At the Meteorological Observatory Lindenberg – Richard-Aßmann-Observatory (MOL-RAO) a Halo Photonics StreamLine (now HALO Photonics by Lumibird) Doppler lidar for simultaneous wind and turbulence profile measurements in the lowest 600 m of the ABL is installed. The instrument is sited on the Falkenberg measurement field a few kilometers away from Lindenberg in east Germany, approximately equidistant between Berlin and the Polish border. The site consists of an open grassland area also hosting a 99 m mast, which is equipped with a USA-1 omnidirectional sonic anemometer (Metek GmbH) at the 50.3 and 90.3 m levels, and various additional instruments. The surrounding area is dominated by patchwork of agricultural land and forest over generally flat terrain. The DL, manufactured in 2019 with a 180 ns pulse length and a variable focus, is positioned relatively close to the mast, with an average distance of approximately 80 m. The applied DL measurement strategy and retrieval method follows the approach proposed in . Using a continuous conical scan mode (i.e. the measurement geometry underlying VAD techniques) with an elevation angle of 35.3° and an azimuthal resolution of Δθ=1–2°, instantaneous radial velocities (Vr) are measured along the line-of-sight of each beam direction with a spatial resolution of 48 m. The elevation angle is particularly chosen so that the contributions of the variances (σu2, σv2, σw2) of the three orthogonal wind components (u,v,w) to the radial velocity variance (σVr2) are equally weighted. This allows σVr2 measured at different azimuth angles to be directly related to the turbulent kinetic energy TKE=0.5(σu2+σv2+σw2),. The high azimuthal resolution enables the structure function method to be used to estimate the EDR. use the latter to calculate a correction term for TKE that compensates for its systematic underestimation in DL measurements, caused by the pulse averaging effect attenuating the contribution of small-scale fluctuations to σVr2. One scan circle takes about 72 s such that 25 full scans are completed within a 30 min averaging time. This ensures statistical robustness of the σVr2 values for each azimuth angle. Note that due to the conical scan patterns the retrieved wind and turbulence variables for each measurement height represent temporal-spatial averages over differently sized circular areas with diameters ranging between about 280 m at 100 m height and 1700 m at 600 m above ground. The DL measurements therefore include not only wind fluctuations that fall into the strict definition of isotropic, shear- or buoyancy induced turbulence as frequently assumed in classical turbulence parametrization schemes, but also contain the kinetic energy of non-turbulent circulations.

When performing conical scans with such a comparably high azimuthal resolution, the number of laser pulses per radial wind measurement is limited to Na=2000 due to the relation Na=Δθfp/ωS . Here ωS=5°s-1 and fp=10 kHz denote the angular rotation rate and pulse repetition frequency of the DL system used. This affects the signal-to-noise ratio (SNR) serving as a measure of the quality of the radial velocity measurements. As a result, the time series of Vr measurements are characterized by an increased level of noise, especially under unfavorable atmospheric conditions (e.g. low aerosol load). An appropriate noise-filtering to deal with this problem has been developed by and was applied in the lidar data analysis for the present study.

Finally, propose a DL based integral length scale LV to retrieve measurements for the size of the most energetic eddies in the atmospheric turbulent flow sampled by the instrument, by combining the DL based TKE and EDR using Kolmogorov's relation, i.e. 1LV=c4TKE3/2EDR with c4 = 0.3796. Equation () originates from Richardson's view of the energy cascade in turbulent flows and from the assumption of an energy balance between energy production by the large eddies at the beginning of the cascade and energy dissipation by the smallest eddies at the end of the cascade – a region commonly referred to as the inertial range. It is valid for well-developed turbulence close to a statistically homogeneous, stationary and isotropic state .

We illustrate our evaluation method for the operational regional configuration of ICON over Germany with 2.1 km mesh size and 65 vertical levels (hereafter D2) with forcing derived from the operational 6.5 km ICON European nest. Given the triangular grid used by ICON, the horizontal mesh size is defined as the square root of the triangular grid cell area. The vertical coordinate is stretched with 18 model levels (and layer thickness ranging from 20 to 40 m) in the lowest 600 m of the ABL. The configuration is comparable to the operational setup, except a more recent model binary (“icon-2026.04”) is used, which is available from the ICON Open Source git repository (https://gitlab.dkrz.de/icon/icon-model/, last access: 2 May 2026). Simulations are initialized at 00:00 UTC from the operational analysis and integrated over 36 h. The D2 configuration uses a subgrid-scale cloud scheme, a shallow convection parameterization, and a parameterization for subgrid-scale orographic drag. An overview of the ICON model can be found in . Given the focus of this paper, the treatment of turbulence will be described in more detail below.

Turbulence is parameterized in ICON with the “Turbdiff” scheme together with the “Turbtran” surface transfer scheme . The scheme is based on a 2nd order closure on level 2.5 of anisotropy according to , and thus applies the standard closure assumptions by and for quasi-isotropic turbulence, so as to substitute additional pressure-correlation terms or dissipation terms in the 2nd order equations, where the latter mainly have the form of a pure equilibrium between source- and sink-terms, except the equation for TKE, which is treated prognostically. Rather than using TKE itself, Turbdiff works with the characteristic velocity scale q:=2TKE. The TKE equation, reproduced here in updated form from their Eq. 9, takes the form: ∂(q2/2)∂t=-∑ijui′uj′‾∂ui‾∂xj︸3D resolved shear+βw′θv′‾︸buoyancy+∂∂zαTlBq∂(q2/2)∂z︸turbulent transport-q3αMlB︸eddy dissipation rate+u1‾∂u1‾∂t|SSO+u2‾∂u2‾∂t|SSO︸subgrid-scale orography2+SH︸horizontal shear where u1,u2,w are the three wind components, mean quantities and their perturbations are denoted by bars and primes, lB is the turbulent length scale, β=g/Θ0 the buoyancy parameter and αM=16.6 and αT=0.2. Note that the first term on the right-hand-side includes the full three-dimensional shear of the resolved winds, while in only the vertical shear was included.

Turbdiff attempts to account for the fact that not all unresolved circulations strictly satisfy the assumption that turbulence be isotropic and fall within the inertial range, which is implicit in conventional turbulence closures. These types of circulations – neither fully resolved, nor part of the parameterized turbulence spectrum – will be denoted as “non-turbulent circulations”, or NTC hereafter. In ICON, subgrid-scale processes such as convection and subgrid-scale orographic drag are represented by their own parameterizations. The energy transfer into the inertial range due to non-linear interactions of these NTC processes is accounted for in Turbdiff by scale-transfer terms. The term labeled “subgrid-scale orography” in Eq. () represents the transfer of TKE into the inertial range from gravity waves, while the term labeled “horizontal shear” represents an additional source of TKE from unresolved, organized horizontal shear associated with e.g. upper level fronts or jet stream exit regions. (The scale-transfer term from convection is not currently included.) The derivation of these terms is described in Sects. 1 and 2 of . Thus horizontal shear is accounted for through two different pathways, by including horizontal shear of the resolved winds and through the additional subgrid source term, making Turbdiff more suitable for use at finer mesh sizes. demonstrate the benefit of including the additional subgrid horizontal shear source term in the turbulence scheme for a mesh size of 1.1 km over complex terrain. While their turbulence implementation differs in other details from the operational scheme described above, the conclusions regarding the importance of including additional horizontal shear applies nevertheless.

Turbdiff uses the vertical length scale 3lB=κ(z-z0)1+κ(z-z0)lm with lm=κmin{Dg,Lpmax}, z0 the roughness length and Dg the horizontal mesh size. κ denotes the von-Karman constant and Lpmax=500m. Lp=min{Dg,Lpmax} is the turbulent peak wave length which delineates the transition from NTCs to the true, isotropic inertial range across which the above described scale-transfer takes place. The value of 500 m for Lpmax denotes the assumed upper limit to which fully isotropic turbulence can be maintained. Together with the representation of horizontal shear, this resolution-dependence of lB constitutes another scale-adaptive feature of Turbdiff that make it more suitable for the application into the turbulent gray-zone.

The turbulent flux parameterization is based on K-theory where turbulent exchange coefficients for momentum and heat, i.e. Km and Kh, play a key role in coupling the SGS turbulence to the resolved-scale flow. These exchange coefficients are defined as Km=qlBfm and Kh=qlBfh. The stability functions fm and fh are those described in . A minimum value for the exchange coefficients of Km,min=0.75 and Kh,min=0.4 is applied to maintain some degree of mixing under stable conditions.

Given the inclusion of the additional horizontal shear terms in the TKE equation above, the exchange coefficients are suitable to be used for the representation of both vertical and horizontal diffusion processes. However, in the first-order prognostic equations of ICON, only the vertical turbulent fluxes are included to date. Therefore, these efforts to include 3D shear in the formulation of the exchange coefficients are not yet being exploited to their full potential.

For a meaningful comparison of simulated TKE with the observations, all TKE contributions from the model representative of the temporal and spatial scales corresponding to those of the retrieval should be considered. Following the description of the Turbdiff scheme above, the parameterized (hereafter subgrid-scale, or SGS) TKE represents the turbulence in the inertial range, including any scale-transfer contributions from NTC. These NTCs (i.e. convection, SSO drag) impact the resolved model state via their own parameterizations, but the TKE associated with them is not accounted for directly. By calculating a grid-scale (GS) contribution to the TKE, we capture the impact of resolved wind fluctuations, and also attempt to capture the contribution from the NTCs via their imprint of the on the resolved flow.

Given the Doppler lidar's elevation angle of 35.3°, the diameter of the scan circle changes with height between about 280 m at 100 m height and 1700 m at 600 m above ground. The TKE retrieval has a temporal resolution of 30 min, meaning the observed TKE convolves both temporal and spatial wind variances. Further details on the TKE retrieval can be found in Sect. .

Given the horizontal mesh size of the ICON D2 configuration (approx. 2.1 km), the scan cone falls entirely within a single grid cell, and we can neglect contributions to the GS-TKE from resolved horizontal wind variability. The GS-TKE contribution from the D2 configuration is therefore purely based on the temporal wind variance at each individual grid point over a 30 min time window. This calculation is performed during the model run using winds at every 20 s time step, applying the method proposed by for calculating incremental variances. In the following explanation, this 30 min temporal variance will be denoted by σt2, and the 30 min average wind at each grid point by ut, where each of these variables can stand for any of the three wind components.

For model simulations with finer mesh size where several grid points fall within the scan diameter, the contribution from horizontal wind variance can be accounted for by calculating an additional spatial variance term from model grid points falling within the spatial range of the (height-dependent) scan diameter. σs2 then represents the spatial variance of the 30 min average winds ut across all M grid points falling within the scan diameter: 4σs2=1M-1∑i=1M(ut,i-ut‾)2 Here, 5ut‾=1M∑i=1Mut,i denotes the spatial average of the 30 min average wind ut across all grid points within the scan circle. Following rules for variance decomposition, the total temporal-spatial variance can then be derived as the sum of these two contributions: 6σtotal2=σt2‾+σs2 and the GS-TKE, representative of the joint temporal-spatial variability is 7TKEGS=0.5σtotal,u2+σtotal,v2+σtotal,w2

The SGS-TKE representative of the 30 min time window is also calculated during the model run as the arithmetic mean of the instantaneous SGS-TKE values predicted at every model time step by the Turbdiff scheme within that time period. For finer mesh sizes, the 30 min mean SGS-TKE would also be averaged across all grid points falling within the scan diameter. Since the SGS-TKE is parameterized through various source and sink terms, variance decomposition does not apply. The sum of these GS and SGS are then added to compare to the observations.

The relative importance of the GS and SGS TKE contributions will be explored in more detail in Sect. .

The time-height plots in Fig. a and b show the breakdown of the total TKE as shown in Fig. g into its respective SGS and GS components. Both components exhibit a pronounced diurnal cycle, reflecting the daily transition of the ABL and the dynamic partitioning of energy between the two components.

To evaluate the model's ability to explicitly resolve turbulent structures in more detail, the ratio of GS-TKE to total TKE was analyzed across the diurnal cycle in Fig. d. When viewed in conjunction with the time-height plot for the simulated wind in Fig. e it is apparent that the GS-TKE contribution is strongest during the passage of the simulated cold pool on 10 June or in association with the development of the nocturnal LLJs. The briefly occurring, high GS-TKE values extending from the surface to 500 m altitude during the cold pool onset reflect the fluctuating resolved winds, and are directly followed by a collapse of the turbulent ABL, which leads to lower SGS-TKE values during the afternoon.

Finally, Fig. c1–c4 present a statistical comparison of median SGS-, GS-, and total TKE profiles against DL-derived measurements. This approach is employed across the four periods (MT, daytime, ET, and nighttime) previously discussed, to provide a more robust assessment of scale-adaptivity. The contrast between e.g. the daytime period, where total TKE is clearly dominated by the SGS contribution, and the evening transition period, where GS and SGS contributions are more similar in magnitude (particularly between 200–350 m altitude) shows that the model is able to flexibly partition the total TKE while maintaining overall good agreement with the observed TKE profile. The increased contribution from the GS-TKE during the evening transition composite profile is primarily driven by the development of the LLJs. The LLJ's strong wind shear creates organized structures that the model resolves directly, causing the GS-TKE component to strengthen above the increasingly stable near-surface layers. This confirms that the model successfully adapts its energy partitioning to different physical drivers.

Regarding the risk of double-counting which would manifest as a significant overestimation of total TKE compared to DL measurements, the model shows good agreement or slight underestimates during the morning and evening transitions and during daytime. An overestimate occurs only at night, and here the SGS component alone already exceeds the observed total TKE. This suggests that the bias is more likely rooted in the Turbdiff parameterization scheme itself rather than being a result of double-counting.

Here, we have considered the TKE partitioning across the temporal evolution of the ABL where scale separation depends on the size of the dominant circulations relative to the (fixed) model mesh size. A corresponding analysis could be applied also to simulations across multiple grid resolutions to evaluate the scale partitioning as the mesh size changes relative to the size of the dominant circulations.

As described in Sect. , a turbulent length scale LV representing the most energetic eddies occurring within the DL scan volume can be derived from observations using Eq. (). While the Turbdiff parameterization also utilizes a length scale lB, this is not directly comparable to the retrieved length scale LV since it describes the eddy size only of the SGS range of turbulence.

For a consistent comparison with DL-derived LV, a model-derived LV* is reconstructed by substituting the estimation of the model's total TKE (i.e. the sum of GS and SGS contributions) and the model EDR i.e. the term “eddy dissipation rate” in Eq. () into Eq. ().

Note that the EDR term in Turbdiff follows the same concept of relating TKE and EDR via a length scale as in Eq. (), but using lB in the model relation. While both the DL and the model relations are conceptually similar, with c4=0.3796 and cϵ:=23/2/αM=0.170 differences in the employed coefficients exist. While this parameter should be a universal constant, it is in fact treated as a tuneable parameter in Turbdiff . Due to the scale independence of the EDR, a distinction between SGS and GS is not necessary here. Then, after some algebraic manipulation a functional relationship can be derived, reading 8LV*=c4cϵlB(1+g)3/2=c4cϵlB1+32g+38g2+… with g defined as the ratio of GS-TKE to SGS-TKE (i.e. g=GS-TKE/SGS-TKE). Note that Eq. () directly relates LV* with lB. In the following we use LV* as a suitable counterpart for a comparison with LV and therewith indirectly enable an evaluation of lB also.

A comparison between DL-derived LV and LV* from Eq. () reflecting model data is shown in Fig. . Since LV retrieved with Eq. () becomes ill-defined for very small EDR values which mainly occurs above nocturnal LLJ maxima (see Fig. e and h), in Fig. a all data are excluded where EDR<10-4 m2s-3, while Fig. b displays all unflagged data. The time-height cross sections in Fig. a reveal a clear stability-dependent evolution of LV over the course of a day. During the morning transition LV values gradually increase from small scale (∼10 m) to medium-sized eddies (200–300 m). As the day progresses, LV continues to increase and reaches maximum values of up to 1000–1500 m in the late afternoon. As the turbulence ceases towards the evening, the size of the most energetic eddies decreases again ranging between 10–200 m. The large LV values in the late afternoon reflect typical examples of NTCs discussed in Sect. .

Considering the time-height cross sections with unflagged observational data (Fig. b), it can be seen in conjunction with the wind and turbulence profiles shown in Fig. , that in vertical regions above nocturnal LLJ maxima, where horizontal flows dominate and turbulence is weak and anisotropic, the application of Eq. () yields unrealistically large values for LV. The same applies to the cold pool event on the afternoon of 8 June (see Sect. ), whose passage involves non-stationary, rapidly evolving wind fields. This suggests that the formula is not applicable in these instances because the underlying assumptions, e.g. isotropy, quasi stationary turbulence, existence of a well-developed inertial range (see Sect. ), are not fulfilled under these atmospheric conditions. This does not invalidate the relation itself, but rather delineates the limits of its applicability if used as a diagnostic for LV from lidar measured TKE and EDR which do not stem from an inertial subrange. Note that this finding does not rule out the use of Eq. () to parameterize the dissipation rate of SGS-TKE in large-eddy simulations, provided that the spatial resolution is high and the cut-off wave number is indeed within the inertial range.

Figure c displays the model-based LV*, which by construction should behave similarly to LV. It becomes obvious, however, that the patterns in the time-height cross sections for LV* strongly differ from the LV observations. The comparison shows that the model does not reproduce the continuous growth of turbulent structures typically observed in a convective ABL. Significant larger-scale structures emerge only transiently, coinciding with the peak-like GS-TKE features identified in Fig. d. Beyond these episodes, the modeled length scales show little temporal evolution throughout the day. A closer examination of Eq. () and Fig. d illustrates that the insufficient growth of the turbulent structures directly reflects the definition of lB. If the SGS-TKE dominates the total TKE yielding g<1, it can be shown mathematically that LV*∼c4cε-1lB, implying that the way lB is parameterized dictates the behaviour of LV* through a direct proportionality relationship. This is graphically illustrated in the similarity between Fig. c and d, showing LV* and lB respectively. Within the context of Turbdiff, lB is specifically constructed to exclude NTCs. One conclusion drawn from the observed differences between LV and LV* might be that the TKE associated with these organized, non-isotropic circulations is not sufficiently accounted for via their parameterized imprint on the resolved flow, and our total TKE estimate is a systematic underestimate due to the missing contribution from NTCs. This might explain the missing eddies in Fig. c for LV*>500 m during daytime. Yet we saw in Fig.  that the magnitude of the total TKE is generally in quite good agreement with the observations, particularly during the day and evening transition where larger organized circulations might be expected. Given the rather minor TKE underestimate seen for the daytime TKE, it is not likely that this argument sufficiently explains the differences in LV and LV*. A second possible interpretation is that the definition of lB based only on fixed (grid) parameters does not sufficiently reflect the effects of stability on the peak wave length Lp=lB/κ marking the upper limit of the inertial range, and a stability-dependent formulation would better accommodate the temporal evolution of LV*.

The EDR time-height cross sections based on DL measurements in Fig. c show noticeably strong vertical gradients at certain altitudes. These gradients indicate a transition from strong turbulent mixing encountered in the ABL to the weakly turbulent free atmosphere above. As shown in and this makes DL based EDR-profiles useful for the MLH determination. An independent evaluation (see Appendix ) based on the five-day period analyzed in this work confirms these findings by comparing the DL-derived MLH with radiosonde soundings (RS hereafter). In this section, ICON-based EDR profiles are used for MLH determination, in analogy with the approach used for DL data, to evaluate its potential as a supplement to traditional Ri-based approaches.

Figure a and b show time-height cross sections for the simulated virtual potential temperature (θv) and EDR, respectively. The additional line drawn in Fig. a is a result of applying the threshold approach on profiles of the bulk Richardson number (RiB) defined on each model level as 9RiB=gz(θv-θs)θs(u2+v2) where u and v are winds on the current model level, and θs is the surface virtual potential temperature after. A critical Richardson number of 0.2 is used, and the MLH is linearly interpolated between model level heights bracketing the critical Richardson number. This diagnostic (offline diagnostic hereafter), while conceptually similar to the operational postprocessing, is in fact different code. We adopt here the bulk Richardson number and critical value used in the MLH diagnostics applied to the radiosonde profiles for consistency. In analogy with the original post-processing, during night the MLH is set to 276 m. Unlike in Fig. h, the time-height EDR cross section in Fig. b, extends up to 4000 m, showing the MLH evolution over the full day. The white contour in Fig. b marks the diagnosed MLH using the EDR-threshold approach described in Appendix .

Panels (c1)–(c2) in Fig.  then show the respective model diagnostics together with the MLH retrieved from RS and DL measurements. It is evident that the threshold method does not always work reliably during daytime conditions, where EDR occasionally drops below the threshold at unrealistically high altitudes. During the night, the EDR-based MLH derived from ICON tends to overestimate the observed MLH. Two aspects contribute to this overestimate. As discussed in Sect.  and shown in Figs.  and , the EDR simulated by ICON is systematically biased high relative to the DL-retrieved EDR. For the purpose of the MLH diagnostic, this could be compensated for by adjusting the EDR threshold used to identify the MLH. Alternatively, the choice of the parameter αM directly affecting the EDR could be revisited (see Eq. ). However, this would not address the situation-dependent overmixing (and therefore overestimated EDR) showcased in Sect. . Here, the overestimated MLH merely reflects the model's poor representation of the stable boundary layer.

It is a well-known drawback of the Richardson number based diagnostic that the method does not work reliably for stably stratified boundary layers. We see here that the assumed value of 276 m at night in the operational diagnostic would be a reasonable choice, but of course this contains no true information about the state of the mixing layer, and leads to an unrealistic jump in MLH at sunrise. There are alternative diagnostic solutions that combine the Ri number based diagnostic with additional criteria for stable conditions e.g.. An update to the ICON post-processing diagnostic is currently under development, and one alternative option considered is the Richardson-number-based diagnostic described in , which differentiates between stable, neutral and unstable conditions and considers a contribution from friction velocity in the shear-production term of the gradient Richardson number calculation (their Eq. 3). The MLH diagnosed thus is included in panel c1–c2 of Fig.  as MLH_Ri_VH, and shows generally good agreement with the observed EDR-based MLH. It should be emphasized that the Richardson number method itself is also subject to uncertainty outside the stable ABL. On the first day for example, the RS-MLH diagnostic is unable to reliably detect the top of the daytime convective ABL. On the 10th, the discrepancy between model MLH and RS-MLH in the afternoon can be attributed to the rapid collapse of the ABL in the wake of the simulated cold pool, which was not in fact observed.

The comparisons between EDR- and Ri-based MLHs over the last two days also point to a timing mismatch in the representation of boundary layer evolution. There is a clear time shift indicating that the mixing layer grows and decays earlier based on EDR than on Ri profiles. Such a behaviour has also been shown in and can be explained by the different physical principles and sensitivities of the two methods. EDR responds almost instantaneously to the onset of turbulence, which typically increases rapidly after sunrise due to surface heating. Ri adjusts more slowly in response to surface-driven turbulence, causing a delayed detection of MLH growth. Taking these different sensitivities into account, could be a further step towards an improved MLH determination based on NWP data.

Despite the MLH overestimate discussed above, we propose the EDR-based approach as a valuable alternative to complement Ri-based formulations under stable conditions, particularly if optimized for systematic model biases in EDR.

While mean wind speed is a primary driver in wind energy, turbulence intensity (TI) also plays a crucial role by affecting both mechanical loads on wind turbines and their power production. The total TI in wind farms results from ambient atmospheric turbulence and turbine-induced wakes. Although the latter often receives more attention, ambient TI is equally important. It frequently serves as input for power prediction, wake modeling and load calculations, influences wake recovery and is essential for site assessment. Ambient TI is typically obtained from site measurements, empirical models and standard assumptions. This section presents preliminary results that are intended to shed light on the reliability with which the ICON model represents this variable, and on its potential as an additional source of information for ambient TI.

In this study, TI is estimated from the TKE using the formulation 10TI=1002TKEVh, in [%], where Vh is the horizontal wind speed. This approach follows as the turbulence parameterization scheme Turbdiff provides only the SGS-TKE in its entirety as part of the total TKE, but no parameterized SGS standard deviations for individual wind components. These would be necessary to calculate TI according to the standard wind energy definition: TI=σu/U, where σu represents the standard deviation of the longitudinal wind component and U is the streamwise mean wind speed . As highlighted in , deriving TI from TKE can lead to an overestimation of TI. Due to this limitation, the TI values derived from TKE can only be considered a proxy for IEC-standard TI and the accompanying turbulence conditions. The aim of this section is therefore not to evaluate absolute TI values in accordance with established standards, but to assess whether the quantity derived from the model provides useful information for the application-oriented characterization of ambient turbulence. It is also important to emphasize that, due to data availability, the TI in this analysis is derived from 30 min averages. Wind energy industry standards typically require 10 min averaging periods for TI assessments. Nevertheless, this approach provides a consistent framework for comparing model simulations with turbulence estimates derived from DL, since the DL retrieval method also yields TKE rather than the variances of the individual components. Figure  shows a comparison between the TI value from the ICON simulations and the DL observations, where the TI value is calculated by substituting the respective wind speeds and TKE for both the model and the observation, as shown in Fig. , into Eq. (). Note that TI values above 100 % can occur during strongly non-stationary wind conditions, such as the cold-pool event on june 8th, but they reflect mesoscale variability rather than true turbulence. According to Eq. () the peak is driven by two coinciding factors: the very low horizontal wind speed (vh≈1 ms-1) and a simultaneous peak in TKE, which is likely caused by the high shear and instability at the gust front. Such events are highly relevant for wind energy applications as the simultaneous peak in wind and TI indicates extreme mechanical loads on the turbine structure. Furthermore, the non-stationary nature of cold pool passages poses a challenge for wind power forecasting and turbine control systems. The diurnal evolution of TI is reproduced quite well by the model, however, with a smaller amplitude than observed within the convective ABL (Fig. a). Overall the relative model error for TI ranges between ±100%, but for the majority of the data it is less than ±30% (Fig. b). This model error is comparable with that for the ICON wind speed simulations (Fig. a) but is smaller than the TKE relative error (Fig. b). The latter implies that TI, as a normalized turbulence variable, is more robust with respect to systematic errors in wind speed and TKE.

Nonetheless, with ±30% the TI bias of the ICON model is relatively large in comparison to the greater precision of more advanced models (e.g. LES) and when compared to accuracy requirements typically associated with detailed wind energy applications. In order to balance accuracy with the amount of effort required, it would be beneficial to determine which practical applications are less sensitive to this TI bias and could therefore benefit from the model's reduced overhead. For instance, in the context of preliminary wind farm site assessment, where the objective is to characterize ambient TI conditions at a broader scale, the model results can still provide valuable insights despite these high levels of uncertainty. A more detailed determination of such acceptance error criteria is, however, beyond the scope of the current work. Here, we deliberately restrict the analysis to a rigorous intercomparison of modeled and observed TI. This provides a brief but transparent and application-independent baseline, which can be used by the wind energy community to judge the suitability of the data for their respective purposes. Future efforts within both the modeling and experimental communities should investigate whether the identified TI model error can be transferred to other locations and whether it is small enough to describe relative TI differences across the entire model domain sufficiently well. ICON wind data are already provided for wind energy applications. Providing the wind energy sector with ICON-based TI products in addition to the existing data would make sense if good agreement can be demonstrated between the TI simulated by ICON and the TI observed from DL measurements across the entire model domain.

Finally, to illustrate the practical implications of the identified discrepancies in wind speed and TI variables from a slightly different perspective, we conducted an additional diagnostic experiment in which both modeled and observed wind speeds and TI were used as input data for a simplified model to estimate wind power production (WPP). It is important to emphasize that this analysis is not intended as a validation of the model results for power prediction applications. Rather, it serves as a sensitivity-type assessment to better understand the relative impact of errors in wind speed and TI on a representative downstream application. In particular, WPP was estimated for a virtual “single turbine park” based on a parametric model of the power curve of wind turbines , for two cases: (i) using wind speed only; and (ii) using wind speed and TI from DL and ICON as input variables. The results are shown in Fig.  and are valid for a fictitious wind turbine with a nominal output of 5 MW and a rotor diameter and hub height of 130 m. The results clearly show that for modeled and observed input data, including TI in the wind power estimation leads to a systematic increase in the predicted output for WPP, particularly under convective conditions and at lower wind speeds (Fig. a and c). However, since turbine power output depends approximately on the third power of wind speed, the results additionally show that not only large wind speed errors in the simulated nocturnal LLJs but even moderate wind speed biases in the convective boundary layer (Fig. ) dominate the resulting power errors, masking any potential improvements from those TI information (Fig. a and b). This finding suggests that, for this type of application, improving TI estimates alone is unlikely to yield substantial benefits unless accompanied by corresponding improvements in wind speed predictions.