the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Dec 2025
Modelling global offshore turbulence intensity including large-scale turbulence, stability and sea state
Abstract. This study delivers a method and datasets for a global offshore atlas for turbulence intensity (TI) from 10 m to 200 m. The method includes both surface driven, three dimensional boundary-layer turbulence, and large-scale two-dimensional turbulence. This systematically includes the effect of large scale eddies, particularly at weak wind conditions, and hence significantly improves TI in weak to moderate wind conditions. This method describes water roughness length through a dependence on wave age and wind speed, which is suitable for moderate to strong wind conditions. The method also includes stability dependence through the Obukhov length. Based on theories and measurements in literature, algorithms for TI have been calibrated for heights up to 200 m. We use the ERA5 atmospheric and wave data to demonstrate the use of the method and create a global dataset. The results show satisfactory agreement with measurements and data from the literature.
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Status: final response (author comments only)
- EC1: 'Comment on wes-2025-245', Etienne Cheynet, 16 Dec 2025
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RC1: 'Comment on wes-2025-245', Anonymous Referee #1, 03 Jan 2026
General comments:
This manuscript presents a global offshore atlas for turbulence intensity from 10 m to 200 m. Generally, the manuscript is well written. The methodology is presented clearly.
In my opinion, constructing a global atlas for turbulence intensity is never easy. Therefore, while I think the errors/uncertainties in the adopted methodology might be significant, my suggestion is that the manuscript can be accepted for publication after minor revision. Some comments are given below for the authors’ consideration.
Major comments:
- There is a general lack of qualitative or quantitative assessment of the possible errors/uncertainties in the methodology. Some models used by the authors may be too simple, leading to high uncertainty when applied to turbulence intensity estimation under various atmospheric and oceanic conditions worldwide. Please consider including a qualitative (or quantitative if possible) discussion on the uncertainty in the manuscript.
- It is suggested to clarify the applicable range for the equations in Eqs. 1 to 24, e.g., surface layer/boundary layer, neutral/unstable/stable stability conditions, low/moderate/high wind speed, etc.
- Section 2.3, if I understand correctly, the effect of atmospheric stability is considered only through the modification to the wind profile according to the flux-profile similarity (i.e., the MOST). However, according to the flux-variance similarity, the variance of wind speed normalized by friction velocity is also a function of z/L (like Eqs. 23 and 24). This effect of atmospheric stability on variance is non-negligible and should be considered.
- Section 2.5, boundary layer height should be a key parameter in the parameterization of turbulence intensity near the turbine hub height, which is 100 m or so nowadays. However, the treatment of boundary layer height seems overly simplistic in this study (based on a friction velocity-dependent formula applicable only under neutral conditions). I speculate that this simplification may introduce significant errors. For example, in the stable boundary layer, the boundary layer height may be lower than 100 m, leading to minimal turbulence at hub heights.
Minor comments:
- Over land, the variation of turbulence intensity with wind speed at low wind speeds may be largely related to atmospheric stability. At low wind speeds, unstable conditions may dominate because low wind speeds usually correspond to low wind shear and high thermally generated turbulence in the daytime. In my opinion, this is why IEC suggests a decrease of turbulence intensity with wind speed. However, over ocean, due to the large heat capacity of the water, the diurnal cycle of atmospheric stability may be negligible or absent. As a result, the decreasing trend of turbulence intensity with wind speed may not be observed. The authors are suggested to consider these factors and revise their presentation of the methodology accordingly.
- 10 and 18, the logarithmic law is used as the wind profile model. However, it is only valid in the surface layer. Wind turbine hub height is usually above the top of the surface layer and located in the Ekman layer or even in the “free atmosphere” for very stable conditions where boundary layer heights can be as low as several tens of meters. Please justify the use of the log law here.
- Section 2.2, since “wave” can refer to atmospheric wave, to avoid ambiguity, the authors may consider specifying that “wave” here refers to “ocean surface wave”.
- Section 2.2, considering wind sea only may be insufficient, as swells are common in windstorms and may influence the high wind speed regime of sea surface roughness. Please include more discussion/justification here.
- It has been widely recognized by field observations and laboratory experiments that the sea surface roughness length and drag coefficient may decrease at high wind speeds (e.g., > 33 m/s). Eq. 13 considers this decrease using a parabola model. Please state explicitly this dependence and the underlying mechanism here (although the authors mentioned these in their discussion about Figure 3). This is also the reason why the Charnock model deviates from the SWAN simulation at high wind speeds in Figure 3.
- 23 and 24, if I remember correctly, these equations are valid only in statically neutral conditions. Eq. 24 is only valid in the “eddy surface layer”. Please state these limitations explicitly. How large may the error be if these formulae are applied to non-neutral conditions?
- When estimating the boundary layer height using h = au*/f, a constant a = 0.3 is used, which is somewhat large to my knowledge. Please justify the use of this constant.
- It seems that the validation data come from sites restricted to European seas. Please discuss this limitation. Other ocean basins (e.g., tropical oceans) may have distinct atmospheric and oceanic conditions.
- Please improve the presentation of contour plots in Figure 4. Finer resolutions could be used.
- Please state explicitly that one limitation of the methodology is the potential for biased estimates in regions where windstorms, such as tropical cyclones and waterspouts, are prevalent.
Citation: https://doi.org/10.5194/wes-2025-245-RC1 -
RC2: 'Comment on wes-2025-245', Anonymous Referee #2, 03 Mar 2026
This paper presents a parametric model to derive a global atlas of turbulence intensity (TI), its 90th percentile and it variance wherever forcing parameters (which can be extracted from global reanalyses) are available. It leverages on a previous model built by the same group and on several parameterizations of physical effects, which can introduce variability in the TI. In particular, the present model includes the effect of 2D, large-scale turbulence in addition to the 3D local turbulence. The objective is interesting and the resulting model will certainly be useful for the offshore wind energy community. However, I found the present paper, though well written, nor so well organized neither always clear about the data used and the results. I give below some suggestions to improve its understanding and its scope.
Major comments
1 - The hypotheses underlying the building of this atlas should be more clearly presented, probably at the beginning of the methods section. These general hypotheses, as far as I understand, should include the following: a few sites (13, but with an homogeneity of location and maybe atmospheric conditions), in N Europe and conditions representative of offshore wind and turbulence, are used to derive relationships which are considered valid over the global ocean. Maybe a discussion about the use of this model (LUT) over the global ocean — especially at place with conditions very different from those of the observing sites used here — could be added in the final discussion.
2- The description of the data used to build the various dependencies of the parameterization and to validate it afterwards are introduced in several parts of the paper in a rather disorganised way. I struggled a bit to understand which datasets were used when and for which purpose exactly. I suggest to include a table with all the data used, the length, heights and maybe specificities (wave age? stratification? water depth? length of the sample used to compute mean wind and variance, in link with the 2D turbulence inclusion, see 6 below) of the measurements. I understand that the Høvsøre site corresponds to one year of measurements from sonic anemometers at 10 and 100 m, but how long are the FINO measurements used here? Is there a good reason the present separately the comparisons with the 11 sites (Fig 5) and the two additional sites (Fig 6)? Maybe all the graphs shown Fig 5 could be gathered in one graph, as the heights of the different sites are close to each other, and the comparisons look rather homogeneous (and are not further commented in the text).
3- The quantification of the comparisons with measurements could be strengthened and made more explicit. Line 330 and below, only the MAE are given. Is this comparison done on the TI for the different bins of wind speed (as in Fig 5) or is it a comparison of the individual measurements of TI (time series?). Please specify. Also, it could be useful to include other metrics like root mean square of the difference or even correlation (if the comparisons are made on time series). A mean bias alone is often not representative of the agreement with the data. Also, the values given for the MAE could be commented: is it a lot? what is the corresponding relative error (percentage of the TI)?
4- The legend of the figures is not always precise. Fig 2: how long are the FINO measurements used here? Fig 4: is it the mean TI over the whole ERA5 time period?
5- The results and their physical meaning could be discussed a bit further. I understand that the objective of the paper is really to present the TI atlas, but some results maybe worth commenting. Fig 5, the agreement looks really good and does not depend on the wind speed range. Is the inclusion of the 2D turbulence responsible for this agreement at low to moderate winds? Fig 6: opposite to Fig 5, the TI looks a bit underestimated by the LUT here, especially in the 4-12 m/s range. Is there a specific reason for that? Fig 4: Is the higher TI level in the intertropical zone only related to weaker winds there, or is there also an effect of the stratification? Is it strongly related to the inclusion of the 2D turbulence (large eddies, stronger instability)? If so, this is a real change with respect to previous TI modelling and should be emphasized.
6- I am not familiar with the use of '2D turbulence' term. I guess it relates to the larger (up to meso scale) eddies that are sometimes termed 'coherent structures' in boundary layer meteorology. Could you add a paragraph to define it more clearly and maybe specify a typical cutoff length or time scale (in link with Fig 1) and some examples of structures (rolls or plumes) and conditions susceptible to generate then? Also, it seems that the inclusion of the 2D turbulence in the TI computation is a major advance in better representing it at moderate and low wind. Is this true at every wind speed, or mainly for low and moderate winds? Is there a link with the stratification?Line-by-line comments:
l. 14: the question of the length T of the time scale use to compute mean/turbulent values can be linked to the 2D/3D turbulence and information about T in the data used to build/validate the model could be added.
l. 23: 'with water areas reaching 200 km from coastlines'; the present model is global, but still based on observations collected less than 200 km offshore, is it correct?
l. 47-52: this is linked to the inclusion of 2D turbulence in the model, is it correct? Please comment.
l. 67-70: this mention of using LES modelling should be separated from the list of datasets and corresponding parametric relationships. I even wonder is this is relevant here?
l. 73: 'we model turbulence'—> we use of the Larsen 2016 model ?
l.124: 3D turbulence is rather weak, relative contribution from 2D turbulence is bigger ??
l. 142: have all the data used for building or validating the model been sampled at (at least) 1h too?
l. 147: '°K' -> K
eq 10 to 13: I do not understand why using a direct formula for computing u* from U is necessary here; the use of the Fan model (eq 12) in conjunction with eq 10 and 11 is enough to define a bulk model, provided one start from an a priori value either for u* or z0 and iterate (3 times typically) from that; introducing a new formula (Andreas et al 2015) could only bring inconsistency here.
2.3 stability effect: could be introduced earlier, for instance close to eq 10
l. 272: Wang et al 2004 -> 2014
l. 282: why using the SWAN Cd expression when another Cd expression (Andreas et al 2015) has been used previously?
fig 7: the legend is not accurate (figs c and d missing); it seems that, at least at 30 and 50 m, the 90th percentiles for wind speed under 12 m/s are significantly higher in the observations than in the model; is it related to the model for 2D turbulence or to the variability of stratification in the observations? Please comment.
Data availability: the site cannot be accessedCitation: https://doi.org/10.5194/wes-2025-245-RC2
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- 1
Given my familiarity with and interest in the subject, I have taken the liberty of providing a few feedbacks. I hope the authors will receive the following comments in a constructive spirit. They are intended primarily to reduce the risk of potential misunderstandings by readers and to improve clarity.
Section 1, Paragraph 2 – Cost and Practical Constraints of Measurements
The argument related to financial cost is relevant and valuable, but it would benefit from clarification. The manuscript currently postulates that sonic anemometers (SA) are the most expensive sensors; however, in practice, lidars are typically 5–20 times more expensive than a 3D sonic anemometer. The major cost driver of in-situ measurements, particularly offshore, is the meteorological mast itself rather than the SA. This is precisely why lidar-based solutions are often preferred in offshore contexts.It would therefore be helpful for the manuscript to explicitly distinguish between sensor costs and infrastructure costs. To give a sense of scale, I mention some order of magnitudes for these sensors (at least from what I remember):
The manuscript highlights a one-year time constraint for wind measurements. In practice, this is not necessarily the dominant limiting factor. Financial, planning, and regulatory processes, particularly permitting and environmental impact assessments, often extend over several years. Wind resource measurements are commonly undertaken at early stages of project development and can usually be conducted in parallel with these processes. As a result, measurement duration is rarely the critical path, unless in-situ measurements are not required or are otherwise constrained by project-specific conditions.
Equation (2) – Turbulence Intensity Definition and ISO Standard
The ISO definition of turbulence intensity (TI) is indeed rooted in the work of Andersen and Løvseth from the 1990s at Frøya (Norway). However, the current wording appears to suggest the reverse, namely, that Andersen and Løvseth based their work on the ISO standard. This should be rephrased for historical accuracy. As an optional but potentially valuable improvement, the turbulence intensity model of Andersen and Løvseth (2006) could be moved from the appendix into the main body of the paper. For reference, this model has been tested against measurements at the FINO1 offshore platform and shown to perform reasonably well, even for wind speeds below 10 m/s (Cheynet et al., 2024).
Equations (1–4) – Relationship Between Turbulence Intensity and Wind Speed
In general, caution is advised when relating turbulence intensity directly to wind speed. By definition, TI is proportional to the inverse of the mean wind speed, which introduces explicit self-correlation and limits physical interpretability. This point is well known but often overlooked, and it may be useful to explicitly warn the reader. A more rigorous approach would involve analysing the standard deviation of the velocity components as a function of mean wind speed rather than TI itself. That said, such an analysis may fall outside the intended scope of the paper.
Relatedly, the Mann model does not possess an inherent turbulence intensity; its implied TI depends on the target spectrum used for calibration. Furthermore, it is unclear where Veers (1988) is proposed as introducing a spectral turbulence model. Rather, Veers refers to existing models (e.g. Frost, Kaimal, von Kármán, Solari). This distinction should be clarified to avoid ambiguity.
Section 2.1 – 2D vs. 3D Turbulence and Historical Context
Additional references are needed to support the discussion of 2D versus 3D turbulence. These concepts significantly predate the 2010s, and placing them in their historical context is important. Relevant foundational references include:
For pedagogical reasons, it would also be helpful to briefly clarify what is meant by “turbulence” in the context of this manuscript. While the distinction between 2D and 3D turbulence is a good idea, many practitioners in wind energy implicitly define turbulence as a strictly 3D phenomenon and classify mesoscale 2D motions as “non-turbulent.” Clarifying that this distinction is largely terminological and discipline-dependent would help avoid misunderstandings.
On the definition of the turbulence intensity
For wind loading on structures, turbulence intensity is defined based on the standard deviation of each velocity component (along-wind, across-wind, and vertical), rather than on the wind speed magnitude itself (cf. Eq. 5). Some wake deficit models, however, may use a turbulence intensity definition consistent with Eq. (5). When applied to wind load modelling, this formulation, based on the standard deviation of wind speed, may therefore be misleading. Notably, IEC 61400-1 provides two different definitions of turbulence intensity, which are not directly compatible. It is therefore important to clearly warn the reader about these limitations and the context in which each definition is used.
Self-Citation Rate and Literature Context
The self-citation rate approaches 30%, which is relatively high. This may indicate that parts of the broader literature on turbulence intensity have been under-represented. Turbulence intensity has been studied for more than six decades, and while the authors have made important contributions to the field, it is important to more explicitly situate recent work within this extensive body of foundational research. Emphasizing this continuity, “standing on the shoulders of giants”, would strengthen the manuscript’s positioning.