| 01 Jun 2026
Lidar probe volume averaging effect on the along-wind turbulence statistics
Abstract. Wind lidars are increasingly used for wind turbine power estimation, load analysis, and control purposes, but their ability to accurately capture turbulence is limited by the large probe volumes of lidars, which attenuate measured turbulence through spatial averaging. We investigate the effects of probe volume averaging on lidar turbulence characteristics as a function of the probe volume over integral length scale ratios using a wind tunnel study. This is facilitated by generating tailor-made turbulent flow conditions using an active grid and by adjusting the focus distance of a short-range continuous-wave (CW) lidar. A hot-wire anemometer is used as reference sensor. First, a spectrum model for the lidar averaging effect is implemented by applying a Lorentzian filter to Mann-model spectra derived from hot-wire measurements, accurately capturing velocity spectrum attenuation with increasing probe volume averaging. Second, the ability of the lidar to estimate turbulence statistics including the integral length scale and velocity variance is evaluated by comparing lidar to hot-wire ratios across all cases. Results show that conventional lidar-derived length scales are overestimated while velocity variances are underestimated with increasing probe volume averaging. Both the modelled and conventionally derived lidar velocity variance are attenuated from 10 % to 80 % with increasing probe volume averaging. In contrast, the spectrum-based lidar variance, derived directly from the averaged lidar Doppler spectrum compensates for probe volume averaging, yielding variance estimates that are significantly less affected by this ratio with an average relative error of +20 % compared to the hot-wire data. The correction for velocity gradients in the wind tunnel flow reduces the average relative error of spectrum-based lidar velocity variances to +10 %.
Mann 2010 found that the turbulence statistics measured by lidar at an experimental outdoor wind farm tended to be smaller than those from a sonic anemometer due to probe volume averaging, and that a new analysis method to take the second moment of the spectrum from the same lidar tended to improve the agreement with the anemometer. This manuscript, "Lidar probe volume averaging effect on the along-wind turbulence statistics," uses wind tunnel measurements to quantify how well the Mann 2010 spectrum-based method of resolving velocity variance works as a function of nondimensional lidar probe volume. This nondimensional probe volume, lp/L, is twice the continuous-wave lidar's Rayleigh length divided by the velocity autocorrelation-measured integral length scale. The wind tunnel measurement tests over-resolved (lp/L < 0.1) and measurements with substantial lidar probe volume averaging (lp/L up to 10), and shows that the Mann method improves the turbulence estimation agreement with a hot-wire anemometer (Figure 12). Figure 12 actually shows this Mann method overcompensating the probe volume attenuation effect, and the authors claim that this overestimation is due to a real feature in the individual PSDs (Fig. 14c) due to velocity gradients across the volume (Fig. B3).
This paper presents a good analysis of a good wind tunnel experiment, isolating one independent variable (lp/L) and showing that the wind tunnel measures over the whole relevant range of that variable (Fig. 4). I was initially concerned that a spectrum-based variance calculation is too vulnerable to user-tuning of the noise spectrum to match the anemometer results, but Figure 6 shows that this noise is very small compared to the signal, and Appendix B does quantify the variance uncertainty due to noise spectrum uncertainty. This work does make me suspect that the alignment of the lidar with the wind is a larger source of uncertainty than the probe volume averaging, but the minimal discussion of beam-wind alignment was appropriate to the scope of this single-variable lab experiment paper.
This paper would be more appropriate to AMT with some small changes to better establish the applicability of the wind tunnel experiments to a wind farm measurement. The opening paragraph does not have any citations that the velocity variance is an important parameter to measure at wind farms. Is the 300 m maximum range of the wind profiler adequate for wind farm scales? How important is it to align the laser with the prevailing wind direction? Would a wind farm measurement instead align the beam in orthogonal directions for a fully 3D measurement, or do a conical scan (which would have a much larger probe volume than a radial beam)? Finally, are the velocity gradients an anticipated issue for outdoor measurements, or only for a small wind tunnel with developing flows? I could imagine the flow gradually developing in the wake of one wind turbine, leading to the velocity gradient issue.
The paper does not provide enough quantitative information to support its claim that the velocity gradients along the probe volume are the primary cause of the spectrum-based velocity variance overestimation in Figure 12. It might be helpful to fit a trendline to the two datasets in Figure B3. Does the "Spec" have a statistically significant slope, and does "Spec with G correction" not have a statistically significant slope with respect to nondimensional probe volume? Is the velocity-gradient correction derived from interpolating the two hot-wire anemometers across the probe volume?
The paper organization makes the velocity gradient discussion confusing. The final abstract sentence about "The correction for velocity gradients...reduces the error...to +10%" is a reference to the figure in appendix B4, which should probably be elevated to the main text. I initially thought the gradient correction was already applied to the data in Figure 12, but it rather is an explanation for the trendline in Figure 12.
The discussion for Figure 9 lists a kcutoff. Is this an empirical result from Figure 9 or is there some other theoretical basis for particular values? For Figure 9a the kcutoff matches a local maximum in the lidar spectrum, and the location at which the theory and measurement diverge, but Figure 9b has lidar different from the Mann model at all wavenumbers.
More generally, how is the Mann-modeled lidar spectra in Figure 9 used throughout the paper? Is the lidar velocity variance shown in Figure 12 somehow scaled by the Mann-modelled velocity filter? What fraction of the velocity variance is due to eddies below L?
Is the lidar probe volume substantially largest in the direction of laser propagation? i.e. is 2zR in Eq. 3 much larger than the beam waist diameter? If not, the lp/L might not be the most appropriate non-dimensionalization.
Technical corrections
- In Figure 7 use a lighter color for the wind profiler to better distinguish from the hot-wire. Include a comment in the figure caption or the end of section 4 about how the conventional centroid method clearly under-resolves the turbulent velocity variance at the largest l_p/L ratio due to lidar probe volume averaging.
- Define turbulence intensity. The early sentence "In the atmospheric boundary layer, the most relevant parameters are typically the along-wind turbulence intensity, velocity variance, and..." is misleading because it makes the paper appear to be more about turbulence intensity than velocity variance, but in fact the TI is easy to derive from velocity variance and the results figures present velocity variance as the dependent variable.
- line 227: "the generated [probe] volume over length scale..."
- line 258: "to remove [the] noise spectrum..."