A comprehensive evaluation and uncertainty quantification of offshore turbulence intensity from WRF mesoscale simulations

Schwegmann, Sandra; Lunel, Tanguy; Vollmer, Lukas; Dörenkämper, Martin

doi:10.5194/wes-2026-103

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https://doi.org/10.5194/wes-2026-103

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18 Sep 2026

| 18 Sep 2026

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

A comprehensive evaluation and uncertainty quantification of offshore turbulence intensity from WRF mesoscale simulations

Sandra Schwegmann, Tanguy Lunel, Lukas Vollmer, and Martin Dörenkämper

Abstract. At the beginning of each wind energy project, an as accurate as possible characterization of the site-specific wind resources is needed for any economic considerations of the project. Besides wind speed and direction, which can be measured easily and of which the representation in models has been investigated in various studies, information about wind turbulence suffers from a lack of confidence yet, although it is one of the key parameters that define the lifetime of wind turbines, and its characteristics are of high importance already in the planning phase. In this study, we analyze the feasibility of the Weather Research and Forecasting Model (WRF) to represent this turbulence in terms of turbulence intensity (TI) over a full year in the North Sea and quantify the range of uncertainties. The impact of the planetary boundary layer scheme used for model simulation on these uncertainties was investigated as well as the usage of model-resolved and subgrid-scale turbulence. Furthermore, results were evaluated for increasing spatial resolution in the model and stability impacts. It was found that TI values based on subgrid-scale turbulent kinetic energy (TKE) are significantly closer to observations than model-resolved TI (i.e. based on standard deviation of wind speed or wind speed components). As modelled TKE decreases with increasing resolution, the factor used in the TI calculation needs to be adapted to obtain comparable TI to observations. Nevertheless, independent of the planetary boundary layer scheme, resolution and test location in the North Sea, the lowest errors for TI are around 0.024 (RMSE) and 30 % (MAPE). For any further improvement either LES simulations or a kind of correction method like Measure-Correlate-Predict (MCP) becomes necessary.

Received: 12 Jun 2026 – Discussion started: 18 Sep 2026

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Sandra Schwegmann, Tanguy Lunel, Lukas Vollmer, and Martin Dörenkämper

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'Comment on wes-2026-103', Anonymous Referee #1, 07 Oct 2026 reply
Dear authors,
I took happily the review of this manuscript as I do think that determining the ability of mesoscale simulations to reproduce turbulence measures is very important for the meteorological community in general. However, I need to recommend the rejection of the manuscript in its current state given a number of major critical concerns I find in your work. On the other hand, I think that if you clearly and sufficiently address these concerns and, maybe more importantly change the focus of your work to explain the results in a scientific manner, you should re-submit it again at a later stage as a full new submission.
Main comments:
The title and scope: This is not a comprehensive evaluation of model results. You are only looking at two sites in the same basin! Yes, you do an interesting sensitivity analysis (different resolutions, PBL schemes and even models) but a “comprehensive” evaluation requires many more measurement sites and, hopefully beyond the North Sea area. Therefore, I do not think you manage to respond to your main objective stated in lines 78-80. Even more important, there is no uncertainty quantification in this study: there is neither uncertainty distributions/bands/limits nor observational uncertainty analysis. You concentrate your evaluation on 3 main error metrics, which are of course of importance but there is no attempt to provide explanation of the results of those metrics and the physical processes behind these results.

The concepts and the obviousness: in lines 9-11 you say, “It was found that TI values based on… or wind speed components)”. Well, yes, of course! What were you expecting, the opposite? Similar values for the resolved and the modeled TI? Most turbulence, and here by turbulence I mean the fluctuations of wind speed within time intervals of 10-30 min that we try to measure/reproduce in wind power meteorology, comes from the energy containing eddies that you obviously cannot resolve (sometimes not even a little fraction of them) with the spatial spacings of mesoscale models. Your quest, I think, should be to try to find out, instead, why the modeled TKE from the PBL scheme(s) reproduces well or not well the TKE that you could eventually measure with instruments. And after that, the conditions in which that modelled TKE fails to reproduce the observed TKE, since as any modeled parameter, it might have challenges under certain atmospheric turbulence conditions. The TKE in three of the PBL schemes you use is a prognostic or a diagnostic variable (I do not know the details of all 3 of them) … probably even the same prognostic equation, so what is the cause of a good match of modeled TKE with observations? Is it that the shear production from the PBL scheme or the buoyancy part are well matched? The TKE budget or computation of parts of that would allow you to study these contributions, which can be your contribution to science! Right now I cannot see what a read might gain from your work.

Section 2.3: Maybe it is here important to make a recap on what is what. TI in wind energy and wind power meteorology is the ratio between sigma_u and the mean wind speed U. This definition is valid when u is defined as the along-wind velocity component. This is not suggested by Larsen (2022), this is textbook! And it turns out that if defined like that sigma_u is nearly the same as sigma_U, where U is the horizontal velocity magnitude, particularly offshore where there the flow streamlines are nearly horizontal. This is the reason why you can compare cup speed variances with the u-variances measured by sonic anemometers. Thus, Eq. (1) and Eq. (2) will give nearly the same estimate, again for the case of u being aligned with the mean wind (did you rotate all winds at all heights correctly?).

The problem is that in this section you did not say how u, v and w are actually defined (you only said that in Larsen, 2022, u corresponded to along-wind). If you do not define what they are, Eqs. 3 and 4 can be fully or partially wrong. For example, Eq. 3 is fully wrong if u is indeed the along-wind component because you will be adding artificially turbulence to the TI estimate with the v component. It is also wrong in the case that u is not the along-wind velocity component. Eq. 4 is only right in case you have isotropic turbulence, which is never the case. So, if you have the time series of observations or simulations of either the horizontal velocity or along-wind velocity, then you just need to use Eqs. (1) or (2), your choice but never Eqs. (3) and (4).

Then you say “TKE (k, Eq. 5) is …. of the wind speed standard deviation”: Yes and no. People convert TKE values into TI but that does not mean they should, precisely because in that process, errors and assumptions are committed and needed. Eq. (5) is of course fine, since this is the definition of TKE. But Eq. (6) assumes zero v and w variances? What is the result of this assumption? Does it make sense? No. Eq. (7) also has issues, since isotropy is again assumed. In reality, at the least, TI=sqrt(c*(2/3)k)/U, where c is a coefficient accounting for the degree of anisotropy of turbulence. Maybe your quest should be to study how c changes depending on atmospheric conditions at these two sites (is it resolution, PBL scheme dependent?) An alternative is that you do your comparisons based on TKE (k) if you have the means to compute it correctly from the measurements, i.e. that you can derive all components from Eq. (5).

Specific comments:
Line 6: “to represent this turbulence” please rephrase.

Line 11-12: “A modelled TKE… TI to observations”: at this point the reader does not what do you mean by factor

Line 13: “The lowest errors for TI”: computed as what?

Line 19: replace “load” by “loads”

Line 34: it is “worldwide”

Line 42: e.g at the end?

Acronyms are defined and not used or used and not defined… see e.g. Line 109 vs line 115… also TI is defined and later again turbulence intensity is used.

k is not defined in table 1

lines 113 and 114 “prognostic equations…. as prognostic variable”: redundancy

Caption figure 1: is not NEWA the acronym of wind atlas then no need to say wind atlas

Check all references and styles (see issues in line 150 and 163) also in line 188

Line 195 “We summarize”

Line 293 needs rephrasing

Units should be normal text and variables italics/math type not like those you have in the axes of the figures

Table 4 lacks units and the caption should say “at” instead of “in” 92 m

What do we gain from Fig. 3 d? If your focused is turbulence forget about YSU!

Table 5 mean TIs do not make sense as TI is wind speed dependent

In nearly all your plots the black lines and red lines cannot be distinguished easily.

I stopped reading at page 16

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Citation: https://doi.org/10.5194/wes-2026-103-RC1

Sandra Schwegmann, Tanguy Lunel, Lukas Vollmer, and Martin Dörenkämper

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This study investigates the feasibility of the Weather Research and Forecasting Model (WRF) to represent turbulence intensity (TI) and quantifies its uncertainties for the North Sea. At mesoscales, using subgrid-scale TKE for TI calculation, a mean absolute percentage error of about 30 % can be achieved. Out of the used PBL schemes, MYNN provides the lowest deviation to observed TI at a resolution of 2 km. Gray-zone simulations with a resolution of up to 111 m do rarely improve TI.


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