 26 Mar 2026 – Discussion started: 24 Apr 2026

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Maarten Paul van der Laan and Simon Watson

Status: open (until 22 May 2026)

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RC1:
'Comment on wes-2026-59', Anonymous Referee #1, 02 May 2026 reply
Review of “Comment on "A theoretical upper limit for offshore wind energy extraction" by Simão Ferreira et al. (2026)” by van der Laan and Watson.
Overview:
van der Laan and Watson have provided a careful and technically rigorous critique of Simão Ferreira et al. (2026) by clarifying the interpretation and the methodological robustness of the proposed “theoretical limit” for offshore wind farm capacity factors. Van der Laan and Watson raise substantive concerns that significantly affect how the original results should be understood and applied.
Most importantly, van der Laan & Watson (vdLW) argue that Simão Ferreira et al.’s (SFLS’s) work cannot be considered a theoretical or universal bound analogous to the Betz limit. I strongly agree with vdLW that “the proposed limit … is not a theoretical limit … but a model limit ….” The SFLS derived capacity factor limit depends explicitly on modeling assumptions (turbine spacing, the treatment of finite wind farm effects). The language used by SFLS risks overstating the generality and physical inevitability of their result. More precise language would be “a model dependent upper bound under specific simplifying assumptions” rather than a “theoretical limit” which implies a fundamental constraint on wind energy extraction.
vdLW carefully examine the finite wind farm correction of SFLS and show that the correction method is ad hoc and insufficiently documented, that it is not reproducible without subjective interpretation. vdLW give a good-faith effort to develop (and document, and provide the python code via zenodo) an effort to provide an automated method to replicate the SFLS approach and demonstrate the insufficiencies of that method, further emphasizing that the SFLS approach is not reproducible. Further, they show clearly in Figs 5 and 6 that the SFLS model is highly sensitive to this parameter. I recommend this important comment for publication in Wind Energy Science.
Major comments:
My main criticism of vdLW is that this comment is not critical enough of the overall premise of SFLS. Wind farm performance cannot be reduced to a single deterministic relationship without careful treatment of atmospheric variability and spatial heterogeneity; this point is not made in the carefully circumscribed comment.

vdLW correctly point out that SFLS's validation of capacity factors not only includes wake effects, but also grid losses, curtailment, and turbine availability losses (lines 187-190), but they could emphasize more clearly the impact of incorporating all these other losses into what SFLS label as wake effects.

vdLW do not comment on the implication of the large scatter in their Fig 6, which it seems might actually suggest that a more rigorous (or at least reproducible) approach than that given by SFLS would imply even more losses, which might argue that national policies overestimate possible capacity by an even larger margin. I recommend that they address this possibility in their conclusions, rather than simply saying that national policies are “difficult to assess.”

Minor comments:
Figure 2 has both red and green, which would make the bars difficult for colorblind readers. I ran the image through the WES-recommended https://www.color-blindness.com/coblis-color-blindness-simulator/ and recommend they choose different colors.

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Citation: https://doi.org/10.5194/wes-2026-59-RC1
RC2: 'Comment on wes-2026-59', Anonymous Referee #2, 13 May 2026 reply

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Citation: https://doi.org/10.5194/wes-2026-59-RC2

Maarten Paul van der Laan and Simon Watson

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Short summary

A theoretical limit for the energy extraction of offshore wind farms has been suggested by Simão Ferreira et al. (2026) based on a simple model of an infinite wind farm and an ad hoc method to correct the model for application to finite wind farms. In this work, we discuss a number of concerns and we conclude that the limit proposed in Simão Ferreira et al. (2026) is not a theoretical limit but a model limit that is strongly dependent on the ad hoc finite wind farm correction.


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