| 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.
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.